Associate Professor, Applied Mathematics
Department of Mathematics & Statistics · Texas Tech University
I am an Associate Professor in the Department of Mathematics and Statistics at Texas Tech University. I earned my Ph.D. in Applied Mathematics from the University of Western Ontario in 2014. My research applies nonlinear dynamics and bifurcation theory to problems in mathematical biology, with an emphasis on in-host disease modeling and mathematical epidemiology.
My work spans the within-host dynamics of HIV, tuberculosis, monkeypox, influenza A virus, and cancer immunotherapy, as well as population-level models of cholera, Zika, and COVID-19. I frequently complement deterministic dynamical-systems analysis with stochastic approaches such as continuous-time Markov chains, multitype branching processes, and stochastic differential equations. Recurring themes include disease recurrence and relapse–remission dynamics, autoimmune disease, predator–prey and population dynamics, population bottleneck effects on the maintenance of viral diversity, and, more recently, optimal control and scientific machine learning for therapy design. My research has been supported by the Simons Foundation.
Comprehensive understanding of combination immunotherapy for cancer treatment via bifurcation theory
Journal of Nonlinear Science 36:74
Maintenance of viral diversity through influenza transmission bottlenecks: a within-host branching-process model
bioRxiv (preprint)
Universal differential equations for optimal control problems and its application on cancer therapy
arXiv:2504.16035 (preprint)
Uncovering the impact of infection routes on within-host MPXV dynamics: insights from a mathematical modeling study
PLOS Computational Biology 21(5):e1013073
Detecting and resetting tipping points to create more HIV post-treatment controllers with bifurcation and sensitivity analysis
SIAM Journal on Applied Mathematics
Transient dynamics in fast–slow predator–prey model with Monod–Haldane functional response and asymptotic behaviors
International Journal of Bifurcation and Chaos 34(4):2450158
Bifurcations of a cancer immunotherapy model explaining the transient delayed response and various other responses
Communications in Nonlinear Science and Numerical Simulation
Modeling and analysis of social obesity epidemic
Journal of Applied Analysis & Computation 14(2):1023–1045
A mathematical model to assess the impact of testing and isolation compliance on the transmission of COVID-19
Infectious Disease Modelling 8(2):427–444
Modeling and analysis of low-level transmission ZIKV dynamics via a Poisson point process on sexual transmission route
Journal of Applied Analysis & Computation 13(2):1044–1069
Deterministic and stochastic in-host tuberculosis models for bacterium-directed and host-directed therapy combination
Mathematical Medicine and Biology: A Journal of the IMA
Disease clearance of tuberculosis infection: an in-host continuous-time Markov chain model
Applied Mathematics and Computation 413:126614
An investigation of tuberculosis progression revealing the role of macrophages apoptosis via sensitivity and bifurcation analysis
Journal of Mathematical Biology 83:31
Revealing the role of the effector-regulatory T cell loop on autoimmune disease symptoms via nonlinear analysis
Communications in Nonlinear Science and Numerical Simulation 93:105529
Analysis of an in-host tuberculosis model for disease control
Applied Mathematics Letters 99:105983
Analysis of solutions and disease progressions for a within-host tuberculosis model
Mathematics in Applied Sciences and Engineering 1(1):39–49
Modeling and analysis of the multi-annual cholera outbreaks with host-pathogen encounters
International Journal of Bifurcation and Chaos 30(8):2050120
Examining HIV progression mechanisms via mathematical approaches
Mathematics in Applied Sciences and Engineering 1(4):309–330
Multiple recurrent outbreak cycles in an autonomous epidemiological model due to multiple limit cycle bifurcation
Journal of Applied Analysis & Computation 10(5):2278–2298
Tristable phenomenon in a predator–prey system arising from multiple limit cycles bifurcation
International Journal of Bifurcation and Chaos 30(9):2050129
Complex dynamics in a unified SIR and HIV disease model: a bifurcation theory approach
Journal of Nonlinear Science
Models of cytokine dynamics in the inflammatory response of viral zoonotic infectious diseases
Mathematical Medicine and Biology: A Journal of the IMA
Cooperative hunting in a predator–prey system with Allee effects in the prey
Natural Resource Modeling
Modeling the argasid tick (Ornithodoros moubata) life cycle
In: Understanding Complex Biological Systems with Mathematics (AWM Series, Springer)
Backward bifurcations, turning points and rich dynamics in simple disease models
Journal of Mathematical Biology 73:947–976
Dynamical analysis and simulation of a 2-dimensional disease model with convex incidence
Communications in Nonlinear Science and Numerical Simulation 37:163–192
Hopf and generalized Hopf bifurcations in a recurrent autoimmune disease model
International Journal of Bifurcation and Chaos 26(8):1650079
Modeling and analysis of recurrent autoimmune disease
SIAM Journal on Applied Mathematics 74(6):1998–2025
Viral blips may not need a trigger: how transient viremia can arise in deterministic in-host models
SIAM Review 56(1):127–155 (SIGEST)
Understanding recurrent disease: a dynamical systems approach
Ph.D. thesis, University of Western Ontario
Conditions for transient viremia in deterministic in-host models: viral blips need no exogenous trigger
SIAM Journal on Applied Mathematics 73(2):853–881