Wave propagation in a diffusive SIR epidemic model with spatiotemporal delay. (29th August 2018)

• Record Type: Journal Article
• Authors: Zhen, Zaili; Wei, Jingdong; Tian, Lixin; Zhou, Jiangbo; Chen, Wenxia
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 16(2018)
• Page Start: 7074
• Page End: 7098
• Publication Date: 2018-08-29
• Subjects: auxiliary system -- SIR epidemic model -- spatiotemporal delay -- traveling wave; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5216
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : In this paper, we propose a SIR epidemic model incorporating Laplacian diffusion and the spatiotemporal delay to model the transmission of communicable diseases. The existence and nonexistence of traveling wave solutions for the model are investigated. It is found that the threshold dynamics are determined by the basic reproduction number R 0 and the minimum wave speed c ∗ . By introducing an auxiliary system and Schauder's fixed point theorem, we establish the existence of traveling wave solutions for the model if R 0 > 1 and c > c ∗ . Employing Fubini theorem and the two‐sided Laplace transform, we obtain the nonexistence of traveling wave solutions for the model if R 0 ≤ 1 or 0 < c < c ∗ . Our results cover and improve some results in the literature.