# American Institute of Mathematical Sciences

2012, 9(1): 165-174. doi: 10.3934/mbe.2012.9.165

## Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes

 1 Unidad Académica de Matemáticas, Universidad Autónoma de Guerrero, Av. Lázaro Cárdenas C.U., Chilpancingo, Guerrero, Mexico

Received  March 2011 Revised  May 2011 Published  December 2011

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 $R_0(\tau)\leq1$, 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).
Citation: Cruz Vargas-De-León. Global analysis of a delayed vector-bias model for malaria transmission with incubation period in mosquitoes. Mathematical Biosciences & Engineering, 2012, 9 (1) : 165-174. doi: 10.3934/mbe.2012.9.165
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