Stability and Bifurcation Analysis of Mpox Transmission Model

In this study, we conducted a thorough and in-depth investigation into the existence and stability of the boundary equilibria of a deterministic mathematical model for Mpox transmission to gain a deeper understanding of the disease dynamics. The investigation begins with the identification and analysis of the Mpox boundary equilibria, which include the rodent-only boundary equilibrium, the human-only boundary equilibrium, and the coexistence of the rodent and human boundary equilibria. Using center manifold analysis, it was demonstrated that both the rodent equilibrium and the human equilibrium exhibit backward bifurcation when the basic reproduction number of the Mpox transmission model is less than unity. This backward bifurcation phenomenon complicates the control and eradication of Mpox in both rodent and human populations, even when the basic reproduction number is below one. To evaluate the robustness of the model results, uncertainty and sensitivity analyses were performed using Latin Hypercube Sampling and Partial Rank Correlation Coefficient