Asymptotic profiles of a nonlocal dispersal SIR epidemic model with treat-age in a heterogeneous environment

Infectious diseases have a significant impact on human life, and additional efforts are required to contain them. Treatment measure is very helpful to contain the epidemic and protect infected persons from disease-related mortality. Therefore, we consider a SIR epidemic model with nonlocal diffusion modeled by a convolution operator and treat-age effect. We show the well-posedness of the solution to the problem that is existence, uniqueness and positivity, and boundedness. Next, we determine the corresponding basic reproduction number R0 that depends on the structure of studied bounded domain omega is an element of R-N, and we show its threshold role in determining the asymptotic profiles of the solution. Moreover, it is proved that the solution map has a global compact attractor. Indeed, for R-0 < 1, there exist a Lipschitz functions S-p such that (S-p, 0, 0) is globally stable, which is related to the extinction scenario of the epidemic. However, for R-0 > 1, we show the solution map is uniformly persistent and there exists a unique endemic steady state denoted (S*, I*, T*) that is globally stable. The influence of the treat-age on the spatiotemporal and threshold profiles is discussed through the research. (C) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.