Organized by: Esteban A. Hernandez-Vargas, Hana Dobrovolny

• Nora Heitzman-Breen Virginia Tech (Mathematics)
  "Modeling within-host and aerosol dynamics of SARS-CoV-2: the relationship with infectiousness"
The relationship between the dynamics of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in a host’s upper respiratory tract and in surrounding aerosols is key in understanding SARS-CoV-2 transmission and informing intervention strategies. We developed a within-host and aerosol mathematical model, accounting for both total RNA and infectious RNA, and used it to determine the relationship between viral kinetics in the upper respiratory track, viral kinetics in the aerosols, and new transmissions in golden hamsters challenged with SARS-CoV-2. We determined that infectious virus shedding early in infection correlates with transmission events, shedding of infectious virus diminishes late in the infection, and high viral RNA levels late in the infection are a poor indicator of transmission. We further showed that viral infectiousness increases in a density dependent manner with viral RNA and that their relative ratio is time-dependent. Such information is useful for designing interventions.
• Melanie Moses University of New Mexico (Computer Science)
  "Spatial Immune Model of Coronavirus (SIMCoV) in the lung"
A key question in SARS-CoV-2 infection is why viral loads and patient outcomes vary dramatically across individuals. Because spatial-temporal dynamics of viral spread and immune response are challenging to study in vivo, we developed Spatial Immune Model of Coronavirus (SIMCoV), a scalable computational model that simulates hundreds of millions of lung cells, including respiratory epithelial cells and T cells. SIMCoV replicates viral growth dynamics observed in patients and shows how spatially dispersed infections can lead to increased viral loads. The model also shows how the timing and strength of the T cell response can affect viral persistence, oscillations, and control. By incorporating spatial interactions, SIMCoV provides a parsimonious explanation for the dramatically different viral load trajectories among patients by varying only the number of initial sites of infection and the magnitude and timing of the T cell immune response. When the branching airway structure of the lung is explicitly represented, we find that virus spreads faster than in a 2D layer of epithelial cells, but much more slowly than in an undifferentiated 3D grid or in a well-mixed differential equation model. We further validate the branching model of the lung by showing that SIMCoV simulations of the spread of inflammation have similar growth rates and shapes to CT scans of SARS-CoV-2 infected lungs. We additionally model spread in the nasal cavity and compare to viral dynamics in that compartment. These results illustrate how realistic, spatially explicit computational models can improve understanding of within-host dynamics of SARS-CoV-2 infection.
• Lars Kaderali Univesity Medicine Greifswald (Institute of Bioinformatics)
  "Modelling the intracellular replication of SARS-CoV-2 and related RNA viruses"
Positive-stranded RNA viruses are the largest group of viruses, and include human pathogens such as Dengue virus, haptitis C virus and coronaviruses, including SARS-CoV-2. They share many similarities in their lifecycle, albeit the diseases they cause show a wide spectrum of manifestations, from mild acute infections over long-term chronic infection to vigorous, life-threatening acute disease. We have developed detailed mathematical models of several positive stranded RNA viruses, and use these models to understand their within-host replication strategies, pan-viral similarities as well as virus-specific differences. In the talk, I will present our models on hepatitis C virus, dengue virus and coxsackievirus B3, and will compare these models to our ongoing work on modeling SARS-CoV-2, including detailed kinetic data and first results we have obtained in modeling the SARS-CoV-2 replication dynamics.
• Hwayeon Ryu Elon University (Mathematics)
  "Mathematical Modeling of Immune Response to SARS-CoV-2"
Despite a tremendous volume of research in understanding the transmission of SARS-CoV-2 virus during the pandemic, how the human immune system responds to SARS-CoV-2 has not been yet fully understood due to limited analysis of the experimental or clinical information to date. In this work, we develop and analyze an in-host model to understand the role of various molecular pathways in successful viral clearance and to identify the key mechanisms responsible for disease severity exhibited by some patients. Our model explicitly represents the virus, innate immune cells, selected cytokines, and their interactions, which is formulated in a system of coupled ordinary and delay differential equations. With calibrated parameters against experimental data and literature we conduct numerical and sensitive analysis to determine the implications of variation of parameters. Our model demonstrates key aspects of immune response to SARS-CoV-2, specifically its sensitive pathways, which might be responsible for differences in disease severity exhibited by COVID-19 patients. Our results of the mechanisms involved in COVID-19 pathology could identify several therapeutic targets that would provide hypotheses to be tested clinically, thus, serving as a foundation for the development of evidence-based therapeutic strategies.
• Mélanie Prague Univ. Bordeaux, Inria, Inserm, Bordeaux Population Health, France (Statistics in Immunology and translational medicine)
  "Joint modeling of viral and humoral response in Non-human primates to define mechanistic correlates of protection for SARS-CoV-2"
Determining correlates of protection is critical to the development of next-generation SARS-CoV-2 vaccines. And even when a correlate of protection has been identified, it is important to understand what level of that correlate needs to be achieved to provide protection from an event (which may be infection, transmission, or symptom severity...). In Alexandre et al. (eLife, 2022), we proposed a model-based approach to identify mechanistic correlates of protection based on dynamic modeling of viral dynamics and data mining of immunological markers using non-human primates studies (NHP). We have shown that RBD/ACE2 binding inhibition is a potent mechanism of protection against infection. Based on the analysis of the reproductive number in the animals, we propose a quantitative method to define a threshold for this correlate of protection against infection. We also extend the model to jointly describe the viral dynamics and the dynamics of the humoral response in naive, convalescent, and vaccinated NHP infected with SARS-CoV-2. We apply the method to three different studies in NHP investigating SARS-CoV-2 vaccines based on CD40 targeting, two-component spike nanoparticles, and mRNA.

