"Disease surveillance systems provide early warnings of disease outbreaks before they escalate into public health emergencies. However, most surveillance frameworks envision disease detection as a static problem based on a threshold condition, often overlooking the interdependence between epidemiological surveillance, disease dynamics, and intervention strategies. Pandemics pose complex challenges in which epidemiological surveillance is essential but may not be sufficient to achieve containment. Waning immunity and the importation or emergence of novel variants (which reshape the population’s immunity landscape) are key obstacles in controlling viral spread. Understanding the genomic composition of ongoing outbreaks is critical for characterizing disease dynamics, elucidating epidemiological outcomes, and informing potential intervention strategies.

In this talk, we introduce a multi-theory modeling framework that integrates genomic surveillance, multi-variant dynamics and intervention strategies to inform a realistic operational course of action based on testing, analysis, and response. We will discuss the effects of the competing dynamics among variants on both the novel variants’ detection time and the effectiveness of different intervention scenarios during a pandemic progression.

We found that (i) the novel variant’s detection conditions are determined by the competitive dominance, which is modulated by the population’s susceptibility; (ii) different intervention scenarios yield better outcomes depending on the target metric; and (iii) the characteristics of the transmission process inherently limit detection and the impact of intervention strategies. This is joint work with the Virginia Department of Health, Princeton University, Indian Institute of Science, and Indian Statistical Institute."

As the search for a cure for chronic hepatitis B virus infection continues, pharmaceutical companies have developed antivirals that target different stages of the intracellular life cycle of the virus. Earlier developed drugs such as pegylated interferon and nucleos(t)ide analogues (NAs) have shown effective viral suppression during treatment in individuals with chronic HBV infection. However, the NAs may need to be taken indefinitely to maintain viral suppression, and pegylated interferon has side effects that limit its use. The development of a new class of drugs, called capsid assembly modulators (CAMs), has created renewed hope for finding a functional cure for chronic HBV infection.  We developed a multiscale mathematical model of chronic HBV infection that incorporates steps in the intracellular life cycle and extracellular kinetics of the virus.  We fit our model to the longitudinal HBV RNA, HBV DNA, and alanine aminotransferase (ALT) measurements from 27 individuals with chronic HBV infection treated with a first-generation CAM, vebicorvir for 28 days. From this, we estimated the effectiveness of vebicorvir in preventing the production of encapsidation pgRNA. We also used our model to identify the biological mechanisms contributing to the different phases of viral decline observed during therapy. Our model provides a quantitative framework for studying the intracellular and extracellular kinetics of chronic HBV infection and a conceptual framework for estimating the in vivo effectiveness of drugs that target different aspects of the intracellular life cycle of the virus.

Thoracoabdominal asynchrony (TAA), the asynchronous volume changes between the rib cage and abdomen during breathing, is associated with respiratory distress, progressive lung volume loss, and chronic lung disease in the newborn infant. Preterm infants are prone to TAA risk factors such as weak intercostal muscles, surfactant deficiency, and a flaccid chest wall. The causes of TAA in this fragile population are not fully understood and, to date, the assessment of TAA has not included a mechanistic modeling framework to explore the role these risk factors play in breathing dynamics and how TAA can be resolved. We present a dynamic compartmental model (“TAA” model) of pulmonary mechanics that simulates TAA in the preterm infant under various adverse clinical conditions, including high chest wall compliance, applied inspiratory resistive loads, bronchopulmonary dysplasia, anesthesia-induced intercostal muscle deactivation, weakened costal diaphragm, impaired lung compliance, and upper airway obstruction. An additional model with a single chest wall compartment was constructed separately to observe effects of ventilatory support measures on airflow and pleural pressure model outputs under surfactant-treated and deficient lung scenarios. Sensitivity analyses of both models screened and ranked model parameter influence on TAA and respiratory volume outputs, showing that risk factors are additive such that maximal TAA occurs in a virtual preterm infant with multiple adverse conditions. Simulated indices of TAA are consistent with published experimental studies and clinically observed pathophysiology, motivating further investigation into the use of computational modeling for assessing and managing TAA.

Individual movements play a central role in disease ecology, where contact and transmission are necessary components of disease spread within populations and across landscapes. Here, I describe a model called movement-driven modeling of spatio-temporal infection risk (MoveSTIR) that formally links empirical movement data with epidemiological theory, enabling data-driven modeling and novel theoretical exploration of infection dynamics on real-world landscapes. First, I describe the mathematical theory behind MoveSTIR that reconceptualizes “contact” and links direct and indirect transmission between hosts along a continuum. Applying MoveSTIR to empirically observed movement data, I show that fine-scale movements can matter greatly for transmission, increasing the explosiveness of pathogen spread within populations. Second, I extend MoveSTIR and show how it directly quantifies the contributions of spatial and social drivers to transmission risk. Using analytical results and simulations, I show that even weak social interactions can drastically change transmission dynamics for short-lived pathogens. Finally, I use MoveSTIR and two years of disease surveillance and movement data from a white-tailed deer population to show that space use and social interactions among white-tailed deer on a real landscape make it nearly impossible for them to act as a long-term reservoir host for the viral pathogen SARS-CoV-2.

