A time-space SIR model for disease spread across two regions: Analysis and numerical simulations

Abstract

This paper handles with a time-space SIR model in two regions which have a common interface. The model is defined as coupled reaction–diffusion system with a robin boundary in interface to predict the immigration between the two regions. As known, the immigration has an influence on the spread of disease, this is caused by immigrants who could carry the disease from their areas to other places. For this reason, this paper deals with the existence of solutions to SIR model with disease spread between different regions by the Fadeo–Galerkin method and validate this result by the numerical simulations.