Research

My research program focuses on understanding how biological mechanisms, disease progression, host heterogeneity, human behavior, and interventions shape infectious-disease dynamics. I am particularly interested in questions that connect mathematical theory with epidemiological or biological data, especially when important disease states are hidden or only partially observed.

My research is organized around three interconnected themes:

Mathematical Epidemiology & Nonlinear Disease Dynamics

I develop and analyze mathematical models to understand the transmission, persistence, and control of infectious diseases. My work uses ordinary differential equations, delay differential equations, nonlinear dynamical systems, stability and bifurcation analysis, reproduction thresholds, and intervention modeling to identify mechanisms that shape epidemic behavior.

A major focus of this work is understanding how biological, behavioral, and public-health processes operating on different timescales can alter disease dynamics. I have studied delayed infectiousness, relapse, imperfect testing, vaccination, treatment limitations, viral variants, cross-immunity, and threshold-based interventions. Recent work includes a delay-differential equation model of human-to-human Nipah virus transmission incorporating delayed infectiousness and relapse, as well as a nonsmooth epidemic model examining threshold-based treatment and dynamic hospital-bed capacity.

I am also developing mathematical models of tuberculosis and COVID-19 co-infection to investigate how human behavioral responses shape co-infection burden and how co-infection, in turn, alters the transmission and burden of tuberculosis and COVID-19 in high-TB-burden settings.

More broadly, I am interested in developing mathematical theory that explains when changes in disease progression, intervention timing, host behavior, or epidemiological interactions lead to qualitatively different disease outcomes.

Data-Informed & Multiscale Mathematical Biology

An important direction of my research is connecting mechanistic models with biological and epidemiological data. I use parameter estimation, model calibration, structural and practical identifiability, sensitivity analysis, bootstrap-based uncertainty quantification, Bayesian methods, and statistical approaches to determine what can reliably be learned from available observations.

I am especially interested in infectious diseases involving hidden states, such as latent and subclinical infection. These systems raise important questions about how unobserved biological processes influence population-level transmission and whether available surveillance data contain enough information to distinguish competing disease mechanisms.

My research also investigates disease dynamics across biological scales. During a research visit to Princeton University, I initiated an ongoing collaboration with Prof. Simon A. Levin on a multiscale tuberculosis framework linking within-host bacterial–immune dynamics with population-level transmission and the evolutionary dynamics of subclinical infection. This work seeks to understand how within-host traits and variation in disease progression shape transmission fitness and pathogen evolution.

One Health, Zoonotic & Environmental Disease Modeling

I develop mathematical and quantitative approaches for infectious diseases involving interactions among humans, animals, and the environment. These problems are particularly important for zoonotic and emerging infections, where effective disease control often requires coordinated interventions across multiple host populations.

At the University of Arizona, my current work includes developing mechanistic models of bovine tuberculosis at the wildlife–livestock–human interface. These models incorporate imperfect surveillance, vaccination, culling, and host heterogeneity to evaluate coordinated disease-control strategies. Earlier work examined two-way disease transmission between humans and animals and the role of culling as a disease-control strategy.

I have also worked on environmental Salmonella surveillance, using generalized linear mixed-effects models to identify environmental and temporal predictors of Salmonella occurrence and characterize serovar co-occurrence patterns in agricultural surface water.

Through these projects, I aim to connect mathematical theory with practical questions in disease surveillance and intervention design.

Current Research Directions

My current and emerging research directions include:

  • multiscale and evolutionary modeling of tuberculosis and subclinical infection;
  • mathematical theory for hidden disease states and heterogeneous disease-progression times;
  • identifiability and uncertainty in partially observed epidemic systems;
  • behavioral and evolutionary processes in co-infection dynamics; and
  • integration of mechanistic models with epidemiological and environmental data.

The broader goal of my research is to develop mathematically rigorous and biologically interpretable frameworks that improve understanding of infectious-disease dynamics and support public health and One Health decision-making.