Organized by: Marissa Renardy, Caitlin Hult

• Marissa Renardy Applied BioMath (Modeling)
  "Capturing CAR-T cell therapy dynamics through semi-mechanistic modeling"
Chimeric antigen receptor T (CAR T) cell therapy has shown remarkable success in treating various leukemias and lymphomas. CARs are engineered to redirect T cells to specific tumor associated antigens. Pharmacokinetic (PK) behavior of CAR T cell therapy is distinct from other therapies due to its 'living' nature; it is characterized by an exponential expansion, fast initial decline (contraction), and slow long-term decline (persistence). Previous models have not mechanistically described all three of these phases. In this work, we develop a semi-mechanistic model of CAR T PK/PD. We use this model to replicate published PK and efficacy data and to explore sources of variability.
• Pariksheet Nanda University of Michigan Medical School (Microbiology and Immunology)
  "Calibrating multivariate models using CaliPro and approximate Bayesian computing"
Mathematical and computational models are increasingly complex and are typically comprised of one-or-more methods such as ordinary differential equations, partial differential equations, agent-based and rule-based models, etc. Lacking analytical methods, fitting such multivariate biological models to experimental datasets requires iterative parameter sampling-based approaches to establish appropriate ranges of model parameters that capture the corresponding experimental datasets. However, these models typically comprise large numbers of parameters and therefore large degrees of freedom. Thus, fitting these multivariate models to experimental datasets presents significant challenges. We build on our previously published mechanistic, multiscale model of lung granuloma formation from infection by Mycobacteria tuberculosis by calibrating to novel imaging data and metadata from non-human primates to more precisely simulate biological behavior. We apply our model agnostic Calibration Protocol (CaliPro) and explore approximate Bayesian computing (ABC) to highlight strengths and weaknesses among these calibration methods.
• Maral Budak University of Michigan Medical School (Department of Microbiology & Immunology)
  "Optimizing regimen treatment during the host-pathogen interaction of tuberculosis using a multi-scale computational model"
Tuberculosis (TB) continues to be one of the deadliest infectious diseases in the world, causing ~1.5 million deaths every year. The World Health Organization initiated an End TB Strategy that aims to reduce TB-related deaths in 2035 by 95%. Recent research goals have focused on discovering more effective and more patient-friendly antibiotic drug regimens to increase patient compliance and decrease emergence of resistant TB. To that end, many antibiotics have been identified through in vivo studies and clinical trials that may improve the current standard regimen by shortening treatment time. However, testing every possible combination regimen either in vivo or clinically is not feasible due to experimental and clinical limitations. To identify better regimens more systematically, we simulated pharmacokinetics/pharmacodynamics of various regimens to evaluate efficacies, and then compared our predictions to both clinical trials and nonhuman primate studies. We used GranSim, our well-established hybrid multi-scale agent-based model that simulates granuloma formation and antibiotic treatment, for this task. In addition, we established a multiple-objective surrogate-assisted optimization pipeline using GranSim to discover optimized regimens based on treatment objectives of interest, i.e., minimizing total drug dosage and lowering time needed to sterilize granulomas. Our approach can efficiently test many regimens and successfully identify optimal regimens to inform pre-clinical studies or clinical trials and ultimately accelerate the TB regimen discovery process.
• Christian Michael University of Michigan - Michigan Medicine (Microbiology & Immunology)
  "Towards digital partners of Mycobacterium tuberculosis infection within a virtual city framework"
Mycobacterium tuberculosis (Mtb) is an infectious, airborne microbe that causes tuberculosis (TB), a pandemic infecting roughly a third of the global population. The primary sites of infection are lung granulomas: structures comprising Mtb, immune cells and dead tissue. The high level of granuloma heterogeneity and the slow, complex progression of the disease impacts the relative efficacy of treatments. Considering the challenges of collecting data in TB, it is of critical importance to supplement both experimental and clinical data on TB with computational models that capture the variety of outcomes observed in granulomas both within and between patients . Our group has created HostSim, a host-scale agent-based model of granulomas. Our hybrid framework links lung, lymph node and blood models at multiple spatial scales and is calibrated to experimental data and synthetic data from our fine-grained cell-based granuloma-scale model (GranSim). We next used HostSim to build a Virtual City: a collection of virtual patients, each treated with various medical interventions to quantify impact. We are using Virtual City to build towards Digital Partners - a method for approximating the impact of interventions on specific patients via their most quantitatively similar virtual patients to obtain efficient predictions for effective personalized treatment.
• Elsje Pienaar Purdue University (Biomedical Engineering)
  "Biofilm impacts in Non-tuberculous mycobacterial infections in the airway"
Incidence and prevalence of MAC infections are increasing globally, and reinfection is common. Thus, MAC infections present a significant public health challenge. We quantify the impact of MAC biofilms and repeated exposure on infection progression using a computational model of MAC infection in lung airways. MAC biofilms aid epithelial cell invasion, cause premature macrophage apoptosis, and limit antibiotic efficacy. In this computational work we develop an agent-based model that incorporates the interactions between bacteria, biofilm, and immune cells. In this computational model, we perform virtual knockouts to quantify the effects of the biofilm sources (deposited with bacteria vs. formed in the airway), and their impacts on macrophages (inducing apoptosis and slowing phagocytosis). We also quantify the effects of repeated bacterial exposures to assess their impact on infection progression. Our simulations show that chemoattractants released by biofilm-induced apoptosis bias macrophage chemotaxis towards pockets of infected and apoptosed macrophages. This bias results in fewer macrophages finding extracellular bacteria, allowing the extracellular planktonic bacteria to replicate freely. These spatial macrophage trends are further exacerbated with repeated deposition of bacteria. Our model indicates that interventions to abrogate macrophages’ apoptotic responses to bacterial biofilms and/or reduce frequency of patient exposure to bacteria will lower bacterial load, and likely overall risk of infection.

Organized by: Esteban A. Hernandez-Vargas, Hana Dobrovolny

• Esteban Abelardo Hernandez-Vargas University of Idaho (Department of Mathematics and Statistical Science)
  "The shape of antibody dynamics of severe and non-severe patients with COVID-19: A mathematical modeling approach"
The COVID-19 pandemic is a significant public health threat with unanswered questions regarding the immune system's role in the disease's severity level. In this paper, based on antibody kinetic data of patients with different disease severity, topological data analysis by the mapper algorithm highlights apparent differences in the shape of antibody dynamics between three groups of patients, which were non-severe, severe, and one intermediate case of severity. Subsequently, different mathematical models were developed to quantify the dynamics between the different severity groups. The best model was the one with the lowest median value of the Akaike Information Criterion for all groups of patients. Although high IgG level has been reported in severe patients, our findings suggest that IgG antibodies in severe patients may be less effective (affinity) than in non-severe patients due to early B cell production and early activation of the seroconversion process from IgM to IgG antibody. A bifurcation associated with a stable virus-positive steady state suggests that a sufficiently rapid viral replication can overcome the T cell response to cause the infection. Our work contributes to the in-host modeling of COVID-19 (and future related diseases), which can lead to effective treatments and an understanding of the disease from a systems perspective.
• Veronika I. Zarnitsyna Emory University School of Medicine (Microbiology and Immunology)
  "Competing Heterogeneities in Vaccine Effectiveness Estimation"
According to epidemiological data, protection from the flu and COVID-19 vaccines could wane within a year. Accurately measuring this fast waning of vaccine effectiveness (VE) is crucial for protecting public health, guiding vaccine development, and informing individual health decisions. Population heterogeneities in underlying susceptibility to infection and vaccine response pose an additional challenge in VE estimation, as they can cause measured VE to change over time, even without pathogen evolution or actual waning of immune responses. VE studies often rely on time-to-infection data and the Cox proportional hazards model. An extension of the Cox proportional hazards model, which utilized scaled Schoenfeld residuals, is commonly used to capture VE waning. We found that this approach is unreliable in capturing both the degree of fast waning and its functional form, especially when vaccination is spread over months, and identified the mathematical factors contributing to this unreliability (Nikas et al., Clinical Infectious Diseases, 2022). We showed that a relatively simple method based on including time-vaccine interaction in the model, with further proposed optimization, performs significantly better. Using this method, we explored the effect of the competing heterogeneities on the estimation of VE waning by analyzing the synthetic data from a multi-scale agent-based model parameterized with epidemiological and immunological data.
• Hana Maria Dobrovolny Texas Christian University (Department of Physics & Astronomy)
  "Virus-mediated cell fusion of SARS-CoV-2 variants of concern"
Many viruses, including SARS-CoV-2, have the ability to cause neighboring cells to fuse into multi-nucleated cells called syncytia. Much is still unknown about how syncytia affect the course of viral infection. Using data from a recent study of virus-mediated cell fusion for different SARS-CoV-2 variants of concern, we use mathematical modeling to estimate the syncytia formation rate and the fusing time of SARS-CoV-2 variants. We find that the alpha variant has a syncytia formation rate higher than other variants. We are also able to estimate the time it takes for fusion to occur, finding that the beta variant takes the longest, followed by the alpha variant, with the delta and original Wuhan strains fusing fastest. This study exemplifies the role that mathematical models can play in helping to quantify the biological characteristics of different viruses.
• Suzan Farhang-Sardroodi University of Manitoba (Department of Mathematics)
  "Mathematical modelling of the humoral and B cell response to SARS-CoV-2"
Mechanistic modelling approaches have become integral to systems biology to describe known physiology and fill in the gaps in our understanding of which complex interactions drive host-pathogen responses. They, therefore, provide valuable insights for public health planning and infectious disease control. In this mini-symposium, I will present our work on developing a mathematical model to study humoral (antibody-mediated) immunity. B cells and their antibodies are critical to protecting against COVID-19 over time. However, it is increasingly evident that waning antibodies after natural infection or vaccination translate to reduced defence against repeated SARS-CoV-2 infections. To understand the dynamics of antibody production from B cells, we constructed a computational biology model describing B cells and IgG-neutralizing antibodies coupled with host-pathogen interactions. This model provides better insight into the kinetic processes and mechanisms driving the humoral response against SARS-CoV-2. Our model delineates the initiation of B cell responses through their differentiation to germinal center cells, long-lived plasma cells, and memory cells. It sheds light on how antibodies are produced in primary and secondary reactions.
• Ruian Ke Los Alamos National Laboratory
  "The relationship between SARS-CoV-2 viral load and infectiousness and quantifying the infectiousness heterogeneity"
The within-host viral kinetics of SARS-CoV-2 infection and how they relate to a person’s infectiousness are not well understood. This limits our ability to quantify the impact of interventions on viral transmission. Here, we develop viral dynamic models of SARS-CoV-2 infection and fit them to data to estimate key within-host parameters such as the infected cell half-life and the within-host reproductive number. We then develop a model linking viral load (VL) to infectiousness and show a person’s infectiousness increases sublinearly with VL and that the logarithm of the VL in the upper respiratory tract is a better surrogate of infectiousness than the VL itself. By fitting mechanistic models to a wide variety of datasets, we directly quantified heterogeneity in individual infectiousness. Significant person-to-person variation in infectious virus shedding suggests that individual-level heterogeneity in viral dynamics contributes to ‘superspreading’.
• Jane Heffernan York University (Mathematics & Statistics)
  "Modelling COVID-19 infection and vaccination"
Immunity is gained after infection and vaccination, but can also wane over time. We have developed mathematical models of COVID-19 infection and vaccination to track the accumulation and decay of effective COVID-19 immunity in individuals. The results from our in-host models are then embedded into epidemiological models of COVID-19 immunity distributions. In this talk I will review our in-host models and discuss our modelling results associated with mild, moderate, and severe COVID-19 infection, and vaccination using Astrazeneca, Moderna, or Pfizer vaccines. An example of immunity distribution modelling for Ontario Canada will also be discussed.

