Uniqueness and stability analysis to a system of nonlocal partial differential equations related to an epidemic model

Abstract

Infectious illnesses have an exceptional affect on the economic system and society. Dynamic models of infectious illnesses are high quality devices for revealing the legal guidelines of illnesses transmission. Quarantine and nonlinear innate immunity are the crucial elements in the manage of infectious illnesses. However, there are no mathematical models that comprehensively find out about the impact of each innate immunity and quarantine. In this paper, we investigate a system of nonlocal partial differential equations related to an epidemic model. Under appropriate hypothesis on the relaxation function and the kernel of the equation, we prove that the traveling wave solutions are globally exponentially stable by applying the variable exponent theory combining with adequate variational methods and a variant of the mountain pass lemma. We also obtain the uniqueness of traveling wave solutions.