Organized by: Yanyu Xiao, Xingfu Zou

• Daozhou Gao Cleveland State University (Mathematics)
  "Influence of Changes in Population Movement on Total Biomass"
How animal dispersal affects the total population abundance and its distribution in a heterogeneous environment is a fundamental question in spatial ecology. In this talk, based on a multi-patch logistic model with asymmetrical migration, we study the dependence of the global and local biomass on the dispersal intensity and dispersal asymmetry. In particular, the total biomass over two patches is either constant, or strictly decreasing, or strictly increasing, or initially strictly increasing then strictly decreasing with respect to dispersal rate. On the other hand, we develop a novel population model with both migration and visitation and show that the presence of visitation can substantially change the influence of population migration on population abundance. This is a joint work with Yuan Lou and Yutong Zhang.
• Xi Huo University of Miami (Mathematics)
  "Linking mosquito trap data with models: identifiability, fitting, and applications"
Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this talk, I will show how we incorporate local entomological and temperature data in an ODE model, investigate the parameter identifiability, and fit the model to mosquito trap data from 2017 to 2019. The well-calibrated model can help us compare the Ae. aegypti population, evaluate the impact of rainfall intensity in different urban built environments, and assess the effectiveness of vector control strategies in Miami-Dade County.
• Marco Tosato Western University (Applied Mathematics)
  "Impact of deer migration on tick population dynamics"
Ticks are the carriers of several vector-borne diseases worldwide. In the past few decades, they have been spreading northward across Canada and have reached areas that were originally tick-free. In this talk, we explain how the interaction between deer mobility and tick population might have played a relevant role in this. In particular, we show using a coupled system of ordinary and delay differential equations in a two-patch environment how deer migration affects tick population dynamics and may modify their suitability for specific patches.
• Tianyu Cheng Western University, Canada (Department of Mathematics)
  "Modelling the impact of society precaution on disease dynamics and its evolution"
Afraid of infection, uninfected individuals may spontaneously protect themselves against infectors in varying degrees, depending on the severity of epidemics. As a result of adopting non-pharmaceutical inventions, people almost exhibit a uniform protection level without individual differences. We introduce a mathematical model formulated by differential equations to describe the severity of epidemics and group-precaution levels relying on the severity level during the epidemics. Our model describes that the group-precaution level mainly affects the severity of epidemics by directly adjusting the number of practically susceptible; In turn, the severity change of epidemics leads to the evolution of the group-precaution level. Mathematical analysis shows that when basic reproduction number is larger than 1, the endemic equilibrium exists and is subjective to a critical parameter that combines the initial protection level and the initial number of the infectious class. Considering the time lag in responding to the severity change of epidemics, we further extend our model, which is a system of delay differential equations. We figure out the condition that Hopf bifurcations occur by theoretical and numerical techniques.

Organized by: Mihrab Uddin Chowdhury, Lale Asik, Benito Chen-Charpentier, Christina Cobbold'

• Saikanth Ratnavale University of Notre Dame (Department of Biological Sciences)
  "Optimal controls of the mosquito-borne disease, Dengue with vaccination and control measures"
Dengue is one of the most common mosquito-borne diseases in the world, and a person can get infected by one of the four serotypes of the virus named DENV-1, DENV-2, DENV-3, and DENV-4. After infection with one of these serotypes, an individual will maintain permanent immunity to that serotype, and partial immunity to the other three serotypes. Therefore, there is a risk of getting infected by this virus a maximum of four times, and the symptoms may vary from mild fever to high fever, bleeding, enlarged liver, and severe shock, and sometimes these symptoms may lead to death. It is obvious that the increase in the number of infected individuals makes a negative impact on a country’s economy. Hence, the use of different control measures such as mosquito repellents and the introduction of a vaccine against the virus is important in controlling the spread of the virus. In this study, I am presenting a methodology on how to estimate the optimal rate of vaccinations based on the QDENGA dengue vaccine and the optimal rate of control measures to reduce the number of new and severe dengue cases while minimizing the overall cost. In addition, this vaccine claims high protection against symptomatic disease and waning protection over time for some DENV serotypes. However, the extent to which protection against disease conditional on infection is unknown. I consider different scenarios subject to the possible combinations of vaccine protection and control measures to investigate the most effective parameter values to control the transmission of the virus. Disease forecasts including the number of newly infected individuals in each serotype, the optimal rate of control measure, and vaccinations for a period of ten years are performed with the help of computer software.
