Hopf bifurcation and its stability for a vector-borne disease model with delay and reinfection

In this study, we investigated a delayed vector-borne disease model with partial immunity to reinfection. The equilibria and the threshold of the model were determined according to the basic reproductive number R0. The analysis showed that a time delay destabilized the system. Using the delay as a bifurcation parameter, we established the conditions for the stability of the equilibria and the existence of a Hopf bifurcation. We determined the properties of the Hopf bifurcation by applying the normal form theory and center manifold argument, and for the first time, we considered the global continuation of the local Hopf bifurcation for a delayed vector-borne disease epidemic model. Furthermore, we performed some numerical simulations to illustrate our theoretical analysis. Sensitivity analysis showed that preventive control to minimize vector-human contacts and using insecticide to control the vector are effective measures for reducing infections.