Organized by: Michael Robert, Zhuolin Qu, Christina Cobbold
Note: this minisymposia has multiple sessions. The other session is MS02-MEPI-1.

• Christina Cobbold University of Glasgow (School of Mathematics and Statistics)
  "Vector population dynamics and trait variation drive trends in global disease incidence"
Climate change is having profound effects on the incidence of vector borne disease. However, developing effective measures of disease risk on a global scale are challenged by the complex ways in which environmental variation acts in vector-host-pathogen systems. Current models over-simplify the interaction between vector traits and environmental variation and so risk mis-estimating disease risk. Here, we derive a mathematical model for Aedes albopictus, the vector of dengue, and demonstrate how the interaction of vector traits and population dynamics explain the location, magnitude and timing of historical dengue outbreaks. We find long lived individuals that developed under favourable conditions can persist within the population long after the environmental conditions that created them have passed and may consequently have a disproportionate effect on pathogen transmission dynamics that cannot be accounted for by approaches that omit trait dynamics.
• Morgan Jackson Virginia Commonwealth University (Department of Mathematics and Applied Mathematics)
  "Evaluating a Temperature-dependent Mosquito Population Model"
Dengue Virus causes over 390 million infections and around 40,000 deaths each year. This virus is primarily transmitted by the mosquito Aedes aegypti. The life cycle of these mosquitos is significantly impacted by temperature, however, temperature in often neglected in mechanistic models. Predictive models of mosquito populations thus require the inclusion of temperature and are valuable for helping medical officials plan for the impact of outbreaks. Using mosquito and climate data collected in Córdoba, Argentina from 2010-2013, we developed a non-autonomous ordinary differential equations model that includes temperature dependent parameters associated with mosquito life history. We performed local sensitivity and identifiability analysis to determine which model parameters should be estimated. We explored the effects of incorporating temperature in different combinations of life history characteristics to find the most parsimonious model that includes temperature. Additionally, we estimated values for combinations of density-dependent parameters to improve the model fit. These parameters control nonlinear population regulation but are often difficult to estimate from data alone. We found that including even just three temperature-based parameters: eggs laid per adult female, development rate of juveniles to adults, and adult mortality rate, produced a model that matches the data well. Additionally, we fit a density-dependent parameter and combinations of density dependent parameters to improve the model fit. We discuss these results in the context of improving mosquito population and dengue epidemiological models.
• Stacey Smith? The University of Ottawa (Department of Mathematics and Faculty of Medicine)
  "Comparing malaria surveillance with periodic spraying in the presence of insecticide-resistant mosquitoes: Should we spray regularly or based on human infections?"
There is an urgent need for more understanding of the effects of surveillance on malaria control. Indoor residual spraying has had beneficial effects on global malaria reduction, but resistance to the insecticide poses a threat to eradication. We develop a model of impulsive differential equations to account for a resistant strain of mosquitoes that is entirely immune to the insecticide. The impulse is triggered either due to periodic spraying or when a critical number of malaria cases are detected. For small mutation rates, the mosquito-only submodel exhibits either a single mutant-only equilibrium, a mutant-only equilibrium and a single coexistence equilibrium, or a mutant-only equilibrium and a pair of coexistence equilibria. Bistability is a likely outcome, while the effect of impulses is to introduce a saddle-node bifurcation, resulting in persistence of malaria in the form of impulsive periodic orbits. If certain parameters are small, triggering the insecticide based on number of malaria cases is asymptotically equivalent to spraying periodically.

Organized by: Michael Robert, Zhuolin Qu, Christina Cobbold
Note: this minisymposia has multiple sessions. The other session is MS01-MEPI-1.

• Carrie Manore Los Alamos National Laboratory (Theoretical Biology and Biophysics)
  "Coupling Earth Systems, Vector Population, and Disease Transmission Models to Predict Mosquito-borne Disease Under Climate Change"
Understanding the non-linear impacts of climate change on climate-driven pathogens such as mosquito-borne disease is an ongoing challenge. Recent research has shown that temperature will change vector species and virus distributions and dynamics. To further understand how temperature, along with changes in water availability, and human populations, will change the dynamics and ranges of West Nile virus and dengue, we developed a suite of coupled models to simulate disease spread across the Americas. This includes a global climate and earth systems model, mosquito population dynamics model, and disease transmission model with host species (e.g. humans and birds) driven by the climate model output and historical data. I will present the mosquito and disease transmission models along with our new tiling method for spatial partitioning along with validation results and challenges.
• Nusrat Tabassum Texas Tech University (Applied Mathematics)
  "Stage-Structured Mosquito Larval Competition: Implications for Aedes Albopictus and Aedes Aegypti Population Dynamics"
Aedes aegypti and Aedes albopictus, two invasive mosquito species that are responsible for spreading a number of viral diseases, are a major danger to global public health. Their ability to reproduce in diverse container habitats, where competition influences population dynamics, is correlated with their capacity to successfully colonize new regions. This competition may influence the distribution and abundance of the species, thereby influencing the transmission of mosquito-borne diseases. The goal of this study is to examine the effects of environmental factors such as temperature and population density on the competitive dynamics between these two species in their larval phases. A stage-structured larval competition model has been developed to analyze both inter and intra-specific competition. Our model permits temperature-dependent competition and carrying capacity variations. We have used sensitivity analysis to evaluate the model’s efficacy and empirical observations to characterize how temperature influences the survival rate, growth rate, and development time of mosquito larvae. We have also conduct a stability analysis of the model to determine if mosquito species can persist under different environmental conditions. This helps to understand how competition between mosquito larvae is influenced by environmental factors, which in turn influences temperature-dependent viral transmission, and also allows us to predict and respond to outbreaks of mosquito-borne diseases.
• Luis Fernando Chaves Indiana University - Bloomington (Environmental and Occupational Health)
  "Nonlinear impacts of climatic variability on vector population dynamics"
Mosquitoes and other vectors have complex life cycles, often including ontogenetic niche shifts. Under such circumstances changing environments could influence insect vector density-dependent regulation and propensity to sudden changes in abundance. Here, I will review results from modelling several mosquito species where field observed density-dependent regulation is strong. For most species, and settings, low environmental kurtosis was a good predictor of sharp changes in the abundance of mosquitoes. The identification of density-independent (i.e., exogenous) variables forcing sharp changes in disease vector populations using the exogenous factors statistical properties, especially higher order moments of their distribution, could be useful to assess the impacts of changing climate patterns on the transmission of vector-borne diseases.
• Suzanne Robertson Virginia Commonwealth University (Department of Mathematics and Applied Mathematics)
  "The impact of changes in avian phenology in a stage-structured model for West Nile virus transmission"
West Nile virus (WNV) has remained an annual public health concern in the United States since its introduction in 1999, yet the ecological triggers leading to seasonal outbreaks are not well understood. Nestlings, birds within the first couple of weeks of hatching, are extremely vulnerable to mosquitoes and may receive a disproportionately high number of mosquito bites compared to other bird life stages. While total avian population size typically increases throughout the season, nestling abundance declines at the end of the brooding season. This temporal variation in host stage abundance can play an important role in structuring WNV transmission. The nesting curve of a species may differ regionally due to climate, and within a region, year to year differences in temperature may also result in year to year variation in the nesting curve of a given species. We use a stage-structured differential equation model for WNV incorporating vector preference for specific host life stages to investigate the impact of changes in the phenology of avian nesting and vector growth due to climate change on enzootic WNV transmission.