• Damie Pak Cornell University
  "Resource availability constrains the proliferation rate of malaria parasites"
The life cycle of the malaria-causing species involves multiple rounds of replication, with a fraction of infected red blood cells (RBCs) being committed to producing specialized stages for onward transmission to vectors. The proliferation rate is limited by the burst size or the average number of daughter cells to emerge from each infected RBC. To increase transmission, parasites would be expected to evolve to the maximal burst size that does not prematurely end the infection by killing its host. The variability in observed burst size, however, suggests that maximizing the burst size is not always the best strategy.Using a within-host model parameterized for the rodent malaria, Plasmodium chabaudi, we investigate how host mortality and resource limitation affect the optimal burst size. We focus on the acute phase which encompasses the first and typically largest wave of parasite abundance with most of the parasite’s transmission success gained disproportionately in this phase. By calculating the cumulative transmission potential at the end of the acute phase, we can then compare the transmissibility of strains with varying burst sizes.We find that greater proliferation leads to the production of more sexual forms, but there are diminishing returns in transmission success. Moreover, the benefits of faster proliferation come at the cost of significantly shortening the period of high infectivity. Therefore, the optimal burst size emerges from the trade-off between the length of the acute phase and the production of the sexual forms. By identifying resource availability as a key mechanism limiting the burst size, we are better able to understand how parasite traits can influence the varying virulence we see in malaria infections.
• Gabriella Torres Nothaft Cornell University (Department of Mathematics)
  "Impact of Disease on a Lotka-Volterra Predation Model"
Quantifying the relationship between predator and prey populations under the influence of disease provides important insight into their roles and behaviors in the ecosystem. This paper uses two models as the base for the analysis: the Lotka-Volterra predation model and the SIR disease model. Developed in the 20th century, the Lotka-Volterra predation model provides a mathematical explanation of this phenomenon and is widely recognized in both the mathematical and biological communities . Epidemiology models such as the standard susceptible-infected-susceptible (SIS) model can be used to understand the dynamics of a disease in a given population or area. There are multiple variations of this predation and infection impacting the prey population, affecting the basic model, all focused on variations on the spread of some infectious agent in the desired population. To fully understand the regulatory mechanisms that the two populations go through, we need to analyze how both predation and infection impact the prey population, which in turn affects the number of predators. In this work, we first go through the dynamics of the original Lotka-Volterra model, then perform stability and further analyses on the combined model.
• Karan Pattni University of Liverpool
  "Eco-evolutionary dynamics in finite network-structured populations with migration"
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We looked at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.

Organized by: Rebecca Tyson, Sarah MacQueen

• Sarah MacQueen University College Dublin (School of Agriculture and Food Science)
  "Model mechanism for choice of foraging site affects predicted pollination services"
Foraging constancy, or repeated return to the same foraging location, is an important aspect of bumble bee behaviour, and should therefore be an important consideration when using modeling to predict the pollination services provided by bumble bees.  However, it is unknown exactly how bumble bees select their foraging sites, and most modelling studies do not account for this uncertainty.  We use an individual based model to explore how predicted pollination services and bee fitness change under different foraging site selection mechanisms.  We considered two different site-searching methods (random and more realistic exploration behaviour) and four different site-selection metrics (random, minimal distance, maximal wild flower density, maximal net rate of energy return) in an agricultural landscape containing wildflower, crop (in bloom), and empty (no resource) patches.  We find that site-selection metric has a greater impact on crop pollination services and bee fitness than either site-searching method or landscape characteristics.  Site-selection based on maximising the net rate of energy return leads to both the highest crop pollination services and the longest foraging trips.  We find that the percent of crop fields visited, amount of time spent foraging, number of foraging sites located in crops, and the number of flowers visited may be used to determine how real bees select their foraging sites.
