Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission

Kuilin Wu and Kai Zhou
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Kuilin Wu: Department of Mathematics, Guizhou University, Guiyang 550025, China
Kai Zhou: School of Mathematics and Computer, Chizhou University, Chizhou 247000, China

Mathematics, 2019, vol. 7, issue 7, 1-22

Abstract: In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic reproduction number of the corresponding reaction system and the minimal wave speed. To prove these results, we apply the Schauder’s fixed point theorem and two-sided Laplace transform. The main difficulties are that the complexity of the incidence rate in the epidemic model and the lack of regularity for nonlocal dispersal operator.

Keywords: SIR model; nonlocal dispersal; traveling wave solutions; nonlocal delayed transmission; Schauder’s fixed point theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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