Organized by: Tin Phan, Ruian Ke, Ruy M. Ribiero, Alan S. Perelson
Note: this minisymposia has multiple sessions. The other session is MS04-IMMU-1.

• Stanca Ciupe Virginia Tech (Mathematics)
  "Mathematical models of Usutu Viral Infection"
Usutu virus, an emerging zoonotic flavivirus that is maintained in the environment through an enzootic cycle involving mosquitoes and birds, is associated with decreased bird populations and occasional spillover to humans. To determine the relationship between Usutu virus kinetics and disease incidence we built a multiscale vector-borne disease mathematical model that connects individual bird infections with the probability of bird-to-mosquito transmission and disease incidence in the bird population. We parametrize the model using viral titer data from birds infected with different Usutu virus strains and bird-to-mosquito transmission probability data and use the results to make predictions on bird infection incidence. Lastly, we investigate the effect of data scarcity on predicted incidence and propose solutions for improving model accuracy.
• Elissa Schwartz Washington State University (Math/Biol Sci)
  "Equine Infectious Anemia Virus (EIAV) dynamics and applications to vaccine development"
Equine infectious anemia virus (EIAV) is a lentivirus similar to HIV that infects horses. Clinical and experimental studies demonstrating immune control of EIAV infection hold promise for efforts to produce an HIV vaccine. Antibody infusions of horses have been shown to block both wild-type and mutant virus infection, but the mutant sometimes escapes. Using these data, we develop a mathematical model that describes the interactions between antibodies and both wild-type and mutant virus populations, in the context of continual virus mutation. We then investigate the effects of repeated immunizations through antibody infusions on both the wild- type and mutant strains of the virus. The model is then extended to include cytotoxic T lymphocyte responses. Numerical analysis shows that stability of the biologically-relevant endemic equilibrium, characterized by coexistence of antibody and CTL responses, requires that the parameters promoting CTL responses need to be boosted over parameters promoting antibody production. This result may seem counterintuitive (in that a weaker antibody response is better) but can be understood in terms of a balance between CTL and antibody responses that is needed to permit existence of CTLs. Thus, an intervention such as a vaccine that is intended to control a persistent viral infection with both immune responses should moderate the antibody response to allow for stimulation of the CTL response. In sum, these results suggest a route forward to design vaccine strategies to control lentivirus infection.
• Wenjing Zhang Texas Tech University (Department of Mathematics and Statistics)
  "Detecting and Resetting Tipping Points to Create More HIV Post-treatment Controllers with Bifurcation and Sensitivity Analysis"
The existence of HIV post-treatment controllers (PTCs) gives a hope for HIV functional cure. Understanding the critical mechanisms determining PTCs represents a key step toward this goal. In this talk, we have studied these mechanisms by analyzing an established mathematical model for HIV viral dynamics. In mathematical models, critical mechanisms are represented by parameters that affect the tipping points to induce qualitatively different dynamics and, in cases with multiple stability, the initial conditions of the system also play a role in determining the fate of the solution. As such, for the tipping points in parameter space, we developed and implemented a sensitivity analysis of the threshold conditions of the associated bifurcations to identify the critical mechanisms. Our results suggest that the infected cell death rate and the saturation parameter for cytotoxic T lymphocyte proliferation most significantly affect post-treatment control. For the case with multiple stability, in state space of initial conditions, we first investigated the saddle-type equilibrium point to identify its stable manifold, which delimits trapping regions associated to the high and low viral set points. The identified stable manifold serves as a guide for the loads of immune cells and HIV virus at the time of therapy termination to achieve post-treatment control.
• Jasmine A. F. Kreig Los Alamos National Laboratory (T6: Theoreticacl Biology and Biophysics)
  "Using an agent-based model to explore affinity maturation of B cells: a SARS-CoV-2 case study"
Successive variants of concern of SARS-CoV-2 have demonstrated an increase in antigenic distance from the original strain. These variants of concern (VOC), with differing amounts of escape from pre-existing immunity, are causing concerns about continued protection gained from vaccination and prior infection. B cells, which are key players in the body’s humoral immune response, undergo a process called affinity maturation in which activated B cells produce antibodies with increased affinity for antigen with the goal of limiting antigen ability to infect more cells. As the antigen moves away from the initial strain, the ability of the body to cross-reactively neutralize the antigen decreases. We investigated this idea via an agent-based model (ABM) that simulates the humoral immune response to SARS-CoV-2. We represent B cells (naïve, plasma, memory), antibodies, and antigens (virus strain or vaccine) as agents. We focus on binding that occurs between receptors (B cells, antibodies) and epitopes (antigens), representing these proteins in Euclidean shape space. In addition to interactions among B cells and antigens, we simulate other cell processes such as division, mutation, and death. In this talk, we will present preliminary results from our ABM. We hope to use this model to inform vaccination strategies in the future, especially given the constantly changing nature of this virus.