Organized by: Lauren Childs, Michael Robert

• Rosemary Aogo National Institutes of Health (Viral Epidemiology and Immunity Unit, Laboratory of Infectious Diseases, National Institute of Allergy and Infectious Diseases)
  "A new model framework offers insights into the role of immune boosting and waning in shaping dengue epidemic dynamics."
Infection with any of the four dengue virus serotypes (DENV1-4) induces serotype-specific and cross-reactive antibodies that may increase disease severity during secondary infection with a different serotype. However, following secondary infection, individuals are at significantly reduced risk of subsequent severe disease with even unexposed serotypes. Previous dengue modeling studies with two or four serotypes have shown that periodicity in dengue incidence can be explained by enhancement between serotypes, transient cross-protective immunity, as well as vector distribution, population size, geography, and seasonality. However, all models have assumed complete protection against previous infecting serotypes and most models have assume complete protection against all serotypes after two sequential infections. Conversely, a recent longitudinal cohort study showed that antibodies wane for many years after secondary DENV infection, at times to the level observed following first DENV infection, suggesting immunity after two infections may not be life-long. In this study, we use a dataset of antibody titers to DENV and ZIKV measured annually in Nicaraguan family and pediatric cohorts from 2017-2021 and developed an immunity-structured SIR-type model that tracks immunity by titer rather than number of prior infections. We show that boosting and waning occur following major dengue and Zika outbreaks in highly immune Nicaraguan adult populations. Using our framework, we show that boosts in highly immune individuals contribute to herd immunity, delaying their contribution to the susceptible population and lowering the rate of dengue cases in future epidemics. However, as their immunity wanes due to lower transmission intensity, the susceptible fraction builds up until a major epidemic that includes re-infection of those with high titers once again depletes the susceptible pool. Comparatively, lifelong immunity in highly immune individuals as previously assumed in most studies results in a complete disease eradication after disease introduction and subsequent epidemic bouts are only sustained with a constant influx of infected individuals into the population by migration. Our model validation shows the interaction of immune boosting and waning in highly exposed adults better explains observed dengue epidemic dynamics than models assuming transient immunity or lifelong immunity in highly immune adult populations. Moreover, we show that ZIKV exposure modulates dengue immunity and create further delays between dengue epidemics. These findings suggest boosting and waning in highly immune individuals contributes to shaping epidemic dynamics and moreover, our study may inform vaccine strategies to maintain immunity over the life-course.
• Derdei M. Bichara California State University, Fullerton (Mathematics)
  "Effects of Heterogeneity in a Class of Bio-systems"
The role of heterogeneity in populations has long been recognized as a driving force in the spread of infectious diseases. Indeed, populations differ in their propensity to transmit or acquire infectious agents in terms of activities, socio-economic or genetic groups. Oftentimes, mathematical models in population dynamics that incorporate such heterogeneities use groups or classes as units and networks to describe the interactions between these units of the model. For many models that describe such phenomena, the complete global behavior of these systems have been open questions. In this talk, I provide a complete characterization of the some these problems.
• Paul Hurtado University of Nevada-Reno (Mathematics & Statistics)
  "Finding Reproduction Numbers for ODE Models of Arbitrary Finite Dimension Using The Generalized Linear Chain Trick"
Reproduction numbers, like the basic reproduction number R0, play an important role in the analysis and application of dynamic models of contagion spread (and parallels exist elsewhere, e.g., in multispecies ecological models). One difficulty in deriving these quantities is that they must be computed on a model-by-model basis, since it is typically impractical to obtain general reproduction number expressions applicable to a family of related models, especially if these models are of different dimensions (i.e., differing numbers of state variables). For example, this is typically the case for SIR-type infectious disease models derived using the classical linear chain trick (LCT). In this talk, I will provide an overview of how to find general reproduction number expressions for such model families using the next generation operator approach in conjunction with the generalized linear chain trick (GLCT). This shows how the GLCT enables modelers to draw insights from these results by leveraging theory and intuition from continuous time Markov chains (CTMCs) and their absorption time distributions (i.e., phase-type probability distributions). I will show an example application of this technique to find reproduction numbers for a family of generalized SEIRS models with an arbitrary number of state variables. These results highlight the utility of the GLCT for the derivation and analysis of mean field ODE models, especially when used in conjunction with theory from CTMCs and their associated phase-type distributions.
• Zhuolin Qu University of Texas at San Antonio (Department of Mathematics)
  "Multistage Spatial Model for Informing Release of Wolbachia-Infected Mosquitoes as Disease Control"
Wolbachia is a natural bacterium that can infect Aedes mosquitoes and block the transmission of mosquito-borne diseases, including dengue fever, Zika, and chikungunya. Field trials have been conducted worldwide to suppress local epidemics. We present a new partial differential equation model for the spread of Wolbachia infection in mosquitoes. The model accounts for both the complex Wolbachia vertical transmission cycle and detailed life stages in the mosquitoes, and it also incorporates the spatial heterogeneity created by mosquito dispersion in the two-dimensional release domain. Field trials and previous modeling studies have shown that the fraction of infection among mosquitoes must exceed a threshold level for the infection to persist. We use the spatial model to identify a threshold condition for having a self-sustainable Wolbachia infection in the field. When above this threshold, the model gives rise to a spatial wave of Wolbachia infection. We quantify how the threshold condition and invasion velocity depend on the diffusion process and other model parameters, and we study different intervention scenarios to inform the efficient releases.