• Laurence Ketchemen Tchouaga McGill University (Mathematics and statistics)
  "Spatial steady states in fragmented landscapes under monostable and bistable growth dynamics"
Many biological populations reside in increasingly fragmented landscapes, where habitat quality may change abruptly in space. A reaction-diffusion model for a single species population which propagates in a heterogeneous landscape in a one-dimensional space is presented. The landscape is composed of two homogeneous adjacent patches with different diffusivities and net growth functions (monostable and bistable). A coupling interface condition between the two patches is involved. We consider various combinations of the reaction term and establish the existence, uniqueness and—in some cases—global asymptotic stability of a positive steady state. We classify the shape of these states depending on movement behaviour and clarify the role of movement in this context. We also give an answer to the following ecological question: how can the total population abundance at a steady state exceed the total carrying capacity? The analysis of the model with a bistable net growth function on one of the two patches yields a rich and interesting structure of steady states. Under certain parameter conditions, some of these states are amenable to explicit stability calculations. These yield insights into the possible bifurcations that can occur in our system. Numerical simulations reveal fold bifurcations.
• Katie Florko  University of British Columbia ( Institute for the Oceans and Fisheries)
  "Linking movement and dive data to prey distribution models: new insights in foraging behaviour and potential pitfalls of movement analyses"
Animal movement data are regularly used to infer foraging behaviour and relationships to environmental characteristics, often to help identify critical habitat. To characterize foraging, movement models make a set of assumptions rooted in theory, for example, time spent foraging in an area increases with higher prey density. We assessed the validity of these assumptions by associating horizontal movement and diving of satellite-telemetered ringed seals (Pusa hispida)—an opportunistic predator—in Hudson Bay, Canada, to modelled prey data and environmental proxies. Modelled prey biomass data performed better than their environmental proxies (e.g., sea surface temperature) for explaining seal movement; however movement was not related to foraging effort. Counter to theory, seals appeared to forage more in areas with relatively lower prey diversity and biomass, potentially due to reduced foraging efficiency in those areas. Our study highlights the need to validate movement analyses with prey data to effectively estimate the relationship between prey availability and foraging behaviour.
• Mennatallah Gouda Utah State University (Mathematics and Statistics Department)
  "Characterization of the long-distance dispersal kernel of white-tailed deer and evaluating its impact on chronic wasting disease spread in Wisconsin"
Chronic Wasting Disease (CWD) is a fatal untreatable neurodegenerative disease that infects cervids. It is highly contagious and caused by abnormal malfunction and assembly of the normal cellular prion proteins (PrPC) into aggregation-prone prions (PrPSc). Centers for Disease Control and prevention (CDC) report that the prevalence of CWD in free-ranging deer in the US is still relatively low. However, in several states the infection rates exceed 1 deer in 10. Cervids may uptake CWD prions from direct interaction with infected individuals or from the environment. Infected individuals shed prions into the environment through feces, urine, saliva or carcass, and long-distance dispersal of infected deer poses a danger of spreading CWD to new regions. We propose an Integrodifference Model (IDE) to capture CWD dynamics and the consequences of long-distance dispersal behavior of White-Tailed Deer (WTD, Odocoileus virginianus). Currently there are no dispersal kernels available to describe the long-distance dispersal behavior of WTD juveniles. Our aim is to characterize long-distance dispersal of WTD juveniles and assess how it may affect CWD spread. We introduce a long-distance dispersal model, based on a diffusion-settling seed transport by vertebrates, accommodating a variety of hypothetical dispersal behaviors of WTD. Four kernels were obtained by solving 2D diffusion-settling Partial Differential Equation (PDE) models and approximating using Laplace’s method. We parameterized the kernels with GPS collar data collected in Wisconsin, US. Using a Maximum Likelihood Estimation (MLE) approach, we fitted the model parameters, and assessed model fits using the Bayesian Information Criterion (BIC). Sensitivity of results was determined using nonparametric bootstrapping and the impact of long-distance dispersal on CWD spread was quantified using the IDE model. A Holling type III settling rate function resulted in the most supported long-distance dispersal kernel reflecting deer preference to not settle down soon after they start dispersal. Our results will assist CWD management facilities in controlling disease spread.

