Mpox transmission dynamics: A mathematical modeling approach with bifurcation analysis of control interventions

Abstract

This study presents a new nonlinear mathematical model to investigate the transmission dynamics of Mpox. This model integrates vaccination, quarantine and hospitalization as key interventions to control the disease, with particular emphasis on the effectiveness of prompt quarantine strategies to limit its spread. A detailed qualitative analysis reveals three distinct epidemiological equilibria, as well as an Mpox-free equilibrium. The local and global stability of these steady states is investigated analytically by obtaining the basic reproduction rate ($\mathscr{R}_o$). Furthermore, the model shows backward bifurcation at a threshold parameter, which suggests that $\mathscr{R}_o$ may not be sufficient to eliminate the disease. To prevent this phenomenon, sufficient conditions were identified to increase the effectiveness of prevention and help eliminate the outbreak, which emphasizes the need for an integrated public health policy to limit disease outbreaks.