Organized by: Tin Phan, Ruian Ke, Ruy M. Ribiero, Alan S. Perelson
Note: this minisymposia has multiple sessions. The other session is MS03-IMMU-1.

• Tin Thien Phan Los Alamos National Laboratory
  "Feasibility of using dynamic models with virus-immune interactions to predict early viral rebound dynamics following HIV-1 antiretroviral therapy interruption"
Most individuals living with HIV-1 experience rapid viral rebound once antiretroviral therapy stops; however, a small fraction retain viral remission for an extended duration. Understanding the factors that determine whether viral rebound is likely once treatment stops can enable the development of optimal treatment regime to potentially achieve a functional cure for HIV-1. We built upon the theoretical framework proposed by Conway and Perelson to construct dynamic models of virus-immune interaction to study factors that influence viral rebound dynamics. We evaluate these models using viral load data (up to one year) from 24 participants with diverse outcomes (9 post-treatment controllers and 15 non-controllers) post antiretroviral therapy interruption. The best performing model accurately captures the heterogeneity of viral rebound dynamics in a statistically robust manner. The model suggests that viral rebound dynamics is significantly influenced by the effector cell expansion rate, where post-treatment controllers and non-controllers can be distinguished based on how fast the effector cell population expands. Our results highlight the potential of using dynamic models incorporating virus-immune interactions to predict early viral rebound dynamics post antiretroviral therapy interruption.
• Ellie Mainou The Pennsylvania State University (Department of Biology)
  "Investigating alternative models of acute HIV infection"
Understanding the dynamics to acute HIV infection may provide insights into the mechanisms of early viral control with potential implications for vaccine design. The standard viral dynamics model explains HIV viral dynamics during acute infection reasonably well. However, the model makes simplifying assumptions, neglecting some aspects of HIV. For example, in the standard model, target cells are infected by a single HIV virion. Yet, cellular multiplicity of infection (MOI) may have considerable effects in pathogenesis and viral evolution. Further when using the standard model, we take constant infected cell death rates, simplifying the dynamic immune responses. Here, we use four models—1) the standard viral dynamics model, 2) an alternate model incorporating cellular MOI, 3) a model assuming density-dependent death rate of infected cells and 4) a model combining (2) and (3)—to investigate acute infection dynamics in 43 people tested very early after HIV exposure. We find that all models explain the data, but different models describe differing features of the dynamics more accurately. For example, while the standard viral dynamics model may be the most parsimonious model, viral peaks are better explained by a model allowing for cellular MOI. These results suggest that heterogeneity in within-host viral dynamics cannot be captured by a single model. Thus depending on the aspect of interest, a corresponding model should be employed.
• Jonathan Cody Purdue University (Weldon School of Biomedical Engineering)
  "Potential for HIV viral control with IL-15 immunotherapy: Stability analysis of a mathematical model"
Cytokines, the chemical messengers of the immune system, can be therapeutically applied to treat tumors and chronic viral infections. However, these cytokines can have multifaceted effects, both activating the immune response and triggering a suppressive regulation of that response. We studied the treatment ramifications of these effects using an ordinary differential equation model of interleukin-15 (IL-15) therapy of human immunodeficiency virus (HIV). Using parameter sets previously fitted to non-human primate data, we conducted numerical stability analysis based on a constant IL-15 effect control parameter. There was a moderate IL-15 effect which minimized viral load, but this was still above what would clinically be considered as safely controlling HIV. We next assessed how parameter changes altered the stability of the system, as an analog for combination therapy. It was found that IL-15 therapy in tandem with blockade of suppressive regulation yielded viral control in all parameter sets. These results highlight the need for a multi-drug approach for immune therapy of complex diseases.
• Baylor Fain Texas Christian University (Physics and Astronomy)
  "Deconstructing agent-based model parameters"
The parameters of agent-based models can be hard to estimate, whether the model parameters are probabilistic or deterministic. The work here focuses on in-host virology and presents a systematic way of mathematically categorizing individual-level interactions as they contribute to the probability of infection. This method is applicable even as the agent-based model becomes more complex, and results in a partitioning of the parameter space that can be generalized to other systems.

Organized by: Morgan Craig, Daniel Reeves

• E. Fabian Cardozo-Ojeda Fred Hutchinson Cancer Center (Vaccine and Infectious Disease Division)
  "HIV-1 reservoir dynamics during hematopoietic stem cell transplantation"
The five known cases of antiretroviral therapy (ART)-free HIV long-term remission have resulted in allogeneic hematopoietic stem cell transplantation (allo-HSCT). In these cases, allo-HSCT may have reduced HIV DNA and HIV RNA levels via conditioning or graft-vs-reservoir (GvR) effects. The international consortium IciStem investigates the potential for HIV cure via allo-HSCT. In this talk, I will present our assessment of the impact of conditioning and GvR effect in the control of HIV in IciSTEM participants using ordinarily differential equation models with a nonlinear mixed-effects approach. We explore two mechanistic assumptions on the impact of allo-HSCT on reservoir reduction: infected cells are depleted (1) by conditioning only or (2) by conditioning and by GvR directly proportional to the donor T-cell chimerism levels. We fit models to longitudinal CD4+ T cell concentrations, multiple viral levels, and anti-HIV antibody levels in blood using interpolated T-cell chimerism levels from 22 IciStem participants. Using model selection theory, we found that a model with conditioning and depletion of cells proportional to the observed T-cell chimerism best explains the timing and magnitude of HIV reduction dynamics. Our model predicts that T cell proliferation allows HIV reservoir levels to recover in response to cell loss during conditioning; therefore, the GvR effect is a primary driver of reservoir reduction dynamics after allo-HSCT.
• Jessica M. Conway Penn State (Mathematics)
  "Modeling on-demand PrEP regimen to prevent HIV transmission"
In 2010, analysis of the iPrEx study results demonstrated that daily dosing with antiretroviral therapy (ART) in advance of exposure to HIV, termed pre-exposure prophylaxis (PrEP), can significantly reduce the risk of HIV transmission and population spread. However, daily adherence to a drug regimen can be difficult to maintain and may come with side-effects. In contrast, the IPERGAY study published in 2015 suggested that short-term use around the time of exposure may be just as effective at reducing HIV risk as daily use. Here we investigate short-term use, termed 'on-demand' or 'event-based' PrEP. We aim to make model-based predictions of effective on-demand drug regimen. Focusing on transmission through sexual exposure, we incorporate a deterministic model of tissue-level pharmacokinetics and pharmacodynamics (PK/PD) of Truvada into a branching-process model of early HIV infection. Thus, we predict the risk of HIV transmission and risk reduction associated with dose size and timing relative to exposure. To evaluate effectiveness of dosing strategies, we simulate strategies by sampling a virtual population and performing extensive sensitivity analyses. Hence, we aim to identify practical dosing strategies that most effectively reduce risk of HIV transmission through sexual exposure.
• Chapin S. Korosec York University, 4700 Keele St, Toronto, M3J 1P3, ON, Canada. (Modelling Infection and Immunity Lab, Mathematics and Statistics)
  "Within-host evolution of SARS-CoV-2: how often are de novo mutations transmitted?"
As of March 10th, 2023, the total number of reported SARS-CoV-2 infections reached over 676 million worldwide. Despite a relatively low mutation rate, the large number of infections has allowed for substantial genetic change in SARS-CoV-2, leading to a multitude of “variants of concern”. Utilizing recently determined mutations rates (per site replication), as well as within-host parameter estimates for hospitalized SARS-CoV-2 infections, we applied a stochastic transmission bottleneck model to describe the survival probability of rare de novo SARS-CoV-2 mutations. In the first part of this talk I will briefly discuss the significance and relevance of our within-host parameters published in ref.[1]. I will then discuss our un-published work on SARS-CoV-2 within-host evolution where we compute the survival probability of neutral muta-tions (no phenotypic effect), and various mutations affecting viral life history. We examine transmission bottlenecks of varying sizes, estimating which mutations are most likely to occur de novo and be transmitted during a single infection. This work offers a null model for SARS-CoV-2 substitution rates and predicts which aspects of viral life history are most likely to suc-cessfully evolve, despite low mutation rates and repeated transmission bottlenecks. [1]. C.S. Korosec et al., JTB, vol. 564, 2023.
• Adnan Khan Lahore University of Management Sciences (Mathematics)
  "Modeling Antibiotic Resistance and Effective Dosing Regimens"
In this talk we will present models for in-vivo transfer of antimicrobial resistance and determine efficient antibiotic regimens in the presence of drug resistant bacteria. We consider resistance acquisition via horizontal gene transfer (HGT) which has been identified as primary mechanism for in-vivo drug resistance. It is known that three different mechanisms are responsible for HGT, these include conjugation, transformation, and transduction. We propose deterministic ODE based models for the three processes incorporating the unique pathways involved in each one. We will look at different antibiotic dosing protocols and show that periodic dosing at a constant level may not be successful in eradicating the bacteria. We set up an optimal control problem for successful antibiotic administration and then use a numerical optimization algorithm to determine the ’best’ antibiotic dosing strategy. We study the effects of varying different model parameters on the qualitative behavior of the optimal dosing. We compare our results to those in the literature.