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.

Organized by: Bruce Pell, Fuqing Wu

• Tin Phan Los Alamos National Laboraty (Theoretical Biology and Biophysics)
  "Integrating wastewater surveillance data with dynamic models to track and predict viral infections and beyond"
Wastewater surveillance has proved to be a valuable tool to track the COVID-19 pandemic. However, most studies using wastewater surveillance data revolve around establishing correlations and lead time relative to reported case data. Yet, wastewater surveillance data is not independent of transmission dynamics and its integration with dynamic within-host and between-host models is necessary to better understand, monitor, and predict viral disease outbreaks. Dynamic models overcome emblematic difficulties of using wastewater surveillance data such as establishing the temporal viral shedding profile. Complementarily, wastewater surveillance data bypasses the issues of time lag and underreporting in clinical case report data, thus enhancing the utility and applicability of dynamic models. The integration of wastewater surveillance data with dynamic models can enhance real-time tracking and prevalence estimation, forecast viral transmission and intervention effectiveness, and most importantly, provide a mechanistic understanding of infectious disease dynamics and the driving factors. Dynamic modeling of wastewater surveillance data will advance the development of a predictive and responsive monitoring system to improve pandemic preparedness and population health.
• Matthew D. Johnston Lawrence Technological University (Department of Mathematics + Computer Science)
  "Integrating Virus Variant Data into a Two-Strain SIR Model with Cross-Immunity"
We consider a dimensionally-reduced infectious disease model involving two competing virus strains with asymmetric temporary immunity periods and partial cross-immunity. In the utilized reduction method, we assume that the original strain remains at its endemic steady state as the emerging strain enters the population. We are then able to derive explicit conditions for competitive exclusion and coexistence of the two strains depending on the relative basic reproduction numbers, temporary immunity periods, and degree of cross-immunity. We are also able to fit to COVID-19 variant data to estimate the changes in a variant's transmissibility and the degree of cross-immunity.
• Fuqing Wu The University of Texas Health Science Center at Houston (Department of Epidemiology, Human Genetics, and Environmental Sciences)
  "A Wastewater-based dynamic model for epidemiological inferrence"
Wastewater-based surveillance (WBS) has been widely used as a public health tool to monitor SARS-CoV-2 transmission. However, epidemiological inference from WBS data remains understudied and limits its application. In this study, we have established a quantitative framework to estimate COVID-19 prevalence and predict SARS-CoV-2 transmission through integrating WBS data into an SEIR-V model. We conceptually divide the individual-level viral shedding course into exposed, infectious, and recovery phases as an analogy to the compartments in a population-level SEIR model. We demonstrated that the effect of temperature on viral losses in the sewer can be straightforwardly incorporated in our framework. Using WBS data from the second wave of the pandemic (Oct 02, 2020–Jan 25, 2021) in the Greater Boston area, we showed that the SEIR-V model successfully recapitulates the temporal dynamics of viral load in wastewater and predicts the true number of cases peaked earlier and higher than the number of reported cases by 6–16 days and 8.3–10.2 folds (R = 0.93). This work showcases a simple yet effective method to bridge WBS and quantitative epidemiological modeling to estimate the prevalence and transmission of SARS-CoV-2 in the sewershed, which could facilitate the application of wastewater surveillance of infectious diseases for epidemiological inference and inform public health actions.
