# On a model for epidemic spread with interpopulation contact and repellent taxis

## TL;DR

This paper introduces a PDE model for epidemic spread considering interpopulation contact and repellent taxis, analyzing the existence of solutions and illustrating dynamics through numerical simulations.

## Contribution

It develops a PDE framework incorporating diffusion and repellent taxis for susceptibles and nonlinear diffusion for infecteds, with existence proofs and simulations.

## Key findings

- Existence of weak-strong solutions in 1D
- Existence of supersolutions in higher dimensions
- Numerical simulations illustrating space-time dynamics

## Abstract

We study a PDE model for dynamics of susceptible-infected interactions. The dispersal of susceptibles is via diffusion and repellent taxis as they move away from the increasing density of infected. The diffusion of infected is a nonlinear, possibly degenerating term in nondivergence form. We prove the existence of so-called weak-strong solutions in 1D for a positive susceptible initial population. For dimension $N\geq 2$ and nonnegative susceptible initial density we show the existence of supersolutions. Numerical simulations are performed for different scenarios and illustrate the space-time behaviour of solutions.