Organized by: Rocio Caja Rivera, Iona McCabe, Dana Pittman, Linda J. Allen

• Holly Gaff Old Dominion University (Department of Biological Sciences)
  "Understanding Ticks and Tick-borne Diseases through Agent-based Modeling"
Tick-borne diseases are on the rise worldwide, and there is a lot of interest to reduce the burden of these diseases. Ticks and tick-borne pathogens are not well studied partly owing to their challenging biology. The dynamics of tick-borne pathogens includes multi-year systems of weather, habitat, and environmental factors plus the availability of hosts required for each life stage. Mathematical models provide an ideal tool to explore this type of complex system by implementing the dynamics that are known and exploring the potential additional components that are less understood. A series of agent-based models will be presented that investigate tick-borne disease dynamics, control, and geographic spread. Each model was based on field and lab data, and the output from each help to identify future experiments.
• Kat Husar & Dana C. Pittman Duke University; Texas A&M University (School of Public Health Epidemiology and Biostatistics)
  "Lyme Disease Models of Tick-Mouse Dynamics with Seasonal Variation in Births, Deaths, and Tick Feeding"
Lyme disease is the most prevalent vector-borne disease in the United States impacting the Northeast and Midwest at the highest rates. Recently, it has become established in southeastern and south-central regions of Canada. Lyme disease is passed by the black-legged tick, Ixodes scapularis, infected with the Borrelia burgdorferi bacterium. One of the hosts most commonly fed on by I. scapularis is Peromyscus leucopus, colloquially known as the white-footed mouse. Understanding this parasite-host interaction is critical as P. leucopus is one of the most competent reservoirs for Lyme disease. The cycle of infection is driven by larvae feeding on infected mice that molt into infected nymphs and then transmit the disease to another susceptible host such as a mouse or human. Lyme disease in humans is generally caused by the bite of an infected nymph. The main aim of this investigation is to study how demographic and seasonal variation and diapause in tick births, deaths, and feedings impact the infection dynamics of the tick–mouse cycle. To account for delays in molting and reproduction in the tick life cycle, we begin by formulating a system of ordinary differential equations (ODEs) describing the transmission cycle between ticks and mice before exploring the use of delay differential equations (DDEs) with fixed delays. Several different tick feeding rates are discussed. We then formulate a new system of ODEs with a more realistic Erlang-distributed delay. We also account for seasonal changes through periodic parameters that depend on the season (spring, summer, fall, or winter). The ODE model is generalized to a new stochastic model with demographic and seasonal variability, a continuous-time Markov chain (CTMC). We calculate and discuss the relevance of the basic reproduction number, R0, for the ODE and DDE models in a constant environment and numerically compute it for the ODE model in a seasonal environment. We also determine the numerical sensitivity of R0, to the prevalence of infected nymphs and mice and to the density of infected nymphs to changes in the parameters in the seasonal ODE model . Lastly, we use the CTMC model to investigate the probability of Lyme disease emergence in a small infection-free population of ticks and mice when a few infected mice or nymphs are introduced. The probability of disease emergence is highly dependent on the season the infection is introduced and which species (ticks or mice) are introduced. The numerical results show that introduction of infected mice during the summer has the highest probability of sustained infection and disease emergence.
• Katherine Royce Harvard University (Law School)
  "Mathematically predicting intermediate host species for emerging zoonoses"
Intermediate host species provide a crucial link in the emergence of zoonotic infectious diseases, serving as a population where an emerging pathogen can mutate to become human-transmissible. Identifying such species is thus a key component of predicting and mitigating future epidemics. Despite this importance, intermediate host species have not been investigated in much detail, and have generally only been identified by testing for the presence of pathogens in multiple candidate species. This talk will present a mathematical model able to identify likely intermediate host species for emerging zoonoses based on ecological data for the candidates and epidemiological data for the pathogen. The model accurately identifies potential intermediate hosts of the three emerging coronaviruses of the twenty-first century, predicting palm civets as intermediate hosts for SARS-CoV-1 and dromedary camels as intermediate hosts for MERS. Further, it suggests mink, raccoon dogs, and ferrets as probable intermediate host species for SARS-CoV-2. With the capacity to evaluate intermediate host likelihood among different species, researchers can focus testing for possible infection sources and interventions more effectively.
• Iona McCabe; Kaia Smith University of California, Santa Barbara; Scripps College (Department of Mathematics; Department of Mathematics)
  "Stochastic Models of Zoonotic Avian Influenza with Multiple Hosts, Environmental Transmission, and Migration in the Natural Reservoir"
Avian influenza virus (AIV) is an infectious disease that circulates among wild bird populations and regularly spills over into domestic animals, such as poultry and swine. This spread raises the risk of a mutation resulting in a human-to-human-transmissible strain, which would pose a serious threat to public health. Mathematical modeling can be a powerful tool to mitigate the risks associated with these strains. Prior models have included factors such as multiple host populations, spillover into humans, environmental transmission, seasonality, and migration. We develop an ordinary differential equation (ODE) model that combines all of these factors, and we translate this into a stochastic continuous-time Markov chain (CTMC) model. We examine and compare the numerical trajectories of the disease using the ODE and CTMC models. Linear approximation of the ODE model near the disease-free solution leads to the basic reproduction number R0, a threshold for both the ODE and CTMC models. Linearization of the CTMC near the disease-free solution leads to a branching process approximation and the corresponding backward Kolmogorov differential equation, which can be used to estimate the probability of disease extinction when R0. Seasonal variation in migration, transmission, birth rate and viral decay results in a seasonally-dependent probability of disease extinction (no disease outbreak). A parameter sensitivity analysis of the ODE model with respect to R0 indicates that our model is sensitive to the wild bird recovery rate and environmental transmission-related parameters, which may inform future research. Additionally, in the CTMC model, we examine the sensitivity of the frequency of a spillover event into the human population from domestic poultry. We find that wild birds can drive infection numbers in other populations even when transmission parameters for those populations are low, and that environmental transmission can be a significant driver of infections.

