Lyapunov Mappings and Analysis of a Nonlinear Spatio-temporal Epidemic Model

Abstract

This paper focuses on the global asymptotic properties of the SIR diffusive model for infectious diseases. Using the analytic technique with Lyapunov functions, we developed conditions for the global attractor of a unique disease steady-state and the disease free equilibrium. The most eminent refuge to the model is the direct Lyapunov mapping. We investigate the global well-posedness of the mathematical model, determine conditions on R_o for which non-trivial equilibrium states exist, and examine their global stability. We are interested in finding the model’s basic reproductive number, which determines whether the disease dies out or persists in the population. Finally, we consider a series of computational results to verify the theoretical results. The extensive numerical simulations show the dynamics of different population groups over time. The effects of different parameters on the compartments are shown in detail. The findings allude that the dynamics of the system are entirely estimated by the deterministic value R_o.

Dhaka Univ. J. Sci. 69(3): 161-170, 2022 (June)