Optimal and Stability Analysis of the Co-Infections Disease Mathematical Model

Abstract

A co-infection of a human or a pig with human influenza or COVID-19 strains and H5N1 strain may result in a pandemic strain, causing a widespread deadly pandemic. In this paper, we consider a new class of co-infections disease epidemic models for a rapid and slow virus. We study the transmission threshold by analyzing the basic reproduction number. The equilibrium points for the model are derived, and their local stability is analyzed with suitable assumptions on the model parameters. Understanding the model parameters is one of the prime subjects in this research work. Therefore, the sensitivity of essential parameters is investigated. Moreover, the optimal control problem for the proposed model is considered, and first-order optimality conditions are derived. Finally, numerical simulations indicate the effects of the model’s basic reproduction number and control variables.