Modeling and optimal control of COVID-19 transmission dynamics in age-structured susceptible populations

Abstract

This study theoretically analyzes the transmission dynamics of COVID-19, its impact on age-structured populations, and associated control methodologies using nonlinear differential equations. A qualitative assessment of the model is conducted using constant control strategies, establishing the positivity and invariant region of the solutions. The next-generation matrix approach determined the model's basic reproduction number, $\mathcal{R}_0$. Both the disease-free and endemic equilibria are analyzed locally by the linearization approach and globally through Lyapunov stability methods. Sensitivity analysis of $\mathcal{R}_0$ is performed to identify the most influential parameters in  COVID-19 transmission dynamics. We also perform a sensitivity analysis using Partial Rank Correlation Coefficient (PRCC) to determine the key parameters that influence the infection prevalence of the disease. The numerical simulations are used to explore the theoretical outcomes of the autonomous deterministic model. Further analysis, based on Pontryagin’s maximum principle, is conducted to examine the impacts of two optimal control strategies on the non-autonomous COVID-19 dynamics, aiming to mitigate disease transmission among the age-structured susceptible populations.