Organized by: Omar Saucedo, Bren Case, Lauren Childs
Note: this minisymposia has multiple sessions. The other session is MS07-MEPI-1.

• Widodo Samyono Jarvis Christian University (Mathematics and Sciences)
  "Parameters Identifiability for selecting the best model using differential equations optimization"
Solving mathematical model based on differential equations (DEs) to match with the data by changing the initial guesses for identifying the parameters interactively by using trial and error methods is needed lots of efforts and time. Additionally, the model could be ill-posed and non-linear in term of the parameters, so specialized computational techniques are needed. To solve these problems, the parameter identification problems were set up as differential equations optimization, where the objective function is the misfit statistical measures between the data and the model solutions, and the constraint is the DE. The optimization can be formulated as constrained and unconstrained optimization. Some specialized numerical methods are presented. The models are the classical mathematical models for cancer cell growths.
• Marisa Eisenberg University of Michigan, Ann Arbor (Epidemiology and Complex Systems)
  "Identifiability and infectious disease interventions: exploring when uncertainty matters"
Identifiability, estimability, and parameter reduction methods provide tools to understand the interactions between parameters, model structure, and outputs—and how these interactions determine what inferences and predictions are possible for a given system. In particular, issues of identifiability and uncertainty can affect whether it is possible to select an optimal intervention—an important question for applied infectious disease modeling. In this talk, we will explore how identifiability can be used in practice to help inform epidemiological decision-making, and when intervention strategies are or are not robust to uncertainty in the model parameters and structure.
• All Participants
  "Open Forum"
The last 30 minutes of this session will include an open forum for discussion with speakers and participants.

Organized by: Joshua Caleb Macdonald, Hayriye Gulbudak
Note: this minisymposia has multiple sessions. The other session is MS07-MEPI-2.

• Anna Jolles Oregon State University (Carlson College of Veterinary Medicine and Department of Integrative Biology)
  "Mechanisms of persistence of highly transmissible foot-and-mouth viruses in their maintenance host, African buffalo (Syncerus caffer)"
Extremely contagious pathogens are a global biosecurity threat because of their high burden of morbidity and mortality, as well as their capacity for fast-moving epidemics that are difficult to quell. Understanding the mechanisms enabling persistence of highly transmissible pathogens in host populations is thus a central problem in disease ecology. Through a combination of experimental and theoretical approaches, we investigated how highly contagious foot-and-mouth disease viruses persist in the African buffalo, which serves as their wildlife reservoir. We found that viral persistence through transmission among acutely infected hosts alone is unlikely. Working with three viral strains (SAT1,2,3), we found that different strains appear to utilize distinct mechanisms to ensure their long-term persistence in their maintenance host: The inclusion of occasional transmission from persistently infected carriers reliably rescues the most infectious viral strain (SAT1) from fade-out. We observed that antibody titers against FMD viruses are surprisingly dynamic in buffalo; and show that frequent drops in antibody protection can allow persistence of the least transmissible strain we studied (SAT3). The persistence of SAT2 remains somewhat enigmatic - additional mechanisms such as antigenic shift, or spillover among host populations may be required for its persistence.
• Simon Gubbins The Pirbright Institute (Transmission Biology)
  "Cross-scale dynamics of foot-and-mouth disease virus: from within hosts to between farms"
Foot-and-mouth disease virus (FMDV) infects cloven-hoofed livestock and wildlife species. It causes foot-and-mouth disease (FMD), which has substantial economic impacts for endemic countries and for disease-free countries when epidemics occur in them. Because of its importance FMDV has been studied at a range of scales from within a host to continental scale. This provides an opportunity to develop data-driven multi-scale models for FMDV and to examine how process at one scale affect process at another. In this presentation we will discuss a mathematical and statistical framework for linking models for FMDV at different scales (within-host, between-host and between-farm) to investigate how the dynamics at one scale influences dynamics at another. For example, we can use the models to show how within-host parameters (e.g. viral growth and clearance rates) influence between-host transmission (reproduction numbers) and how within-farm transmission (e.g. via direct contact or a contaminated environment) affects between-farm transmission. The models are parameterised using Bayesian methods applied to a combination of data from transmission experiments, within-farm outbreaks and regional epidemics. This allows us to test model assumptions and to incorporate parameter uncertainty at one scale in predictions at another.
• Jan Medlock Oregon State University (Biomedical Sciences)
  "The Persistence of Foot-and-Mouth Disease Virus in African Buffalo"
Foot-and-mouth disease virus (FMDV) is a very important trade-restricting livestock disease. In sub-Saharan Africa, buffalo act as reservoir for FMDV, challenging global eradication and local economies. However, little is known about the dynamics of FMDV in African buffalo. We conducted FMDV infection experiments to quantify epidemiologic parameters of FMDV transmission in buffalo, and a 3-year cohort study to document birth timing, and duration of maternal protection from FMDV infection. We used Bayesian inference to estimate parameters, and constructed a rigorous quantitative framework that explicitly incorporates individual variation in birth rates, waning of maternal antibodies, and epidemiological parameters into predictions about disease persistence from an individual-based stochastic model. We used our model to show that FMDV's high transmission rate, short infectious period, and long-term immunity, when combined with the buffalo’s seasonal variation in births, fails to explain the persistence of FMDV from year to year. We showed that an alternative hypothesis, based on infection experiments, that FMDV forms some long-term carriers after acute infection does explain the persistence for one of the three circulating serotypes in southern Africa. I will also discuss work-in-progress on hypotheses that may explain the persistence of the two remaining serotypes.
• Cameron Browne University of Louisiana at Lafayette (Mathematics)
  "Environmental adaptation and seasonality in cholera eco-evolutionary dynamics"
Cholera epidemics are largely driven by direct transmission from person to person or indirectly through environment, although Vibrio cholerae is also capable of growth and long-term survival in aquatic ecosystems. In this talk, I will discuss recent mathematical modeling work showing how fluctuations and strain evolution in the environment impacted the cholera outbreak in Haiti beginning in 2010. First, we calibrate a stochastic multi-strain mixed-transmission dynamic model of V. cholerae to phylogenetic, case and seasonal rainfall data from Haiti. Along with fitting the clinical incidence, we connect genetic diversity and a coalescence process in model simulations to the effective population size computed from serially sampled cholera genomes. The results suggest that environmental replication actively contributes to genetic diversification and environmental adaptation, which can impact the success of different control measures. Mathematical analysis of the underlying deterministic model is challenging, however competitive exclusion is proved in the absence of environmental replication and seasonality. Assuming only partial cross-immunity in this case does induce coexistence of two strains (called serotypes) and serotype cycling with seasonal forcing, which may explain switching of serotype dominance observed in Haiti.