• Shokoofeh Nourbakhsh Public Health Agency of Canada (PHAC) (National Microbiology Lab / Public Health Risk Sciences / Infectious Disease Modelling)
  "A Wastewater-based Epidemic Model for SARS-CoV-2"
Wastewater-based epidemiology has proven to be a reliable indicator of community incidence. It provided valuable ongoing information on the state of the COVID-19 pandemic, mainly when the Omicron variant emerged and overwhelmed clinical surveillance. We present a mathematical model coupled with wastewater and clinical data from Canadian cities to estimate disease prevalence in the sampled communities and provide short-term epidemic forecasts to support public-health decision-making. Our endeavour highlighted the lack of a quantitative framework on viral pathogen fates within the urban sewer system hamper the epidemiological interpretation and the calibration of wastewater-based epidemic models due to the significant variance in measured viral concentration downstream at the wastewater treatment plants.

Organized by: Linh Huynh, Deena Schmidt

• Heyrim Cho University of California Riverside (Mathematics)
  "Modeling of CAR T-cell and neural stem cell therapy for brain cancer"
Recent advances in cell and gene engineering technologies enabled a variety of cell based treatments to be used as part of a treatment for a variety of diseases and conditions. Many different types of cells are available to be transplanted to replace or repair damaged tissue and/or cells. In this talk, I will discuss chimeric antigen receptor (CAR) T-cell therapy and neural stem cell (NSC) therapy for brain diseases, and the potential of how mathematical models can help increase the treatment efficacy. A hybrid stochastic agent based and partial differential equation model of CAR T-cell therapy is developed to understand the effect of timing in a combination treatment for heterogeneous brain cancer. Similarly, a hybrid model of NSC treatment is developed to study the effect of injection location and to predict its migration path. I will also present results using ordinary differential equation models on better understanding of the cellular dynamics in a population level.
• Alexandru Hening Texas A&M (Mathematics)
  "Population dynamics under random switching"
An important question in ecology is the relationship between the coexistence of species and environmental fluctuations. A natural way to model environmental fluctuations is to use stochastic differential equations (SDE) or piecewise deterministic Markov processes (PDMP). In a PDMP, the environment switches between a fixed finite number of states to each of which we associate an ordinary differential equation (ODE). In each state the dynamics is given by the flow of its associated ODE. After a random time, the environment switches to a different state, and the dynamics is governed by the ODE associated to the new state. I will look at two and three species examples of SDE and PDMP and explain how the randomness can lead to some very interesting and counterintuitive behavior.
• Khanh Ngoc Dinh Columbia University (Irving Institute for Cancer Dynamics)
  "Modeling and simulation of cancer evolution in bulk and single-cell DNA-sequencing data"
We explain how models of population genetics can be used to provide quantitative inference of clonal evolution of cancer. The talk has two parts. Part 1 is devoted to the definition and mathematical properties of the Site Frequency Spectrum (SFS), one of the commonly used characteristics of cell populations undergoing growth and mutation. We explore the basic consistency of the approaches based on Wright-Fisher or Moran coalescents versus those based on birth-death processes. This provides building blocks for Part 2, which introduces the heuristic estimation equations, which employ the observable characteristics of the SFS, and allow an exact solution providing estimates of the growth and mutation rates and origin times of the clones. Examples based on simulations and available tumor data are presented. Accuracy of the estimates and their possible applications are discussed. Contributions of Emmanuel Asante, Khanh Dinh, Roman Jaksik, Andrew Koval, Paweł Kuś, and Simon Tavaré are acknowledged.
