Dynamics and parameter estimation of a monkeypox model via non-standard finite difference

In this paper, we propose a discrete-time monkeypox epidemic model with a saturated incidence rate using a non-standard finite difference (NSFD) scheme. The model consists of four human population compartments and three animal population compartments. We have investigated that the model has non-negative and bounded solutions. The model has three fixed points: disease-free, endemic in humans, and endemic in all populations. Each fixed point exists and is stable under certain conditions, which depend on the basic reproduction number and Jury’s conditions. We have performed a case study through parameter estimation using weekly monkeypox data in the United States. The metaheuristic methods GA and PSO are employed to estimate the model parameters and evaluate both performances. The fitted series show that both models offer good estimates, which is supported by [Formula: see text] values close to one. Based on RMSE, the model calibration with different step sizes shows that PSO generally offers better performance than GA. We have also performed numerical simulations that confirm the stability properties of each fixed point and show that the NSFD scheme preserves dynamical consistency compared with the fourth-order Runge–Kutta and the standard Euler scheme. Hence, the NSFD scheme captures biological phenomena more effectively than the standard scheme.