The spreading speed of an SIR epidemic model with nonlocal dispersal

Article type: Research Article

Authors: Guo, Jong-Shenq^{a; *} | Poh, Amy Ai Ling^{b; c} | Shimojo, Masahiko^d

Affiliations: [a] Department of Mathematics, Tamkang University, Tamsui, New Taipei City, Taiwan. E-mail: jsguo@mail.tku.edu.tw | [b] Department of Mathematics, Okayama University, Okayama, Japan. E-mail: amypoh.al@s.okayama-u.ac.jp | [c] Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tokyo, Japan | [d] Department of Applied Mathematics, Okayama University of Science, Okayama, Japan. E-mail: shimojo@xmath.ous.ac.jp

Correspondence: [*] Corresponding author. E-mail: jsguo@mail.tku.edu.tw.

Abstract: In this paper, we study an SIR epidemic model with nonlocal dispersal. We study the case with vital dynamics so that a renewal of the susceptible individuals is taken into account. We characterize the asymptotic spreading speed to estimate how fast the disease under consideration spreads. Due to the lack of comparison principle for the SIR model, our proof is based on a delicate analysis of related problems with nonlocal scalar equations.

Keywords: Epidemic model, spreading speed, nonlocal dispersal

DOI: 10.3233/ASY-191584

Journal: Asymptotic Analysis, vol. 120, no. 1-2, pp. 163-174, 2020