Mathematical Modelling of COVID-19 Dynamics with Vaccination and Reinfection

Final Defense
Mathematical Modelling of COVID-19 Dynamics with Vaccination and Reinfection

by Maria Czarina T. Lagura
PhD Mathematics Candidate

Date: Monday, 14 August 2023
Time: 4 pm
Venue: SEC A 321

Advisers:
Elvira P. de Lara-Tuprio, PhD
Roden Jason A. David, PhD
Ateneo de Manila University

Panelists:
Elvira P. de Lara-Tuprio, PhD
Ateneo de Manila University
Timothy Robin Y. Teng, PhD (Reader)
Ateneo de Manila University
Mark Anthony C. Tolentino, PhD (Reader)
Ateneo de Manila University
Juancho A. Collera, PhD
University of the Philippines Baguio
Angelyn R. Lao, PhD
De La Salle University

This study uses mathematical modelling and stability analysis to construct a qualitative insight into the transmission dynamics of COVID-19 incorporating the vaccination program and considering the possibility of reinfection among recovered individuals.
Two six-compartment differential equation models for the transmission dynamics of COVID-19 with bilinear incidence are developed by dividing the human population into susceptible, vaccinated, exposed, infectious, confirmed, and recovered. The first model, called SVEICR model, assumes no reinfection among recovered individuals while the second model, called SVEICRE model, considers the possibility of reinfection among recoveries. A rigorous analysis of these models establishes the basic properties of the model, namely, existence, uniqueness, nonnegativity and boundedness of solutions. The basic reproduction number R0 of both models, derived using the next generation matrix approach, is used to determine when the disease will die out and when it will stay in the community. The stability analyses of the equilibrium points of SVEICR model, using La Salle’s invariance principle, show the following: when R0 < 1, then the disease-free equilibrium solution is globally asymptotically stable; and when R0 > 1, the endemic equilibrium exists and is globally asymptotically stable. Moreover, in SVEICRE model, when R0 < 1, conditions are established for the global asymptotic stability of the disease-free equilibrium solution. On the other hand, when R0 > 1, then there exists a unique endemic equilibrium solution and conditions are imposed for its global asymptotic stability. Finally, we use numerical solutions to confirm the results of our stability analyses.

Key Words: COVID-19, compartmental model, vaccination, reinfection, next generation matrix, basic reproduction number, stability analysis, numerical solution