Spatial propagation phenomena for diffusive SIS epidemic models

This paper is concerned with the propagation phenomena for a class of susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with two different kinds of incidence posed on an unbounded domain. The main difficulty of such model system is the lack of comparison principle because it shares a similar structure to the predator-prey system. Additionally, compared with S-I type disease-transmission models, the cyclic structure involved in SIS models contributes to extra difficulties in the analysis. This means that the techniques accessible to diffusive S-I type models or classic predator-prey like system cannot be directly applied to the current model. The first goal of this paper is to show how the localized initial introductions of infective behave spatially and then the asymptotic speed of spread for the infection is derived from the model with separable incidence (e.g., mass-action mechanism) based on the weak dissipativity and uniform persistence idea on dynamical system. In the case where the standard incidence is taken into consideration, the existence of the asymptotic speed of spread and the full information on the traveling wave solutions are presented. Unlike the S-I type epidemic models with standard incidence, the uniform boundedness of solutions for the current Cauchy problem is not readily available due to the constraint from the cyclic structure. The construction of an appropriate invariant set is adopted to obtain the uniform boundedness. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.