Organized by: Kang-Ling Liao, Wing-Cheong Lo, Huijing Du, Wenrui Hao, Yuan Liu

• Wing-Cheong Lo City University of Hong Kong (Mathematics)
  "Modeling COVID-19 transmission dynamics with self-learning population behavioral change"
Many regions observed recurrent outbreaks of COVID-19 cases after relaxing social distancing measures. It suggests that maintaining sufficient social distancing is important for limiting the spread of COVID-19. The change of population behavior responding to the social distancing measures becomes an important factor for the pandemic prediction. In this study, we develop a SEAIR model for studying the dynamics of COVID-19 transmission with population behavioral change. In our model, the population is divided into several groups with their own social behavior in response to the delayed information about the number of the infected population. The transmission rate depends on the behavioral changes of all the population groups, forming a feedback loop to affect the COVID-19 dynamics. Based on the data of Hong Kong, our simulations demonstrate how the perceived cost after infection and the information delay affect the level and the time period of the COVID-19 waves. This is joint work with Tsz-Lik Chan (University of California Riverside) and Hsiang-Yu Yuan (City University of Hong Kong).
• Wenrui Hao Penn State University (Mathematics)
  "data driven modeling of Alzheimer’s disease"
With over 5 million individuals affected by Alzheimer’s disease (AD) in the US alone, personalized treatment plans have emerged as a promising approach to managing this complex neurological disorder. However, this approach requires sophisticated analysis of electronic brain data. This talk proposes a mathematical modeling approach to describe the progression of AD clinical biomarkers and integrate patient data for personalized prediction and optimal treatment. The proposed model is validated on a multi-institutional dataset of AD biomarkers to provide personalized predictions, and optimal controls are added to enable personalized therapeutic simulations for AD patients.
• Kang-Ling Liao University of Manitoba (Mathematics)
  "A simple in-host model for Covid-19 with treatments-model prediction and calibration"
We provide a simple ODEs model with a generic nonlinear incidence rate function and incorporate two treatments, blocking the virus binding and inhibiting the virus replication to investigate the SARS-CoV-2 infection dynamics. We derive conditions of the infection eradication for the long-term dynamics using the basic reproduction number, and to complement the characterization of the dynamics at short-time, the resilience and reactivity of the virus-free equilibrium are considered to inform on the average time of recovery and sensitivity to perturbations in the initial virus free stage. Then, we calibrate the treatment model to clinical datasets for viral load in mild and severe cases and immune cells in severe cases. Combining analytical and numerical results, we explore the impact of calibration on model predictions.
• Xiaojun Tian Arizona State University (School of Biological and Health Systems Engineering)
  "Modeling Emergent Dynamics in Engineering Synthetic Gene Circuits"
The interplay between synthetic gene circuits and their host organisms, such as growth feedback and resource competition, can give rise to unexpected dynamics. In this presentation, I will discuss our latest research to use mathematical modeling to quantitatively understand and predict the impact of network topology, host physiology, and resource competition on the functional behaviors of gene circuits. Furthermore, I will highlight how resource competition affects the circuit noise behavior and present practical control strategies to engineer more robust gene circuits.

• Benjamin Whipple University of Idaho
  "Regulation of CD8+ T cells may explain age dependent immune response to influenza infection"
Influenza viral infection is known to have more serious consequences on elderly populations. Previous modeling efforts for influenza infection have found differences in the immune response dynamics to influenza infection between young and aged mice. A better understanding of the immunological mechanisms by which aging leads to discrepant immune responses may inform treatment strategies. One possible explanation for these differences may be a difference between ages in the intensity of the activation of CD8+ T cell proliferation by the presence of virus. In order to further investigate this proposed mechanism and the difference in immune response dynamics, we consider several ordinary differential equation models describing the dynamics of CD8+ T cell and viral titer count. We apply these models to existing experimental data of viral titer and CD8+ T cell counts collected periodically over a period of 19 days from mice populations infected with influenza A/Peurto Rico/8/34 (H1N1). The models we consider are fit to our data by the differential evolution method for global optimization. After fitting the models, we use Akaike information criterion with small sample corrections in order to identify the model which best represents the considered data. Our chosen model differs from previously considered models by the inclusion of viral regulation of CD8+ T cells. We perform identifiability analysis of the selected model by considering loss profiles across the parameter search range. We identify that relationships between model parameters present challenges for model identifiability. We find that when clearance rate of virus by T cells is assumed to differ between populations then our model predicts two key differences in immune response dynamics. First, it predicts delayed proliferation response for the younger mice. Second, it predicts higher CD8+ T cell regulation by virus for the younger mice.
• Bryan Shin University of Vermont Larner College of Medicine
  "Examining B-cell dynamics and responsiveness in different inflammatory milieus using an agent-based model"
Introduction: B-cells are essential components of the immune system that neutralize infectious agents through the generation of antigen-specific antibodies and through the phagocytic functions of naïve and memory B-cells. However, the B-cell response can become compromised by a variety of conditions that alter the overall inflammatory milieu, be that due to substantial, acute insults as seen in sepsis, or due to those that produce low-level, smoldering background inflammation such as diabetes, obesity, or advanced age. This B-cell dysfunction, mediated by the inflammatory cytokines Interleukin-6 (IL-6) and Tumor Necrosis Factor-alpha (TNF-α), increases the susceptibility of late-stage sepsis patients to nosocomial infections and increases the incidence or severity of recurrent infections, such as SARS-CoV-2, in those with chronic conditions. We propose that modeling B-cell dynamics can aid the investigation of their responses to different levels and patterns of systemic inflammation. Methods: The B-cell Immunity Agent-based Model (BCIABM) was developed by integrating knowledge regarding naïve B-cells, short-lived plasma cells, long-lived plasma cells, memory B-cells, and regulatory B-cells, along with their various differentiation pathways and cytokines/mediators. The BCIABM was calibrated to reflect physiologic behaviors to: 1) mild antigen stimuli expected to result in immune sensitization through the generation of effective immune memory, and 2) severe antigen challenges representing the acute substantial inflammation seen during sepsis, previously documented in studies on B-cell behavior in septic patients. Once calibrated, the BCIABM was used to simulate the B-cell response to repeat antigen stimuli during states of low, chronic background inflammation, implemented as low background levels of IL-6 and TNF-α often seen in patients with conditions such as diabetes, obesity, or advanced age. The levels of immune responsiveness were evaluated and validated by comparing to a Veteran’s Administration (VA) patient cohort with COVID-19 infection known to have a higher incidence of such comorbidities. Results: The BCIABM was successfully able to reproduce the expected appropriate development of immune memory to mild antigen exposure, as well as the immunoparalysis seen in septic patients. Simulation experiments then revealed significantly decreased B-cell responsiveness as levels of background chronic inflammation increased, reproducing the different COVID-19 infection data seen in a VA population. Conclusion: The BCIABM proved useful in dynamically representing known mechanisms of B-cell function and reproduced immune memory responses across a range of different antigen exposures and inflammatory statuses. These results elucidate previous studies demonstrating a similar negative correlation between the B-cell response and background inflammation by positing an established and conserved mechanism that explains B-cell dysfunction across a wide range of phenotypic presentations.
• Quiyana M. Murphy Virginia Tech
  "Understanding Neutrophil Dynamics during COVID-19 Infection"
Infection with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) results in varied clinical outcomes, with virus-induced chronic inflammation and tissue injury being associated with enhanced disease pathogenesis. To determine the role of tissue damage on immune populations recruitment and function, a mathematical model of innate immunity following SARS-CoV-2 infection has been proposed. The model was fit to published longitudinal immune marker data from patients with mild and severe COVID-19 disease and key parameters were estimated for each clinical outcome. Analytical, bifurcation, and numerical investigations were conducted to determine the effect of parameters and initial conditions on long-term dynamics. The results were used to suggest changes needed to achieve immune resolution.

