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arXiv · 1802.05308

On a Vector-host Epidemic Model with Spatial Structure

Pierre Magal·G. F. Webb·Yixiang Wu
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Abstract

In this paper, we study a reaction-diffusion vector-host epidemic model. We define the basic reproduction number $R_0$ and show that $R_0$ is a threshold parameter: if $R_0\le 1$ the disease free steady state is globally stable; if $R_0>1$ the model has a unique globally stable positive steady state. We then write $R_0$ as the spectral radius of the product of one multiplicative operator $R(x)$ and two compact operators with spectral radius equalling one. Here $R(x)$ corresponds to the basic reproduction number of the model without diffusion and is thus called local basic reproduction number. We study the relationship between $R_0$ and $R(x)$ as the diffusion rates vary.

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Pierre Magal, G. F. Webb, Yixiang Wu. 2018-02-14. On a Vector-host Epidemic Model with Spatial Structure. https://doi.org/10.1088/1361-6544/aae1e0

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