• James MacLaurin New Jersey Institute of Technology (Mathematics)
  "From blips to puffs: estimating the probability of noise-induced calcium waves"
Intracellular calcium signalling is widely hypothesized to be a stochastic phenomenon that bridges scales. Microscopic calcium channels open and close stochastically, producing small blips in the local calcium concentration. If enough of them open, then the local elevation in calcium concentration can be sufficient to initiate a cell-wide calcium wave or 'puff'. We estimate the probability / frequency of calcium puffs using the theory of Large Deviations: this theory facilitates accurate estimates for the most probable way that numerous microscopic channels (coupled by the concentration of calcium and other signalling molecules) can organize to produce a cell-wide puff.

Organized by: Renee Brady-Nicholls, Harsh Jain, Jason George

• Maximilian Strobl Cleveland Clinic (Department for Translational Hematology and Oncology Research, Lerner Research Institute)
  "Using mathematical modeling to design protocols for preclinical testing of evolutionary therapies"
Over the past two decades it has become clear that cancers are complex and evolving diseases. Genetic and non-genetic processes generate diverse subpopulations of tumor cells which can thrive under a variety of conditions and stressors. This provides a rich pool of variation that by means of natural selection and continued evolution enables adaptation to even the most modern treatments, especially in advanced cancers. Based on this novel understanding, so-called “evolutionary therapy” or “evolution-informed treatment strategies” have emerged which try to leverage, and potentially even steer, tumour evolution by strategically and dynamically sequencing and combining existing therapies and adjusting dose levels. In particular, adaptive therapy, which dynamically changes treatment levels to maintain drug-sensitive cells in order to competitively suppress emerging drug resistance, has produced a number of promising theoretical, preclinical and also clinical results. However, unlike for new drugs for which there are clear established frameworks for translation from bench to bedside, the design of preclinical protocols to ensure efficacy and safety of evolutionary therapies is an open question. In this study, we use mathematical modeling to develop and interpret in vitro experimental protocols and apply them towards the development of an adaptive therapy for Osimertinib for the treatment of Non-Small Cell Lung Cancer. In the first step, we consider the question of how to measure ecological interactions between tumor subpopulations. To do so, we build on the “Game Assay” previously developed by our group, in which cells are co-cultured at different frequencies to measure how a population’s fitness depends on its frequency in the environment. Using an agent-based model of our in vitro experiments, we study how different aspects of the design (number of replicates, number of proportions) and analysis (regression technique, regression window) impact the accuracy and precision of the assay. Subsequently, we use our optimized protocol to quantify the frequency-dependent interactions between Osimertinib sensitive and resistant PC9 cells under different drug levels. In the next step, we use our model to explore whether and how so-obtained fitness differences translate to the ability to steer the composition of the tumor in long-term in vitro experiments, in which cells are co-cultured and passaged at regular intervals. In particular, we explore the role of the population size, passaging frequency, and passage fraction (proportion of cells carried forward to next passage). To conclude, we will present preliminary data in which we use this assay to trial a potential adaptive Osimertinib therapy protocol in vitro. Overall, we demonstrate how mathematical models can help to understand and improve experimental assays, and we contribute towards the important discussion as to how to translate evolutionary therapies from the blackboard to the bedside.
• Rebecca A. Bekker H. Lee Moffitt Cancer Center & Research Institute (Department of Integrated Mathematical Oncology)
  "The Immunological Consequences of Spatially Fractionated Radiotherapy"
Radiotherapy (RT) is the single most frequently used cancer treatment, with approximately 60% of patients undergoing RT alone or in conjunction with other therapeutics. However, many patients develop RT-induced lymphopenia, which has been associated with decreased overall survival in head and neck cancer patients. Thus, it is conceivable that sparing select immune populations may improve patient outcomes. One potential method of minimizing the adverse effects of RT on the immune response is the use of spatially fractionated radiotherapy (SFRT), administered through GRID blocks to create areas of low and high dose exposure. We hypothesize that the regions receiving low dose may act as immune reservoirs wherein the anti-tumor immune population is protected from RT-induced death. We develop and calibrate a mechanistic agent-based model of tumor-immune interactions to investigate the therapeutic utility of SFRT. Initializing the model with the multiplex immunohistochemistry / immunofluorescence slides of 30 patients with head and neck cancer, we identify specific GRID block architectures and treatment schedules that are better suited, with respect to anti-tumor immune infiltration and patient outcome, for specific pre-treatment tumor immune microenvironment states.