Heterogeneity in malaria transmission is a critical factor that influences the effectiveness of control strategies and the dynamics of disease spread. In this talk, I will address several key sources of heterogeneity in malaria models, including spatial, temporal, and age-related variations, particularly in light of the recent approval of the RTS,S malaria vaccine.

I will present two models: the first is an age-structured PDE malaria (P. falciparum) model that couples vector-host epidemiological dynamics with immunity dynamics. This model tracks the acquisition and loss of anti-disease immunity over time and examines its nonlinear feedback on transmission parameters. Motivated by the newly approved RTS,S vaccine, the model also investigates the impact of vaccination, revealing a reduction in severe disease among young children but a slight increase in severe malaria among older children due to delayed exposure and lower acquired immunity.

The second model addresses genetic heterogeneity in susceptibility to Plasmodium vivax malaria. It explores the role of the Duffy-negative genotype in modifying transmission dynamics, using a seasonal framework to track genotype changes and derive the basic reproduction number, $R_0$. Calibrated with data from the Amazonas region in Brazil, this model identifies the critical proportion of Duffy-negative individuals required to protect the population without additional interventions. It also assesses how different Duffy-negative proportions influence monthly P. vivax incidence, providing insights into the interaction between genetic resistance and malaria burden.
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This work presents mathematical modeling approaches to two age-related chronic conditions, obesity-induced type 2 diabetes mellitus (T2DM) and senescence-induced osteoporosis, highlighting how physiological changes affect disease progression and treatment efficacy. The first study addresses obesity-induced T2DM by expanding on the traditional glucose-insulin regulatory model, integrating a detailed mechanism of glucose transport between the blood and liver. This approach improves accuracy in modeling blood glucose levels and evaluating anti-diabetic therapies, especially those that also target weight reduction. The second study investigates osteoporosis, a condition marked by bone density loss due to cellular senescence. Using a mathematical model, the authors assess how the proliferation rate of senescent cells contributes to osteoporosis, quantifying bone density loss over age 50-100 and evaluating the impact of senolytic drugs like fisetin and hormonal therapies. Both models underscore the role of underlying physiological mechanisms in disease and provide a basis for exploring treatment efficacy in T2DM and osteoporosis.

This research aims to develop a novel approach to quantify endosomal escape after delivering siRNAs into ovarian cancer cells using fusogenic peptides. The peptides protect siRNAs from degradation within endosomes by facilitating their transfer into the cytosol. From a mathematical and computational perspective, the focus is on creating and optimizing statistical models to accurately measure the success of siRNA endosomal escape. Additionally, machine learning models are applied to predict experimental conditions, enhancing the future effectiveness of siRNA delivery methods in cancer treatment.

Malaria is caused by Plasmodium parasites that are transmitted to humans by Anopheles mosquitoes. Currently, over half of the world’s population is at risk of malaria, although progress towards local eradication is being made in some parts of the world. Malaria infection is known to influence levels of biogenic amines in human blood. Specifically, individuals with severe malaria may exhibit increased concentrations of histamine and decreased concentrations of serotonin. The altered amine levels also impact the biology and behavior of Anopheles mosquitoes that ingest them in bloodmeals, but it remains to be seen what role these changes have on mosquito population dynamics and malaria transmission. We developed a stage-structured discrete time mathematical model of mosquito population dynamics coupled with population-level malaria transmission dynamics to investigate how these altered amine levels may play a role in the malaria transmission cycle. We incorporated demographic, behavioral, and parasite reproduction data into the model and explored scenarios that consider the effects of different possible concentrations of histamine and serotonin in bloodmeals on mosquito population size and malaria incidence and prevalence. We explore different possible extensions of the model and discuss our findings in the context of malaria control as well as ongoing and future experimental work.

Several harmful populations, such as pests that harm crops or parasites that cause diseases, are controlled through pulsed applications of control reagents. Impulse models of particular systems are often used to determine effective and optimal control strategies. With the goal of generalizing principles, in this talk, we will develop results on the persistence (or elimination) of broad classes of pulsed population models. In particular, we examine how population structure, such as in life stages or genetics, impacts when and how populations persist. We demonstrate the implications of our results in two empirical examples.

Drug overdose fatalities have become a significant health issue in many countries, with the United States experiencing a particularly alarming rise over the past two decades. In this study, we examine the geographical patterns of drug overdose deaths at the county level across the United States by utilizing five newly defined spatial weights, developed using mobility data from Google and Facebook. Google Mobility Data, derived from users' location services, provides insights into how populations move between various categories of places, while Facebook Mobility Data, collected through its Data for Good program, tracks population movements between geographic areas. These spatial weights are based on the correlation of mobility data between two spatial units and a threshold distance decay between them. We analyze the spatial distribution of drug overdose deaths using datasets from County Health Rankings and Roadmaps, as well as the Centers for Disease Control and Prevention, focusing on the COVID-19 era spanning 2020, 2021, and 2022. By incorporating spatial covariate information into the new spatial weight definitions, these methods more accurately represent the relationships between spatial units and enhance the performance of spatial analysis techniques. Three of the methods effectively captured nearly all high-incident counties and accurately identified hot and cold spot clusters over the years. In contrast, the other two methods failed to identify many counties with high cases, classifying them as insignificant. 

