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Keywords = nonlocal delayed transmission

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22 pages, 803 KiB  
Article
Traveling Waves in a Nonlocal Dispersal SIR Model with Standard Incidence Rate and Nonlocal Delayed Transmission
by Kuilin Wu and Kai Zhou
Mathematics 2019, 7(7), 641; https://doi.org/10.3390/math7070641 - 18 Jul 2019
Cited by 4 | Viewed by 2898
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 [...] Read more.
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. Full article
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