Modelling of spatial infection spread through heterogeneous population: from lattice to PDE models

Abstract

We derive a PDE model of the infection spread, which takes population density into account. This model is a continuum limit of agent-based model of human movement. Numerical simulations of the model show that dense population areas encounter higher probability of outbreak, which shows consistency with reality. We also investigate the effect of having large diffusion rate in the model. Our further studies show propagation of disease in the domain, which its speed varies with population density. We estimate this speed in the slow diffusion rate regime. Its propagation between two dense areas that are connected with a very low population density area is proven to be possible by our works. As a case example, we examine coronavirus spread in the Canadian province of Nova Scotia which enable us to verify our understanding of "tunneling" between two dense regions. Lastly, we propose several generalizations of the model towards future studies.