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 malariatransmission with incubation period in mosquitoes[J]. Mathematical Biosciences and Engineering, 2012, 9(1): 165-174. doi: 10.3934/mbe.2012.9.165
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).