• Jason E. Shoemaker University of Pittsburgh
  "Sex-specific immunoregulation: Computational modeling approaches to determine why biological females may experience greater inflammation during influenza infection"
In humans, biological males and females often experience different outcomes during respiratory infections. Here, we are referring to differences in biological sex (XX and XY) and not gender, which includes behaviors and activities that are determined by society or culture in humans. During the 2009 H1N1 influenza pandemic, adult females were at greater risk than their male, age-matched counterparts for hospitalization and death. Many factors may determine sex-specific outcomes, but there is considerable evidence that sex-specific immune regulation is a key driver of enhanced disease pathology. Severe influenza infections are characterized with aggressive inflammatory responses, and studies show that male and female inflammatory responses differ when infected with a common virus. Yet, it remains unknown how the inflammatory differences emerge. In complex systems, a change in a single component’s behavior impacts the temporal response of other system components. Computational modeling is a powerful tool for determining how changes in the behavior of immune system components lead to changes in the overall system response, and computational modeling can consider multiple hypotheses on how sex-specific immune responses emerge. Our research team develops knowledge-based, mechanistic models of the lung immune system and then employs state-of-the-art optimization and Bayesian inference approaches to rigorously determine how the lung immune system is differently regulated between cohorts. These models can be constructed to consider several factors impacting sex-specific regulation simultaneously, including the effects of hormones and sex chromosome dependent gene regulation. Here, we will discuss our most recent effort where we constructed a computational model of the mouse lung innate immune system and used computational models to determine how the immune system is differently regulated in male and female mice infected with a pandemic H1N1 virus. Our results suggest that not only do the rates of key immune processes, particularly those associated with interferon induction, have to be different between males and females, but that the effectiveness of therapeutic intervention using anti-inflammatory compounds is also sex-specific. The model is now being expanded to include additional immune components and we are currently developing strategies for incorporating hormone regulation.
• Elizabeth R Duke Fred Hutchinson Cancer Center
  "Intrahost mathematical modeling of CAR T cells for HIV cure"
The primary barrier to cure from human immunodeficiency virus (HIV) is a reservoir of long-lived, latently infected CD4+ T cells. This reservoir causes viral rebound when people with HIV stop taking daily antiretroviral therapy (ART). One approach to reducing viral rebound is to use T cells with HIV-specific chimeric antigen receptors (CAR T cells) to target and destroy reservoir cells after they activate. In a pilot study, four rhesus macaques (n = 4) infected with Simian-HIV (SHIV) were given a single infusion of CAR T cells during ART to induce post-rebound control after ART was interrupted. Macaques that received CAR T cells had a lower viral peak after analytical treatment interruption (ATI) than before compared to controls. To model this intervention, we first developed ordinary differential equations (ODE) to recapitulate viral loads during primary infection and post-ATI rebound in the control animals. Then, using viral parameter values from the control model, we fit candidate ODE models to plasma viral loads and the CD4+ and CD8+ CAR T cell measurements from SHIV-infected macaques that received CAR T cells. Using the best fitting version of the model, we found the parameter that modulates CAR T cell proliferation in response to SHIV correlated with significantly lower post-ATI viral peaks. We simulated the data-validated model for each macaque to find conditions in which the CAR T cell infusion achieved ART-free, SHIV remission. Although gene and cell therapy strategies for HIV cure are in the initial stages, mathematical modeling might accelerate the success of these approaches.
• Vitaly V. Ganusov University of Tennessee
  "Using mathematical modeling to determine pathways of Mycobacterium tuberculosis dissemination in mice"
Tuberculosis (TB) remains a major disease of humans claiming lives of 1.6 millions in 2021. TB is caused by bacteria Mycobacterium tuberculosis (Mtb) that are transmitted by aerosol and initiate the infection in the lung. Over time, Mtb often disseminates from the initial infection site to other parts of the lung and in some cases, to extrapulmonary sites such as lymph nodes or spleen. In mice, infection with aerosolized Mtb also initially infects the lung but over time, Mtb is typically found in many extrapulmonary tissues such as lung-draining lymph nodes (LNs), spleen, or liver. The specific pathways of Mtb dissemination from the lung to other tissues, however, remain unclear. One study (Chackerian et al. 2002) measured dissemination of Mtb Erdman in two strains of mice (B6 and C3H) and suggested that Mtb first disseminates from the lung to the LNs and then to spleen and liver. We developed several alternative mathematical models describing how Mtb could disseminate from the lung to other tissues. Interestingly, we found that these data were insufficient to establish the Mtb dissemination pathway based on model fits; for example, the models in which Mtb spreads from the lung to LNs, and then from LNs for spleen/liver or from the lung to spleen/liver and then to LNs described the data with similar quality. However, the second model predicted extremely high rate of Mtb replication in the spleen/liver and high dissemination rate to the LNs; estimating these rates in future experiments may help falsify the model. The results were similar for two strains of mice (B6 and C3H). Interestingly, while Mtb causes stronger pathology in C3H mice, we also found that the rate of Mtb replication in the lung and other tissues were smaller in C3H mice than those in B6 mice. Our best models suggest that after lung infection, most Mtb (75% or more) exiting the lung disseminate to lung-draining LNs suggesting that control of Mtb replication in the LNs with an appropriate vaccine could be a strategy to prevent systemic dissemination of Mtb.
• Alexis Hoerter Purdue University
  "Agent Based Model Investigating Latent and Naïve In Vitro M. Tuberculosis Infection Dynamics"
Prior to COVID-19, tuberculosis (TB) was the leading cause of death due to a single infectious agent – Mycobacterium tuberculosis (Mtb). The hallmark of Mtb infection is the formation of granulomas – unique microenvironments orchestrated by the immune response to contain Mtb and localize host-pathogen interactions. The host immune status is an important determinant in the formation of granulomas during Mtb infection. Approximately 90% of individuals infected with Mtb harbor granulomas that control bacterial spread, resulting in asymptomatic disease known as latent TB infection (LTBI). In vitro granuloma models have helped to understand granuloma development as they allow for highly controllable and high time-resolution investigations into granuloma formation. Specifically, an in vitro model that generates 3D granuloma-like structures through infection of human donor PBMCs with Mtb has shown that cells from LTBI donors better control Mtb growth compared to cells from naïve donors (those never exposed to Mtb before). But identifying mechanisms behind these differences is challenging, using experimental data alone. Here, we present a complementary approach using our agent-based model of these in vitro granulomas to help elucidate differences between LTBI and naïve host cell responses. Our computational model mimics Mtb infection through interactions between virtual macrophages, CD4+ T cells and Mtb. Mechanisms include Mtb growth, macrophage phagocytosis resulting in Mtb death or macrophage infection, macrophage and T cell activation, T cell proliferation, and cytokine/chemokine diffusion and degradation. The model is implemented using Repast Simphony. The model has been calibrated to published data from LTBI and naïve donor cells. Model outputs are calibrated to fall within A) 0.5-1.5x the experimental intracellular bacterial fold change for 3, 4, 5, 7, and 8 days post infection, B) 0.6-1.8x the experimental total cell fold change at day 7 post infection, and C) day of first granuloma formation (day 3 or 4 post infection for LTBI and day 5 or 6 post infection for naïve). We used Latin Hypercube Sampling (LHS) along with the Alternating Density Subtraction (ADS) method to perform iterative calibrations to identify a robust parameter region in which at least 75% of our parameter sets passed our criteria. We calibrate parameters for both LTBI and naïve datasets in parallel after the first LHS-ADS calibration iteration. Calibration was complete after 5 iterations with 89% and 84% parameter sets passing our criteria for LTBI and naïve groups respectively. Results show that starting at Day 2 post infection, LTBI-like simulations had a significantly higher number of activated TB-specific CD4+ T cells than the naïve-like simulations. This early activation of CD4+ T cells corresponded with an early increase in the number of total activated macrophages and activated infected macrophages in the LTBI-like simulations. Macrophage activation in the naïve group seemed to lag by approximately 3 days behind the LTBI group. Interestingly, the total number of infected macrophages was lower in the LTBI simulations, but despite less total infected macrophages throughout the infection, LTBI-like simulations controlled bacteria better than the naïve-like simulations having both less intracellular and extracellular bacteria by Day 8. Parameters that may have contributed to the quick activation of TB-specific CD4+ T cells and infected macrophages in LTBI-like simulations include lower CD4+ T cell deactivation probability and lower cytokine thresholds for macrophage activation. Our computational model, calibrated to LTBI and naïve experimental data, shows that the quick activation of TB-specific CD4+ T cells in LTBI-like simulations results in early and sustained activation of infected macrophages that leads to more bacterial control in LTBI-like simulations compared to naïve-like simulations. Despite having less overall infected macrophages, having a greater percentage of activated infected macrophages means that LTBI-like simulations can control Mtb infection better than naïve-like simulations.

