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Periodic traveling wavefronts of a multi-type SIS epidemic model with seasonality. (English) Zbl 1439.35497

Summary: This paper is concerned with a time-periodic and nonlocal system arising from the spread of a deterministic epidemic in multi-types of population by incorporating a seasonal variation. The existence of the critical wave speed of the periodic traveling wavefronts and its coincidence with the spreading speed were proved in [S.-L. Wu et al., J. Math. Anal. Appl. 463, No. 1, 111–133 (2018; Zbl 1390.35380)]. In this paper, we prove the uniqueness and stability of all non-critical periodic wavefronts. Of particular interest is the influences of time-periodicity on the spreading speed in one-dimensional case. It turns out that, in comparison with the autonomous case, the periodicity of the infection rate increases the spreading speed, while the periodicity of the combined death/emigration/recovery rate for infectious individuals decreases the spreading speed. We also find that the contact distribution increases the spreading speed.

MSC:

35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D30 Epidemiology
35B10 Periodic solutions to PDEs
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35C07 Traveling wave solutions
35F55 Initial value problems for systems of nonlinear first-order PDEs
35R10 Partial functional-differential equations

Citations:

Zbl 1390.35380
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Full Text: DOI

References:

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