• Ibrahim Chamseddine Massachusetts General Hospital, Harvard Medical School (Radiation Oncology)
  "Towards Personalized Oncology: Machine Learning-Driven Radiotherapy Across Multiple Disease Sites"
Radiotherapy (RT) is a prominent modality in cancer treatments, utilized in over half of the patients, either as a standalone therapy or in combination with other treatments. However, current RT planning predominantly focuses on dose prescription, neglecting patient-specific properties and leading to variable responses between patients. This highlights the need for personalized strategies to enhance treatment outcomes. To advance towards personalized RT, we employed machine learning (ML) techniques across hepatocellular carcinoma (HCC), prostate cancer, and brain and head and neck cancers. By leveraging ML feature selection on clinical data, we identified predictors of tumor control, survival, and toxicity. We incorporated medical images in prostate and brain cancers using deep learning to further enhance the predictive models. These models facilitated the stratification of patients into low- and high-risk groups, enabling treatment modifications for those in need. We refined our approach by generating an ML-based decision map for personalized treatment selection in HCC and integrating ML techniques with treatment planning systems to optimize patient-specific therapies. We aimed through ML to identify risk groups in multiple disease sites and adapt therapies accordingly, with the future goal of introducing a paradigm shift towards fully personalized RT.
• Alexander B. Brummer College of Charleston (Department of Physics and Astronomy)
  "Data-driven model discovery and interpretation for CAR T-cell killing using sparse identification and latent variables"
In the development of cell-based cancer therapies, quantitative mathematical models of cellular interactions are instrumental in understanding treatment efficacy. Efforts to validate and interpret mathematical models of cancer cell growth and death hinge first on proposing a precise mathematical model, then analyzing experimental data in the context of the chosen model. In this work, we present the first application of the sparse identification of non-linear dynamics (SINDy) algorithm to a real biological system in order discover cell-cell interaction dynamics in in vitro experimental data, using chimeric antigen receptor (CAR) T-cells and patient-derived glioblastoma cells. By combining the techniques of latent variable analysis and SINDy, we infer key aspects of the interaction dynamics of CAR T-cell populations and cancer. Importantly, we show how the model terms can be interpreted biologically in relation to different CAR T-cell functional responses, single or double CAR T-cell-cancer cell binding models, and density-dependent growth dynamics in either of the CAR T-cell or cancer cell populations. We show how this data-driven model-discovery based approach provides unique insight into CAR T-cell dynamics when compared to an established model-first approach. These results demonstrate the potential for SINDy to improve the implementation and efficacy of CAR T-cell therapy in the clinic through an improved understanding of CAR T-cell dynamics.

Organized by: Ashlee N. Ford Versypt

• Ying Zhang Brandeis University (Mathematics)
  "Studying the Effects of Oral Contraceptives on Coagulation Using a Mathematical Modeling Approach"
The use of oral contraceptives (OCs) is known to increase the risk of thrombosis, but the mechanisms underlying this risk and the determinants of the tests that assess this risk are not fully understood. In this study, we used a mathematical model to study the effects of the OC levonorgestrel (lev) on blood clotting. Lev is reported to change the plasma levels of blood clotting factors. The model simulates coagulation reactions in a small injury under flow, takes clotting factors as inputs and outputs time courses of the coagulation enzyme thrombin. We created a virtual patient population with factor levels before and after lev use that were based on published patient data. After analyzing the simulated thrombin, we found that changes in factor levels due to lev increased the amount and speed of thrombin generation for all virtual patients. This suggested that the factor level changes alone can heighten the prothrombotic state of the model system. We extended the model to include generation of the inhibitor APC so we could test the effects of lev on the systems’ sensitivity to APC. In line with literature reports, the use of lev decreased the APC sensitivity, which correlates with increased thrombosis risk.
