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

Cruz Vargas-De-León; Cruz Vargas-De-León

doi:10.3934/mbe.2012.9.165

Mathematical Biosciences and Engineering

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

Received: 01 March 2011 Accepted: 29 June 2018 Published: 01 December 2011
MSC : Primary: 34K20, 92D30.

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).
- Malaria transmission,
- global stability,
- time delay,
- Lyapunov functional.
Citation: Cruz Vargas-De-León. Global analysis of a delayed vector-bias model for malariatransmission with incubation period in mosquitoes[J]. Mathematical Biosciences and Engineering, 2012, 9(1): 165-174. doi: 10.3934/mbe.2012.9.165

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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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