Organized by: Omar Saucedo, Bren Case, Lauren Childs
Note: this minisymposia has multiple sessions. The other session is MS06-MEPI-1.

• Madeline A. E. Peters Michigan State University (Microbiology and Molecular Genetics)
  "Challenges in forming inferences from limited data: a case study of malaria parasite maturation"
Inferring biological processes from population dynamics is a common challenge in ecology, particularly when faced with incomplete data. This challenge extends to inferring parasite traits from within-host infection dynamics. We focus on rodent malaria infections (Plasmodium berghei), a system for which previous work inferred an immune-mediated extension in the length of the parasite development cycle within red blood cells. By developing a system of delay-differential equations to describe within-host infection dynamics and simulating data, we demonstrate the potential to obtain biased estimates of parasite (and host) traits when key biological processes are not considered. Despite generating infection dynamics using a fixed parasite developmental cycle length, we find that known sources of measurement bias in parasite stage and abundance data can affect estimates of parasite developmental duration, with stage misclassification driving inferences about extended cycle length. We discuss alternative protocols and statistical methods that can mitigate such misestimation.
• Bren Case University of Vermont (Computer Science)
  "Restricted Marginal Divergence: an efficient Bayesian measure of practical identifiability for nonlinear systems in biology and epidemiology"
Practical identifiability (PI) analysis seeks to quantify the reliability in estimates a researcher can expect when fitting a mathematical model to data. Such analyses generally reflect an intrinsic property of a particular model and proposed experimental design, rather than uncertainty in any single realization of data. Traditionally, PI has been studied using the variance-covariance matrix of an estimator for the true parameter values. However, such second-order approximations underestimate uncertainty in limited data settings, where the distribution of plausible values may be incorrectly centered or highly skewed. Here we introduce a novel method, the Restricted Marginal Divergence, which reflects the average amount of posterior shrinkage that would occur in a Bayesian analysis, without requiring computationally expensive methods such as MCMC. We show the method has attractive properties in both limited and big data regimes, and discuss its relationship to other PI methods. An in-depth application of the method follows, illustrating the amount of time that is required to learn different model-based summary statistics in an emerging epidemic, such as the basic reproductive number or fraction of individuals who will become infected.
• All Participants
  "Open Forum"
The last 30 minutes of this session will include an open forum for discussion with speakers and participants.

Organized by: Joshua Caleb Macdonald, Hayriye Gulbudak
Note: this minisymposia has multiple sessions. The other session is MS06-MEPI-2.

• Summer Atkins Louisiana State University (Department of Mathematics and Statistics)
  "An immuno-epidemiological model of foot-and-mouth disease in African buffalo"
We present a novel immuno-epidemiological model of Foot-and-Mouth Disease (FMD) in African buffalo host population. Upon infection, the hosts can undergo two phases, namely the acute and the carrier stages. In our model, we divide the infectious population based upon these two stages so that we can dynamically capture the immunological characteristics of both phases of the disease and to better understand the carrier’s role in transmission. We first define the within-host immune kinetics dependent basic disease reproduction R0 and show that it is a threshold condition for the local stability of the disease-free equilibrium and existence of endemic equilibrium. By using a sensitivity analysis (SA) approach developed for multi-scale models, we assess the impact of the acute infection and carrier phase immunological parameters on R0. Interestingly, our numerical results show that the within-carrier infected host immune kinetics parameters and the susceptible individual recruitment rates play significant roles in disease persistence, which are consistent with experimental and field studies.
• Leah LeJeune Virginia Tech (Department of Mathematics)
  "Cross-immunity and transmission influences in a multistrain host-pathogen cholera model"
We investigate possible long-term outcomes of the spread of cholera in a human population by considering the effects of pathogen growth in the environment and strain diversity on human transmission and recovery dynamics. The bacteria Vibrio cholerae relies heavily upon an aquatic reservoir as a transmission route. There are two main cholera strains, called serotypes, which induce distinct host immune response, with a degree of cross-immunity upon recovery. To better understand disease dynamics to combat future outbreaks, this work combines and extends two previously studied ordinary differential equation epidemiological models to consider interactions between the host population and two strains of the pathogen in an aquatic reservoir. Of particular interest are undamped, anti-phase periodic solutions which display a type of coexistence observed in past outbreaks where strains routinely switch dominance. Equilibria analysis and simulations show cross-immunity and transmission pathways are key influencers of oscillatory dynamics and should be considered when constructing efficient control measures against outbreaks.
• Alun L. Lloyd North Carolina State University (Biomathematics Graduate Program and Department of Mathematics)
  "Spatial Spread of Dengue Virus: Appropriate Spatial Scales for Transmission"
Dengue virus is the most significant viral mosquito-borne infection in terms of its human impact. Mathematical modeling has contributed to our understanding of its transmission and control strategies aimed at halting its spread. We consider the spread of dengue at the level of a city. Because the Aedes aegypti mosquito that transmits dengue has relatively low dispersal over its lifetime, human movement plays a major role in its spread and the household is a key spatial scale on which transmission occurs. Simple multi-patch deterministic models---metapopulation models, which consider the population to be described as a network of well-mixed patches---have been used to model city-level spatial spread and can provide expressions for key epidemiological quantities such as the basic reproduction number, $R_0$. We compare dynamics predicted by such models with results from individual-based network models and illustrate several discrepancies. We argue that the small size of households and local depletion of susceptibles are key features of the dynamics that are not captured in the standard $R_0$ analysis of the ODE model. In order to gain analytic understanding, we propose the use of household-level models, which can be analyzed using branching process theory. Our work, which echoes results previously found for directly-transmitted infections, highlights the importance of correctly accounting for the relevant spatial scales on which transmission occurs.
• Erin Gorsich University of Warwick (Zeeman Institute for Systems Biology and Infectious Disease Epidemiology)
  "Modelling endemic Rift Valley fever virus"
Rift Valley fever (RVF) is a mosquito-borne virus that causes haemorrhagic fever in livestock and wildlife, as well as spill-over infections in humans. Large-scale epidemics occur sporadically in Africa following heavy rainfall. In some regions, infection also cycles endemically at low levels in livestock, yet the mechanisms influencing transmission and the scale at which they occur remains relatively unknown. Here, we integrate a mathematical model with longitudinal infection, entomological and climate data from multiple villages in Kwazulu-Natal, South Africa. Our modelling approach accounts for nonlinearities in the risk of exposure, susceptible depletion, and variable sampling effort to evaluate potential drivers of infection. Hypotheses representing high heterogeneity in RVF incidence across the study villages were supported, and variation was mechanistically explained by climatic and entomological data. This highlights the value of methods that harness statistical model selection in a mechanistic framework.

