Monkeypox disease with saturated incidence rates: mathematical analysis

In this study, we explore the dynamics of monkeypox disease by developing and examining a deterministic mathematical model that describes the interactions between human and rodent populations. First, we demonstrate the well-posedness of the model. The basic reproduction number is expressed as a function of the human reproduction number and the rodent reproduction number. The problem admits three equilibria, namely the disease-free equilibrium, the human-only endemic equilibrium, and the endemic equilibrium. We then analyze the local and the global stability of those equilibria. To further assess the equilibria stability, different numerical simulations are executed in order to support the theoretical findings and to highlight the impact of different parameters in eradicating the disease.