Global behavior and traveling waves of a Monkeypox epidemic model with vaccination impact

This study looks at the worldwide behavior of a monkeypox epidemic model that includes the impact of vaccination. A mathematical model is created to analyse the vaccine impact, assuming that immunisation is administered to the susceptible population. The system’s dynamics are determined by the fundamental reproduction number, R0. When R0 < 1, the illness is expected to be eradicated, as evidenced by the disease-free equilibrium’s global asymptotic stability. When R0 > 1, the illness continues and creates a globally stable endemic equilibrium. Furthermore, we investigate the existence of traveling wave solutions, demonstrating that (i) a minimal wave speed, designated as c* > 0, exists when R0 > 1; (ii) when R0 ≤ 1, no nontrivial traveling wave solution exists. Additionally, for wave speeds c < c*, no nontrivial traveling wave solution is found, whereas when c ≥ c*, the system admits a nontrivial traveling wave solution with speed c. Numerical simulations are performed to further validate these theoretical results, confirming both the stability of the equilibrium points and the traveling wave solutions.