Dynamics and Bifurcation Analysis of a Monkeypox Transmission System With Two Time Delays

ABSTRACT A monkeypox transmission system with two time delays is developed in this paper. To address how the time delays influence the transmission progress, sufficient conditions for local asymptotic stability of the equilibrium points are established analytically. Subsequently, we analyze the existence and direction of transcritical bifurcation and obtain sufficient conditions for Hopf bifurcation of system with two time delays. Furthermore, by applying the center manifold theory and the normal form theory, we determine the direction and stability of Hopf bifurcation near the bifurcation curves. Finally, we conduct numerical simulations on the sufficient conditions for the emergence of bifurcations and demonstrate the influence of bifurcations on the system. This study provides a novel theoretical perspective on the prevention and control of monkeypox.