Dynamical analysis of a monkeypox spread model with human to human saturated incidence rate and environmental transmission

In this paper, we study the behavior of monkeypox spread by constructing a compartmental model describing virus transmission between humans, animals, and the environment. The model incorporates vaccination on susceptible humans, quarantine on exposed humans, and hospitalization on infected humans. A saturated incidence rate is applied to obtain a more realistic model. The model's basic reproduction number ($R_0$) is obtained by applying the next generation matrix method. The analysis shows that the local stability of the equilibrium points depends on the value of $R_0$, and it is also shown that the model undergoes forward bifurcation. Furthermore, sensitivity analysis and numerical simulations were conducted to illustrate the analytical results.