Chemotaxis-inspired PDE model for airborne infectious disease transmission: analysis and simulations

TL;DR

This paper introduces a chemotaxis-inspired PDE model for airborne infectious disease transmission that better captures human mobility and contact patterns, demonstrating its effectiveness through mathematical analysis and simulations.

Contribution

It presents a novel PDE model incorporating a chemotaxis-like term to improve the description of airborne disease spread, with proven well-posedness and demonstrated advantages over diffusion models.

Findings

Model captures long-distance propagation and hotspot formation.

Mathematically proven well-posedness of the PDE system.

Simulations show improved realism over standard diffusion models.

Abstract

Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics, with Fickian diffusion being the most common such term. However, while diffusion may be appropriate for modeling vector-borne diseases, or diseases among plants or wildlife, the spatial propagation of airborne diseases in human populations is heavily dependent on human contact and mobility patterns, which are not necessarily well-described by diffusion. By including an additional chemotaxis-inspired term, in which the infection is propagated along the positive gradient of the susceptible population (from regions of low- to high-density of susceptibles), one may provide a more suitable description of these dynamics. This article introduces and analyzes a mathematical model of infectious disease incorporating a modified chemotaxis-type term. The model is analyzed mathematically and the well-posedness of the resulting PDE system is demonstrated. A series of numerical simulations are provided, demonstrating the ability of the model to naturally capture important phenomena not easily observed in standard diffusion models, including propagation over long spatial distances over short time scales and the emergence of localized infection hotspots