Monkeypox is an infectious disease that threatens human life. The recent spread of the virus has increased global health concerns and risks. In this paper, an innovative mathematical modeling approach is presented to investigate the transmission dynamics of the monkeypox virus. The mathematical model is constructed considering the spread of the virus in both human and rodent populations. It also provides a more realistic approach by including a saturated incidence rate. The model is usable by including potential interventions that governments can adopt. The local and global asymptotic stability of the equilibrium points with the basic reproduction number R0 is examined. In addition, a bifurcation analysis is conducted to reveal significant changes in the dynamics of the model. Sensitivity analysis is given to evaluate the effects of potential measures that can be taken to eliminate the disease. Finally, the obtained theoretical results are supported by numerical simulations.