• Susan Rogowski, Alejandra D. Herrera-Reyes, and Yena Kim Florida State University (Mathematics)
  "Parameter Estimation for COVID-19 SVIRD Model Using Predictor-Corrector Algorithm"
Stable parameter estimation is an ongoing challenge within biomathematics, especially in epidemiology. Oftentimes epidemiological models are composed of large numbers of equations and parameters. High dimensionality makes classic parameter estimation approaches, such as least square fitting, computationally expensive, and the presence of observational noise and reporting errors that accompany real-time data can make these parameter estimation problems ill-posed and unstable. The recent COVID-19 pandemic highlighted the need for efficient parameter estimation tools. In this paper, we develop a modified version of a regularized predictor-corrector algorithm aimed at stable low-cost reconstruction of infectious disease parameters. This method is applied to a new compartmental model describing COVID-19 dynamics, which accounts for vaccination and immunity loss (from vaccinated and recovered populations). Numerical simulations are carried out with synthetic and real data for COVID-19 pandemic. Based on the reconstructed disease transmission rates (and known mitigation measures), observations on historical trends of COVID-19 in the states of Georgia and California are presented. Such observations can be used to provide insights into future COVID policies.
• Yeona Kang Howard University (Mathematics)
  "Extended-release Pre-Exposure Prophylaxis and Drug Resistant HIV"
The pharmacologic tail of long acting cabotegravir (CAB-LA, injectable PrEP) allows months-long intervals between injections, but it might encourage the growth of drug-resistant HIV strains during the acute infection stage. We present a within-host, mechanistic Ordinary Differential Equation model of the HIV latency and infection cycle in CD4+ T-cells to investigate. We develop a pharmacokinetic/pharmacodynamic model for long acting cabotegravir (CAB-LA, injectable PrEP) to relate the inhibitory drug response to the drug concentration in plasma as well as rectal, cervical, and vaginal fluids and tissue. After validating our model against experimental results, we build in-silico trials. First, we separately administer CAB-LA to the in-silico macaque and human patients prior to and post-SHIV/HIV exposure, to observe SHIV and HIV infectivity dynamics, respectively. The model does not include a mechanism for CAB-LA to generate drug-resistant HIV mutations, but we observe the result when mutations arise naturally. We find CAB-LA may encourage the drug-resistant strain to grow and to outcompete the wild-type in the acute stage. The in-silico trials show that the level of drug resistance, the effectiveness of CAB-LA against the mutations, and the degree of fitness for the mutant strain of virions to infect T-cells determine the course of the drug-resistant strain.
• Rayanne Luke Johns Hopkins University (Applied Mathematics and Statistics)
  "Towards a mathematical understanding of ventilator-induced lung injury in preterm rat pups"
Approximately 1 % of infants are born extremely preterm and are prone to respiratory distress. Typical treatments are less effective for this group and invasive mechanical ventilation applied as a last resort causes trauma, leading to ventilator-induced lung injury (VILI). Further, maternal infection can cause prenatal and neonatal lung infection, inflammation, and often very preterm birth. Inflammation is expected to stiffen the lungs, but exceptions occur, and a complete picture of the mechanisms of stiffening remains unknown. To better understand these mechanisms, we present an application of parameter estimation to a compartment model of pressure-volume lung dynamics along with newly designed image analysis metrics. We also apply optimization to data from a neonatal rat model and identify key parameter differences between healthy and unhealthy groups that may suggest the mechanisms of VILI in infected respiratory systems. Finally, combined analyses of our strategies identify correlations between inflammatory markers and model parameters with no analog in the data, suggesting that mathematical approaches provide an important path towards understanding VILI and infection.