Mathematical Analysis of Compartmental Infectious Disease Models with Time-varying Parameters

Final Defense
Mathematical Analysis of Compartmental Infectious Disease Models with Time-varying Parameters

by Destiny S. Lutero
PhD Mathematics Candidate

Date: Wednesday, 06 December 2023
Time: 5 pm
Venue: Online

Advisers:
Timothy Robin Y. Teng, PhD
Mark Anthony C. Tolentino, PhD
Ateneo de Manila University

Panelists:
Timothy Robin Y. Teng, PhD
Ateneo de Manila University
Jay Michael R. Macalalag, PhD (Reader)
Caraga State University
Luis S. Silvestre, Jr., PhD (Reader)
Ateneo de Manila University
Roden Jason A. David, PhD (Reader)
Ateneo de Manila University
Jomar F. Rabajante, DSc
University of the Philippines Los Baños

Mathematical models have long been used to obtain insights about the spread of infectious diseases. Par- ticularly, the transmission dynamics of an infectious disease can be studied using compartmental models in which the involved population is partitioned according to each individual’s health state with respect to the disease. Such models can then be represented using systems of differential equations with parameters that govern the transitions between compartments. For diseases like COVID-19 or some vector-borne dis- eases, it is likely that some of the parameters (e.g., transmission rates) are not constant over time; that is, they are time-varying. Motivated by this idea, we have studied two compartmental infectious disease models described by systems of ordinary differential equations that involve time-varying transmission parameters. Each model is further classified according to whether the time-varying disease transmission rate is continu- ous or piecewise constant over time. In each case, we have established properties of solutions, determined equilibrium solutions, computed threshold parameters (e.g., basic reproduction number), and established attractivity or stability properties of these equilibria with respect to the corresponding threshold parameters. To carry out the mathematical analysis, we have employed different techniques such as linearization, Lya- punov’s direct method, the fluctuation method, and the invariance principle for switched systems.