Modeling the transmission dynamics of the co-infection of COVID-19 and Monkeypox diseases with optimal control strategies and cost–benefit analysis

Abstract

This study explores a mathematical model in continuous time, elucidating the transmission dynamics of the co-infection of COVID-19 and Monkeypox. We implemented an optimal control strategy that includes adherence to wearing nose/face masks, practicing social distancing, employing rodenticides, and getting vaccinated against these lethal illnesses. The goal is to reduce their spread among people, consequently lessening their impact on the human population. Utilizing the discrete-time Pontryagin maximum principle, we determined optimal control strategies through an iterative approach to solve the optimal system. By utilizing the MATLAB optimization toolbox with the Runge–Kutta forward–backward sweep technique, we performed numerical simulations to demonstrate how these control parameters impact different sections of the human population, including both infected and uninfected compartments. We conducted a comprehensive cost–benefit analysis to identify the control measures that would produce the best outcome in minimizing both the expenses and the incidence of co-infection cases involving COVID-19 and Monkeypox diseases. Our analyses indicated that intensifying the utilization of nose/facemasks, rodenticides, personal protective equipments (PPEs) in Monkeypox treatment facilities, immunization, and implementing social distancing measures can notably diminish the prevalence of COVID-19, Monkeypox, and their concurrent infections among the human populace.