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.

• Christopher Mitchell Tarleton State University
  "Using Bayesian Methods to Infer Parameters for ODE Epidemic Systems"
Classical models of disease outbreaks rely on systems of nonlinear ordinary differential equations. ODE models have been widely successful and are credited with saving millions of lives worldwide. However, ODE models involve parameters that are often poorly understood and difficult to infer from limited and noisy data. This is especially problematic for rare, novel, or neglected diseases with unreliable reporting mechanisms. While some parameters can be deduced from biological or social facts, many must be inferred from data. Traditional least-squares point-estimates are fragile when applied to noisy data common in disease modeling. Bayesian inference replaces fragile point-estimates with posterior distributions that are more robust against data quality issues. Whereas point-estimate models produce a single outbreak forecast, Bayesian models generate an ensemble of forecasts through repeatedly sampling model parameters from their posterior distributions and numerically solving the resulting ODE. These multiple forecasts can be pooled and statistically analyzed at each time step (min, max, mean, etc) to give insight into potential outbreak scenarios (best-case, worst-case, most likely, resp). This project aims to create well-functioning ODE models using a new mathematical idea called amortized Bayesian inference implemented in the BayesFlow Python library. This exciting new tool was created in 2020 to help fight Covid-19 and other common diseases. This project will enhance the BayesFlow library to compensate for data quality issues and provide the improved models epidemiologists need to effectively fight NTDs.
• Rodolfo Blanco-Rodriguez University of Idaho
  "Modeling the impact of contact network and viral evolution on lockdown and vaccination strategies"
The transmission of infectious diseases is heavily influenced by the network topology of the population through which the disease spreads. However, the effectiveness of control strategies in diverse and complex social structures is poorly understood. A key lesson learned with COVID-19 is that public health measures were very different from country to country. While some implemented strongly restrictive lockdowns while others focused on mass vaccination campaigns, leaving a concern about which strategies are most effective according to certain social structures. Additionally, during a pandemic, viral evolution forces us to reconsider our control strategies. To gain insight into this, we computationally analyzed the spread of two variants of a virus through three well-known network models, small-world networks (Watts-Strogatz), random networks (Erdös-Rényi), and scale-free networks (Barabási-Albert). We contrasted two lockdown policies in the different networks, one continuous and the other by intervals, and compared different vaccination strategies by varying the number of nodes vaccinated per day. Our results showed that scale-free networks reached the highest outbreak peaks and the peak values of the infected population were independent of the infectivity of the virus variant. In addition, in this scale-free network, lockdown and vaccination strategies decreased the number of infected regardless of the strategy considered. Furthermore, for the small-world or random networks we found that confinement for 15-day intervals can reduce the peak number of infected nodes. Interestingly, we also found that a 20-day vaccination campaign yields lower infected cases than a 10-day campaign. These findings underscore the importance of considering social network topology to predict the course of epidemics and design more effective control measures.
• Soyoung Kim National Institute for Mathematical Sciences
  "Optimal antiviral stockpile for influenza pandemic"
A stockpile of antiviral drugs is important for mitigating a novel influenza pandemic. Recently, intervention strategies against such a pandemic have improved significantly, affecting the required size and composition of the stockpile. Our goal is to estimate the optimal ratio of conventional to newer antiviral drugs. Epidemic parameters are estimated from daily-case data about H1N1pdm09 in the Republic of Korea, and used a deterministic ordinary differential equation model and stochastic simulation to predict the number of patients in a future pandemic. An antiviral stockpile containing neuraminidase inhibitors and a new drug, cap-dependent endonuclease inhibitor are considered, seeking the optimum ratio of the two drugs under different epidemiological and economic assumptions.
• Zitao He University of Waterloo
  "Predicting measles outbreaks from vaccine sentiments on social media"
Vaccinating decisions for childhood diseases such as measles have been studied with coupled models of disease dynamics and individual behaviors. Such models applied evolutionary game theory to model people's vaccination strategies and how they are affected by social norms. Recent studies incorporated bifurcation theory to identify early warning signals (EWS), such as increasing variance and lag-1 autocorrelation, of critical transitions. Deep learning models have also been used to classify different types of bifurcation from time-series data near a tipping point. On the other hand, the rise of social media has made it easier for pro- and anti-vaccine sentiments to spread. Researchers have used high-frequency social media data to study population dynamics of infectious diseases and have found critical slowing downs in geocoded Tweets about the MMR vaccine and measles-related Google searches before the 2014-15 Disneyland, California measles outbreak. This project aims to use deep learning models to predict potential disease outbreaks from social media data and provide novel methods for disease outbreak prediction near thresholds. We improved existing coupled behavior-disease models by considering different social groups and investigating the effect of homophily on disease dynamics near tipping points. We showed that a deep learning model, such as a CNN-LSTM framework, could capture EWS directly from real-world social media data and predict a potential disease outbreak in the future.