The risk of mosquito-borne disease outbreaks depends critically on mosquito biting frequency. However, standard models of mosquito-borne disease transmission assume that mosquitoes blood-feed only once per reproductive cycle – an assumption contradicted by empirical evidence. I will present a novel framework for incorporating more complex mosquito biting dynamics into transmission models. Despite this added complexity, key epidemiological measures such as the basic offspring and basic reproduction numbers remain analytically tractable, allowing for direct comparisons to standard models. To demonstrate the utility of this framework, I compare the standard model to several alternatives, including one grounded in a mechanistic representation of the biting process, revealing how different assumptions about mosquito behavior influence outbreak risk predictions. Key parameters for disease control are identified through a sensitivity analysis of a mechanistic model. This work offers a straightforward approach for integrating biological and ecological knowledge of mosquito biting behavior into epidemiological models and underscores the role of behavioral dynamics in shaping disease transmission. 

Desert ecosystems have been characterized by Noy-Meir (1973) as "water-controlled ecosystems with infrequent, discrete and largely unpredictable water inputs," with the limiting resource of water arriving in short-lived pulses.  These dry climates are known to support regular, large-scale patterns of vegetation growth organized into evenly spaced bands that are separated by swaths of bare soil, and studies suggest that this may provide improved resilience to drought.  I will present a modeling framework for vegetation pattern formation in drylands that treats storms as instantaneous kicks to the soil water, which then interacts with vegetation during the long dry periods between the storms. The spatial profiles of the soil water kicks capture positive feedbacks in the storm-level hydrology that act to concentrate water within the vegetation bands. This flow-kick model predicts that variance in rainfall introduced through randomness in the timing and magnitude of water input from storms decreases the parameter range over which patterns appear and may therefore negatively impact ecosystem resilience

Many studies have suggested that the complex dynamics during heart arrhythmias may be chaotic, however, little experimental evidence has quantified the chaotic behavior of excitations in living cardiac tissue. In this talk, I aim to quantify and qualify the chaotic nature of cardiac tissue with voltage measurements from simulations of a cardiac mathematical model and measurements from ex-vivo single-cell and whole-heart experiments. I will show a period-doubling bifurcation with a cascade to chaos from a mathematical model and in single-cell microelectrode recordings obtained in bullfrog hearts. The voltage dynamics of the model and microelectrode recordings are correlated with Lyapunov exponents. Additionally, I will show stable period-three orbits and several examples of unstable periodic orbit shadowing obtained in the single-cell microelectrode experiments. Spatially distributed unstable periodic behavior from optical mapping will also be shown from the ventricular surfaces of frogs and even humans. These findings indicate chaotic factors partly govern cardiac tissue voltage dynamics, and nonlinear control can be employed to stabilize and terminate arrhythmias. We finish by showing how fast, biphasic perturbations can be used to stabilize or destabilize periodic orbits and complex dynamics in cardiac experiments.

Posttraumatic stress disorder (PTSD) is a debilitating condition triggered by traumatic events. Notable symptom differences exist between combat-exposed veterans and active-duty personnel PTSD cases. However, the underlying biological mechanisms remain elusive. This study aims to uncover the shared biological core modules associated with PTSD by leveraging extensive omics data among various PTSD subtypes. To achieve this, we employed the Core Module Biomarker Identification with Network ExploRation (COMBINER) approach on DNA methylation data to identify key network modules of epigenetic modification across PTSD subtypes resulting the production of key networks associated with PTSD. These findings not only enhance our knowledge of PTSD diverse symptomatology but also pave the way for the development of biomarkers and personalized treatments.

Ecological communities are fundamentally built upon the pairwise interactions between individuals and species. These interactions can be classified into three main types: negative-negative (competition), negative-positive (predation and parasitism), and positive-positive (mutualism and cooperation). Of these three, positive-positive interactions remain to most enigmatic. This is because basic analysis states they should be the least stable of all interactions, whether ecologically due to the positive feedbacks that cause population collapse or evolutionarily due to the temptation of cheating. And yet, they remain significant in ecological communities as seen, for example, in the widespread use of cooperation in social species and the trade of services and resources in plants and other species. In this talk, I outline my work exploring the dynamics of positive-positive interactions. Starting with the ecological dynamics of cooperative species, I show a fundamental mismatch between stable population equilibria and stable behavioral equilibria which leads to unstable population dynamics. I then continue with an exploration of the legume-rhizobium mutualism, seeking to understand how it maintains diversity within and between species.