• Adquate Mhlanga Loyola University Chicago
  "Mathematical modeling of hepatitis D virus and hepatitis B virus interplay during anti-HDV treatment"
Hepatitis D virus (HDV) and hepatitis B virus (HBV) coinfection is the most severe form of chronic viral hepatitis. HDV is considered a satellite virus because it relies on hepatitis B surface antigen (HBsAg) to propagate. Treatment against HDV chronic infection with pegylated interferon-α2a (pegIFN) therapy is suboptimal and affects both HDV and HBV. The investigational drug called lonafarnib (LNF) targets HDV only, providing a unique opportunity to study the interplay between HDV and HBV. We recently developed a mathematical model to study the interplay between HDV and HBV in chronic HDV/HBV patients [1]. I will present our efforts to characterize the frequent kinetic data of HDV, HBV, HBsAg, and LNF pharmacokinetics obtained from 15 patients who were treated with LNF, LNF+ritonavir, or LNF+pegIFN [2].In addition, I will present our modeling efforts in extending our model [1] to account also for HBsAg kinetics and to estimate HDV/HBV kinetic parameters and LNF±pegIFN efficacies using both individual and population fitting approaches.
• Caroline I. Larkin University of Pittsburgh
  "Rule-based modeling of Eastern Equine Encephalitis Virus replication dynamics"
Eastern Equine Encephalitis Virus (EEEV) is an arthropod-borne, single-stranded positive-sense RNA virus that poses a significant threat to public health and national security. Compared to similar viruses such as SARS-CoV-2 or Hepatitis C virus, EEEV causes severe encephalitis when neuroinvasive leading to a human mortality rate of ~30-70%. Moreover, there are no preventative or standardized therapies, leaving patients to rely solely on supportive care. In addition, studies have shown that EEEV is easily aerosolized making it an ideal biowarfare agent. Although the molecular components and interactions of infection, replication, and amplification of EEEV within the host cell are well-studied, how these mechanisms integrate to determine the dynamics of RNA viral replication and host immune responses remains unclear, limiting our ability to advance therapeutic development. Computational models provide a powerful tool for probing both quantitative and qualitative effects arising from the modulation of viral infections. Here, we present a systems modeling approach to elucidate the mechanisms regulating the precise dynamics of EEEV replication through the development of a mechanistic mathematical model. Specifically, this model describes attachment, entry, uncoating, replication, assembly, and export of both infectious virions and virus-like particles within mammalian cells. The model recapitulates known characteristics of EEEV infection, including the timing and amplitude of virion production, and identifies genome replication as the significant rate-limiting step during infection. Additionally, this model highlights the possibility, which will be tested experimentally, that a mismatch between the production of viral RNA and viral proteins could result in the inability to produce infectious virions 12 hours post-infection. We are currently working to expand the model to incorporate type I interferon induction within an infected host cell. This will provide a comprehensive perspective on the conditions required for maximizing host response efficacy and determine the key steps of immune system activation required for successful suppression of viral infection.
• Hayashi Rena Kyushu University
  "Establishment chance of a mutant strain decreases over time after infection with the original strain."
After infecting a host, a viral strain may increase rapidly within the body and produce mutants with a faster proliferation rate than the virus itself. However, most of the mutants become extinct because of the stochasticity caused by the small number of infected cells. In addition, the mean growth rate of a mutant strain decreases with time because the number of susceptible target cells is reduced by the wild-type strain. In this study, we calculated the fraction of mutants that can escape stochastic extinction, based on a continuous-time branching process with a time-dependent growth rate. We analyzed two cases differing in the mode of viral transmission: (1) an infected cell transmits the virus through cell-to-cell contact with a susceptible target cell; (2) an infected cell releases numerous free viral particles that subsequently infect susceptible target cells. The chance for a mutant strain to be established decreases with time after infection of the wild-type strain, and it may oscillate before convergence at the stationary value. We then calculated the probability of escaping stochastic extinction for a drug-resistant mutant when a patient received an antiviral drug that suppressed the original strain. Combining the rate of mutant production from the original strain and the chance of escaping stochastic extinction, the number of emerging drug-resistant mutations may have two peaks: one soon after the infection of the original type and the second at the start of antiviral drug administration. Hayashi R, Iwami S, and *Iwasa Y. 2022. Escaping stochastic extinction of mutant virus: temporal pattern of emergence of drug resistance within a host. Journal of Theoretical Biology 537, 111029. Hayashi R., and Iwasa, Y. Temporal pattern of the emergence of a mutant virus escaping cross-immunity and stochastic extinction within a host. (in review)
• Quintessa Hay Virginia Commonwealth University
  "A Mathematical Model for Wound Healing in Reef-Building Coral Pocillopora damicornis"
Coral reefs, among the most diverse ecosystems in the ocean, currently face major threats due to multiple stressors such as pollution, unsustainable fishing practices, and perturbations in environmental parameters brought on by climate change. Reefs also sustain regular wounding from other sea life and human activity. Recent reef preservation practices have even involved intentional wounding by systematically breaking coral fragments and relocating them to revitalize damaged reefs. Despite its importance, very little research has explored the inner mechanisms of wound healing in corals. Some reef-building corals have been observed to initiate an immunological response similar to those observed in humans and other vertebrates. Utilizing past models of inflammation and early proliferation and remodeling, we formulated a mechanistic model for wound healing in corals. The model consists of four differential equations mediating wound debris, inflammation, proliferation, and wound closure. The model is coupled with experimental data for linear and circular shaped wounds on Pocillopora damicornis fragments. A preliminary parameter set was obtained by fitting to the wound closure times obtained empirically and to expected temporal trends observed in other coral species and in humans and other vertebrates. A variety of mathematical methods were applied for model analysis including local sensitivity analysis. Results were used to define an identifiable set of parameters. The parameter space was also explored to exhibit the diverse model outcomes and their biological implications. Keywords: stony corals, inflammation, differential equations, parameter estimation, sensitivity analysis