• Kiel Corkran University of Missouri- Kansas City
  "An Agent-Based modeling approach to Investigate Pandemic Preparedness of Nursing Homes"
The pandemic preparedness of nursing homes has been a major concern for decades. The COVID-19 pandemic proved that the concerns were valid, as it caused devasting death tolls in nursing home facilities. This study presents an agent-based modeling framework to better understand the dynamics of pandemics within and between nursing homes. This is sharply distinct from many agent-based modeling works that resemble the spread of the infection within a single nursing home. We first calibrate the model of multiple nursing homes using the available COVID-19 data. Then we investigate the effects of shared staff on the efficacy of Covid-19 preventive policies through extensive simulations. It is shown that shared staffing can significantly diminish the efficacy of preventive policies. In conclusion, the nursing workforce is a determining factor for pandemic preparedness.
• Sansao Pedro Eduardo Mondlane University
  "An Agent-Based Model for Studying the Spread of COVID-19 in Mozambique: Pandemic Planing Implications of Population Mobility Patterns"
Background: The COVID-19 pandemic has become a new global public health crisis, and to large extent, its capacity to cross natural geographic barriers is attributed to human mobility and contact patterns which vary with time and specific locations. Therefore, an agent-based model (ABM) which relates populations mobility patterns in different locations in compliance with on site COVID-19 control measures is proposed to investigate how opening and closing protocols would have been best implemented in Mozambique. Methods: For spatial dynamics, a survey was carried out in the city of Maputo as a case study to estimate populations mobility patterns and contact matrices among individuals in different locations (home, school, work place, worship place, market and any other place of gathering) during specific periods of the day (morning, afternoon and night) for both week days and weekends. Individuals are explicitly represented by agents associated to disease characteristics and their decision to remain or move to a new place is based on a probability estimated from the survey and on site declared control measures. Results: The results show that at $50%$ of social distancing compliance, complete lockdown of schools, workplaces, worship places with exception of markets is the only scenario that result in the reduction and shift of the peak by $3%$ and 3 days respectively. School closure showed significant effect that at $75%$ and $85%$ of social distancing adherence resulted in the reduction and shift of the peak by $15%$ and 4 days, and $51%$ and 24 days respectively. While closure of worship places rendered little effect due to limited frequency and duration of activities in a given location. Conclusions: This study has demonstrated the use of simulation models to investigate the implementation of opening and closing policies for the control of COVID-19 pandemic at local scale by leveraging between the mobility of individuals and adherence to social distancing.
• Theresa Sheets University of Utah
  "Forecasting SARS-CoV-2 Hospitalizations in Utah with Multiple Public Health Metrics"
Percent positivity, the ratio of positive SARS-CoV-2 tests to total number of tests, has been used throughout the COVID-19 pandemic as a proxy for the current level of transmission in a community. Simultaneously, wastewater SARS-CoV-2 monitoring has been implemented, but is a highly variable metric whose direct utility has yet to be fully explored. As we transition from pandemic response to endemic management, testing efforts have been reduced and the predictive value of test percent positivity has been called into question. We build a series of models incorporating SARS-CoV-2 test positivity, wastewater SARS-CoV-2 levels, and syndromic surveillance data streams to explore changing transmission dynamics. A county level model is developed to forecast hospitalizations and tested against an ARIMA based on hospitalizations alone. A 21-day forecast is developed with sliding scale cross validation. We validate and quantify uncertainty in commonly used public health metrics and explore differences in model selection between variants. Data from the winter 2022-23 season are reserved as a final test for the model. In this work, we examine how to effectively predict hospitalizations in a changing testing environment.

• Chunyi Gai The University of British Columbia
  "Localized outbreaks in S-I-R model with diffusion"
We investigate an SIRS epidemic model with spatial diffusion and nonlinear incidence rates. We show that for small diffusion rate of the infected class DI , the infected population tends to be highly localized at certain points inside the domain, forming K spikes. We then study three distinct destabilization mechanisms, as well as a transition from localized spikes to plateau solutions. Two of the instabilities are due to coarsening (spike death) and self-replication (spike birth), and have well-known analogues in other reaction-diffusion systems such as the Schnakenberg model. The third transition is when a single spike becomes unstable and moves to the boundary. This happens when the diffusion of the recovered class, DR becomes sufficiently small. In all cases, the stability thresholds are computed asymptotically and are verified by numerical experiments. We also show that the spike solution can transit into an plateau-type solution when the diffusion rates of recovered and susceptible class are sufficiently small. Implications for disease spread and control through quarantine are discussed.
• Keoni Castellano University of Nevada, Las Vegas
  "Dynamics of classical solutions of a multi-strain diffusive epidemic model"
We study a diffusive epidemic model and examine the spatial spreading dynamics of a multi-strain infectious disease. In particular, we address the questions of competition-exclusion or coexistence of the disease's strains. Our results indicate that if one strain has its local reproduction function spatially homogeneous, which either strictly minimizes or maximizes the basic reproduction numbers, then the phenomenon of competition-exclusion occurs. However, if all the local reproduction functions are spatially heterogeneous, all strains may coexist. In this case, we provide complete information on the large time behavior of classical solutions for the two-strain model when the diffusion rate is uniform within the population and the ratio of the local transmission rates is constant. Particularly, we prove the existence of two critical superimposed functions that serve as threshold values for the ratio of the transmission rates and that of the recovery rates. Furthermore, when the populations' diffusion rates are small, our results on the asymptotic profiles of coexistence endemic equilibria indicate a spatial segregation of infected populations.
• Laura F. Strube Virginia Tech
  "Appearance of Multistability and Hydra Effect in a Discrete-Time Epidemic Model with Ricker Growth"
One-dimensional discrete-time population models, such as Logistic or Ricker growth, can exhibit periodic and chaotic dynamics. Incorporating epidemiological interactions through the addition of an infectious class causes an interesting complexity of new behaviors. Previous work showed that infection that abrogates fecundity can lead to unexpected increases in total population size, a phenomenon known as the ‘hydra effect.’ Here, we examine a two-dimensional susceptible-infectious (SI) model with underlying Ricker population growth and show that the disease-free system has a distinct bifurcation structure from the system with infection. We use numerical bifurcation analysis to determine the influence of infection on the types and appearance of qualitatively distinct long-time dynamics. We find that disease-induced mortality leads to the appearance of multistability, such as stable four-cycles and chaos dependent upon the initial condition. In addition, we examine the appearance and extent of the hydra effect, particularly when infection is introduced during cyclic or chaotic population dynamics.
• Neda Jalali University of Notre Dame
  "Impact of the interaction among DENV, ZIKV, and CHIKV on disease dynamics"
Aedes aegypti and Aedes albopictus mosquitoes are the causative agents of dengue (DENV), chikungunya (CHIKV), and Zika (ZIKV) virus infections in humans. The co-circulation of at least two viruses/serotypes, which is common in countries worldwide, such as Columbia and Brazil in Latin America, can cause potential interactions among the viruses/serotypes and misdiagnosis in the lack of adequate laboratory tests due to similar clinical symptoms among their disease courses. We generalized a deterministic compartmental model to analyze how each disease dynamics changes under the potential antagonistic or synergistic interaction among the viruses/serotypes. Our simulation studies showed that under no DENV vaccine, vector control, and interaction among the viruses/serotypes, the peak of the incidence rates for people with no prior infections happens earlier than those cases with one or two prior infections, mostly because the proportion of fully susceptible people is larger than people with at least one prior infection. We observed higher incidence rates for single/multi infections and an earlier peak of the epidemics for single infections when a prior infection by a virus such as ZIKA causes synergistic cross-immunity against CHIKV and DENV serotypes, compared to the situation when it causes antagonistic cross-immunity. Identification of the cross-immunity is not possible when susceptibility statuses of the population are unknown because the high/low incidence rates could be either the results of high/low baseline transmission rates or antagonistic/synergistic interaction effects among the viruses.

