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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
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