Extensive Analysis and Projection of the Impact of High-Risk Immunity Using a Mathematical Model That Incorporates a Convex Incidence Rate of Multiple Covid-19 Exposures

Abstract

In this research study, we investigate the impact of multiple exposure of individuals on the prevalence of COVID-19 and the efficacy of high-risk immunity measures in controlling its transmission dynamics. Through a qualitative analysis of a mathematical model, which includes the positivity of solutions, existence and uniqueness of solutions, and study of invariant regions, we demonstrate that the model can be utilized to examine pandemic outbreaks in a physical system. Our analysis of the basic reproductive ratio reveals that the implementation of high-risk immunity can reduce the number of secondary infections even in scenarios of multiple exposures. Numerical simulations, based on real-life COVID-19 data from the Nigeria center for disease control, were conducted using the homotopy perturbation method, yielding results that support the outcome of the basic reproductive ratio analysis and providing insight into strategies to mitigate the spread of the disease.