Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes

Cruz Vargas-De-León

doi:10.3934/mbe.2012.9.165

Article Contents

2012, Volume 9, Issue 1: 165-174. Doi: 10.3934/mbe.2012.9.165

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

Cruz Vargas-De-León^1,

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

Received: March 2011

Revised: May 2011

Published: December 2011

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Abstract

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).

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Mathematics Subject Classification: Primary: 34K20, 92D30.

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