Qualitative Analysis of Mpox Transmission Model Incorporating Vaccination And Quarantine Measures

A deterministic six-compartmental model has been built to explain the transmission dynamics of MPox. The population has been divided into six epidemiological classes: susceptible S(t), exposed E(t), infected I(t), vaccinated V(t), quarantined Q(t), and recovered R(t). Control measures like vaccination and quarantine have been included, and natural and disease-induced mortality have been taken into account. The boundedness and positivity of the model solutions have been proven to guarantee well-posedness in a biologically reasonable region. The basic reproduction number R_0 has been obtained to represent the threshold dynamics of the system. It has been revealed that for R_0<1, the disease-free equilibrium is stable and the disease will eventually disappear. Conversely, when R_0>1, the infection continues to circulate in the population, and the system has a stable endemic equilibrium.Both the equilibria have been demonstrated to exist and be stable for appropriate parametric conditions. Sensitivity analysis has also been carried out to determine the impact of significant epidemiological parameters on R_0. In addition, the possibility of forward bifurcation has been explored, with the implication of potential multiple endemic equilibria when R_0<1. Numerical simulations have been carried out to illustrate the qualitative dynamics of the system.