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 τ 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, ℛ₀(τ). If ℛ₀(τ) ≤ 1, the disease-free equilibrium is globally asymptotically stable. If ℛ₀(τ) > 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).