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Dynamics on a degenerated reaction-diffusion Zika transmission model. (English) Zbl 1533.35200

Summary: In view of environmental transmission and spatial heterogeneity, a degenerated reaction-diffusion Zika transmission model is established and analyzed with more realistic factors. Besides the mosquito reproduction number \(\mathcal{R}_m\), a novel computation formula of the basic reproduction number of disease \(\mathcal{R}_0\) in terms of the principal eigenvalue of an elliptic eigenvalue problem is provided. Dynamic analysis results show that the proposed system follows a threshold dynamics based on \(\mathcal{R}_m\) or \(\mathcal{R}_0\). Especially, for the critical case of \(\mathcal{R}_0 = 1\), global attractiveness of the disease-free steady state is obtained by constructing a new Lyapunov function, which is usually one of challenges for some spatially heterogeneous models.

MSC:

35K57 Reaction-diffusion equations
35K51 Initial-boundary value problems for second-order parabolic systems
92D25 Population dynamics (general)
Full Text: DOI

References:

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