Stability Analysis for the Equilibria of a Monkeypox Model

Abstract

Monkeypox virus was first identified in 1958 and has since been an ongoing problem in Central and Western Africa. Although the smallpox vaccine provides partial immunity against monkeypox, the number of cases has greatly increased since the eradication of smallpox made its vaccination unnecessary. Although studied by epidemiologists, monkeypox has not been thoroughly studied by mathematicians to the extent of other serious diseases. Currently, to our knowledge, only three mathematical models of monkeypox have been proposed and studied. We present the first of these models, which is related to the second, and discuss the global and local asymptotic stability of its equilibrium points. We prove the global asymptotic stability of the endemic equilibrium which has been previously incomplete. We expand this model to include a situation where the contact rate is a function of time and not simply a constant and then consider an expansion of the model with more than two populations. Then we present the results of numerical simulations for the original model and the modified models. Finally, we propose a basic network model, discuss the limitations of this model in its current form, and propose modifications for future study.