Traveling waves for a diffusive SIR-B epidemic model with multiple transmission pathways

Song, Haifeng and Zhang, Yuxiang: Traveling waves for a diffusive SIR-B epidemic model with multiple transmission pathways. Electronic journal of qualitative theory of differential equations 86. pp. 1-19. (2019)

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Abstract

In this work, we consider a diffusive SIR-B epidemic model with multiple transmission pathways and saturating incidence rates. We first present the explicit formula of the basic reproduction number R0. Then we show that if R0 > 1, there exists a constant c ∗ > 0 such that the system admits traveling wave solutions connecting the disease-free equilibrium and endemic equilibrium with speed c if and only if c ≥ c Since the system does not admit the comparison principle, we appeal to the standard Schauder’s fixed point theorem to prove the existence of traveling waves. Moreover, a suitable Lyapunov function is constructed to prove the upward convergence of traveling waves.

Item Type: Article
Journal or Publication Title: Electronic journal of qualitative theory of differential equations
Date: 2019
Number: 86
Page Range: pp. 1-19
ISSN: 1417-3875
DOI: https://doi.org/10.14232/ejqtde.2019.1.86
Uncontrolled Keywords: Reakció-diffúziós egyenlet
Additional Information: Bibliogr.: p. 17-19. ; összefoglalás angol nyelven
Date Deposited: 2020. Jan. 27. 13:22
Last Modified: 2020. Jan. 27. 13:22
URI: http://acta.bibl.u-szeged.hu/id/eprint/64730

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