GLOBAL ANALYSIS OF A DELAYED VECTOR-BIAS MODEL FOR MALARIA TRANSMISSION WITH INCUBATION PERIOD IN MOSQUITOES

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) <= 1, the disease-free equilibrium is globally asymptot ically 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).