A mathematical model examining the role of self-treated individuals in the geographical spread of COVID-19

Abstract

This study examines a spatio-temporal mathematical model that explores the role of self-medicating individuals in the spread of COVID-19. The model consists of a system of equations representing four population groups: susceptible, infected, self-treated, and recovered. It conceptualizes disease transmission as a physical diffusion process, where infected and self-medicated individuals move like fluids through a medium of susceptible individuals. To analyze the spatial dynamics, the Fifth-Order Weighted Essentially Non-Oscillatory (WENO) scheme was applied for spatial discretization of the resulting partial differential equations (PDEs), while the Fourth-Order Runge-Kutta method was used for temporal discretization. The model was tested using COVID-19 data from the Embakasi and Kasarani regions of Nairobi, Kenya. Findings highlighted areas with high contact rates and underscored the need for organized public health initiatives to reduce the prevalence of self-medication in the affected communities.