# zbMATH — the first resource for mathematics

Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes. (English) Zbl 1259.34071
Summary: A delayed vector-bias model for malaria transmission with incubation period in mosquitoes is studied. The delay $$\tau$$ corresponds to the time necessary for a latently infected vector to become an infectious vector. We prove that the global stability is completely determined by the threshold parameter, $$R_0(\tau)$$. If $$R_0(\tau) \leq 1$$, the disease-free equilibrium is globally asymptotically stable. If $$R_0(\tau) > 1$$ a unique endemic equilibrium exists and is globally asymptotically stable. We apply our results to Ross-MacDonald malaria models with an incubation period (extrinsic or intrinsic).

##### MSC:
 34K20 Stability theory of functional-differential equations 92D30 Epidemiology
Full Text: