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Threshold dynamics of a West Nile virus model with impulsive culling and incubation period. (English) Zbl 1501.92159

Summary: In this paper, we propose a time-delayed West Nile virus (WNv) model with impulsive culling of mosquitoes. The mathematical difficulty lies in how to choose a suitable phase space and deal with the interaction of delay and impulse. By the recent theory developed in [3], we define the basic reproduction number \(\mathcal{R}_0\) as the spectral radius of a linear integraloperator and show that \(\mathcal{R}_0\) acts as a threshold parameter determining the persistence of the model. More precisely, it is proved that if \(\mathcal{R}_0<1\), then the disease-free periodic solution is globally attractive, while if \(\mathcal{R}_0>1\), then the disease is uniformly persistent. Numerical simulations suggest that culling frequency and culling rate are strongly influenced by the biting rate. We also find that prolonging the length of the incubation period in mosquitoes can reduce the risk of disease spreading.

MSC:

92D30 Epidemiology
34K45 Functional-differential equations with impulses
34K13 Periodic solutions to functional-differential equations
Full Text: DOI

References:

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