• Daniel B Reeves Fred Hutchinson Cancer Center
  "Modeling antibody mediated prevention of HIV to derive in vivo potency of VRC01"
The Antibody Mediated Prevention (AMP) trials demonstrated that passive administration of the broadly neutralizing monoclonal antibody VRC01 could prevent some HIV acquisition events. Here we used mathematical modeling to demonstrate that VRC01 influenced viral loads in AMP participants who acquired HIV. Instantaneous inhibitory potential (IIP), which integrates VRC01 serum concentration and VRC01 sensitivity of acquired viruses in terms of both IC50 and IC80, had a dose-response relationship with first positive viral load (p=0.03), which was particularly strong above a threshold of IIP=1.6 (r=-0.6, p=2e-4). Next, combined pharmacokinetic, pharmacodynamic and viral load kinetic modeling revealed that VRC01 neutralization predicted from in vitro IC80s and serum VRC01 concentrations overestimated in vivo neutralization by 600-fold (95% CI: 300-1200). We show how the trained model can be naturally conducive for informing design and projecting efficacy in coming preventive and therapeutic HIV trials of combination monoclonal antibodies.
• David W. Dick York University
  "HIV-1 neutralization potential of red blood cells viral traps"
Management of human immunodeficiency virus (HIV) infection requires strict adherence to a daily drug regiment to prevent viral rebound. Red blood cells (RBCs) that lack nuclei and other organelles required for viral replication have been proposed as viral traps for HIV-1 as an alternative treatment for HIV-1. RBCs persistence in-host would require less frequent treatment offering a promising long-lasting augmentation to the existing highly active antiretroviral therapy (HAART). We develop an in-vitro model to assess the neutralization potential of RBCs targeting HIV-1 by expressing CD4, CCR5, or a CD4-glycophorin A (CD4-GpA) fusion protein and seek to elucidate the requirements for successful use of red blood cell viral traps for both treatment of HIV-1 and prophylaxis against both HIV-1 and SARS-CoV-2 infection.
• Katherine Owens Fred Hutchinson Cancer Center
  "Heterogeneous SARS-CoV-2 kinetics and in vitro overestimates of nirmatrelvir potency in humans"
SARS-CoV-2 viral loads have been linked with COVID-19 severity and transmission risk, and their kinetics vary across individuals. We clustered data from 1355 infections in the National Basketball Association cohort to identify six distinct patterns of viral shedding, which differ according to peak, duration, expansion rate and clearance rate. We then developed a mechanistic mathematical model that recapitulated observed viral trajectories, including viral rebound. Our results suggest that more rapid viral elimination occurs following vaccination and during omicron infection due to enhanced innate and acquired immune responses. We extended this model to include nirmatrelvir pharmacokinetics. In a published randomized double-blinded clinical trial, ritonavir-boosted nirmatrelvir decreased hospitalization and death by 95% and decreased nasal viral load by 0.5 log relative to placebo when given early during symptomatic infection to high-risk individuals. Our results from simulating this trial demonstrate niramtrelvir IC50 (50% inhibitory concentrations) estimates from in vitro assays are 100-fold less than plasma concentration required to reduce viral infection by 50% in humans. A maximally potent agent would reduce viral load by 3 orders of magnitude. We also project modifications to the treatment regimen that can reduce the frequency of viral rebound.
• Mohammad Aminul Islam University at Buffalo, The State University of New York, Buffalo, NY
  "Mathematical Modeling of Impacts of Patient Differences on COVID-19 Lung Fibrosis Outcomes"
Patient-specific premorbidity, age, and sex are significant heterogeneous factors that influence the severe manifestation of lung diseases, including COVID-19 fibrosis. The renin-angiotensin system (RAS) plays a prominent role in regulating effects of these factors. Recent evidence suggests that patient-specific alteration of RAS homeostasis with premorbidity and the expression level of angiotensin converting enzyme 2 (ACE2), depending on age and sex, is correlated with lung fibrosis. However, conflicting evidence suggests decreases, increases, or no changes in RAS after SARS-CoV-2 infection. In addition, detailed mechanisms connecting the patient-specific conditions before infection to infection-induced fibrosis are still unknown. Here, a mathematical model is developed to quantify the systemic contribution of heterogeneous factors of RAS in the progression of lung fibrosis. Three submodels are connected—a RAS model, an agent-based COVID-19 in-host immune response model, and a fibrosis model—to investigate the effects of patient-group-specific factors in the systemic alteration of RAS and collagen deposition in the lung. The model results indicate cell death due to inflammatory response as a major contributor to the reduction of ACE and ACE2, whereas there are no significant changes in ACE2 dynamics due to viral-bound internalization of ACE2. Reduction of ACE reduces the homeostasis of RAS including angiotensin II (ANGII), while the decrease in ACE2 increases ANGII and results in severe lung injury and fibrosis. The model explains possible mechanisms for conflicting evidence of RAS alterations in previously published studies. Also, the results show that ACE2 variations with age and sex significantly alter RAS peptides and lead to fibrosis with around 20% additional collagen deposition from systemic RAS with slight variations depending on age and sex. This model may find further applications in patient-specific calibrations of tissue models for acute and chronic lung diseases to develop personalized treatments.