• Alexander Dolnick Meyer University of Notre Dame
  "Risk and size of Aedes-borne disease outbreaks are poorly predicted by climate-based suitability indices"
The recent geographical expansion of Aedes mosquito-borne diseases (ABDs) is a global health threat. Quantifying these pathogens’ epidemiology and identifying at-risk populations are key steps toward preparing for future ABD outbreaks. Data from past outbreaks should be central to informing these efforts, but leveraging these data toward generalizable conclusions is often difficult. Outbreak data are context-dependent and take various forms (e.g., a time-series of cases or retrospective serology data), precluding straightforward comparisons. In this presentation, we approach this problem from two angles, using chikungunya virus (CHIKV) as an example. First, we show how outbreaks with different types of data can be compared directly through the framework of Bayesian inference and mathematical modeling. We use this approach to estimate several measurements of outbreak risk and potential size, such as the basic reproduction number (R0), for 87 CHIKV outbreaks. Second, we test whether these risk estimates can be predicted using local, pre-outbreak information, including demographic factors and previously published climate-based indices of suitability for ABD transmission. Our results suggest that climate-based indices may approximate where outbreaks can occur, but do not predict R0, outbreak risk, or potential outbreak size. More broadly, we illustrate the importance of combining a biologically realistic model with various data sources when quantifying the risk of ABD transmission.
• Arash Arjmand University of Missouri Kansas City
  "Incorporating Biosecurity Adherence into a Modeling Framework to Analyze Dynamics of Antimicrobial Resistance in Cattle Farms"
Antimicrobial Resistant Organisms (ARO) pose a significant threat to human and animal health. Adherence to biosecurity measures is critical in preventing the spread of infectious diseases and minimizing the emergence of AROs. This study aims to develop a modeling framework to quantify the effects of biosecurity adherence on the dynamics of antimicrobial-resistant bacteria in cattle farms. A deterministic Susceptible-Infected-Recovered-Susceptible (SIRS) model is formulated, accounting for drug-susceptible and drug-resistant pathogen strains capable of growth and survival within and between hosts. First, the possible outcomes of the SIRS model are analytically derived and numerically verified as a benchmark. Then, the SIRS model is further extended by stochastically incorporating cattle-farmworker-environment interactions. Using numerical simulations and sensitivity analysis, the likelihood of ARO emergence is investigated under different degrees of compliance with biosecurity measures, such as cattle quarantine, hand hygiene, equipment disinfection, animal health check-ups, and proper use of antibiotics. The present work is the first step toward understanding the influence of biosecurity adherence on human and animal health.
• Aurod Ounsinegad Tarleton State University
  "Dynamics of Eastern Equine Encephalitis Infection Rates: A Mathematical Approach"
The Eastern Equine Encephalitis virus (EEEV) is an erratic and deadly neurological disease that spans the northeastern coast of the United States and Canada. An analysis of the migration patterns of both the mosquito vector and the avian host species was conducted to determine the rate at which the virus is spread between the Black-Tailed Mosquito (Culiseta melanura) and select avian species. It was found that certain species of avians shared similar, or even identical, migration patterns with the Black-Tailed Mosquito. A system of ordinary differential equations (ODEs) was developed and analyzed to gain insight into the transmission dynamics of EEE between the two host classes. A host stage-structured model was incorporated where the avian host group is split into two categories, adults, and hatch-year avians. By using this, the extent to which fluctuations occurred in transmission rates according to host/vector abundances, mosquito biting rate, and type of host was explored. Elasticity analysis was then conducted on all parameters that form the basic reproductive number (ℛ0­) to find the parameters that cause the greatest change in ℛ0. The hypothesis that is evaluated is that hatch-year avians are more readily exposed to the mosquito vector as they lack a defense mechanism, unlike their adult counterpart, allowing for a better understanding of how hatch-year avians drive the infection.
• Cormac LaPrete University of Utah
  "Characterizing spatiotemporal variation in transmission heterogeneity during the 2022 Mpox outbreak in the USA"
Transmission heterogeneity plays a critical role in the dynamics of an epidemic. During an outbreak of an emerging infectious disease, efforts to characterize transmission heterogeneity are generally limited to quantifications during a small outbreak or a limited number of generations of a larger outbreak. Understanding how transmission heterogeneity itself varies over the course of a large enduring outbreak not only improves understanding of observed disease dynamics but also informs public health strategy and response. In this study, we employ a simple method, adaptable to other emerging infectious disease outbreaks, to quantify the spatiotemporal variation in transmission heterogeneity for the 2022 mpox outbreak in the United States. In line with past research on mpox and following reports of potential superspreading events early in this outbreak, we expected to find high transmission heterogeneity as quantified by the dispersion parameter of the offspring distribution, k. Our methods use maximum likelihood estimation to fit a negative binomial distribution to transmission chain offspring distributions informed by a large mpox contact tracing dataset. We find that, while estimates of transmission heterogeneity varied across the outbreak with spatiotemporal pockets of high heterogeneity, overall transmission heterogeneity was low. When testing our methods on simulated data from an outbreak with high transmission heterogeneity, k estimate accuracy depended on the contact tracing data accuracy and completeness. Since the actual contact tracing data had high incompleteness, our values of k estimated from the empirical data may therefore be artificially high. However, it is also possible that our estimates accurately reflect low transmission heterogeneity for the United States mpox outbreak, which could differ substantially from the patterns observed elsewhere.