Journal of Mathematical Analysis and Applications | 2021
Existence of traveling waves for a nonlocal dispersal SIR epidemic model with treatment
Abstract
Abstract This paper is concerned with the existence and nonexistence of traveling wave solutions for a nonlocal dispersal epidemic model with treatment. The existence of traveling wave solutions is established by Schauder s fixed point theorem, while the nonexistence of traveling wave solutions is proved by two-sided Laplace transform. From the results, we conclude the minimal wave speed, which is an important threshold to predict how fast the disease invades. Compared with the work in [35] , we obtain more accurate results about the existence and nonexistence of nontrivial traveling wave solutions. We prove that when the basic reproduction number R 0 > 1 , there exists a critical number c 1 ⁎ > 0 such that for each c > c 1 ⁎ , the system has a nontrivial traveling wave solution with speed c, while for 0 c c 1 ⁎ the system admits no nontrivial traveling wave solution. When R 0 1 , we show that there exists no nontrivial traveling wave solution. In addition, based on [24] , we obtain the existence of traveling waves with the critical speed c = c 1 ⁎ under certain conditions.