Metapopulation dynamics of a respiratory disease with infection during travel

TL;DR

This paper develops a compartmental model for respiratory disease spread across interconnected patches, emphasizing the impact of travel, network structure, and multiple strains on disease dynamics and control strategies.

Contribution

It introduces a novel model incorporating infection during travel, network topology effects, and multi-strain interactions, providing new insights into disease stability and control.

Findings

Network structure significantly influences disease transmission.

Infection during travel can destabilize disease-free equilibrium.

Exit screening effects vary depending on patch prevalence.

Abstract

We formulate a compartmental model for the propagation of a respiratory disease in a patchy environment. The patches are connected through the mobility of individuals, and we assume that disease transmission and recovery are possible during travel. Moreover, the migration terms are assumed to depend on the distance between patches and the perceived severity of the disease. The positivity and boundedness of the model solutions are discussed. We analytically show the existence and global asymptotic stability of the disease-free equilibrium. We study three different network topologies numerically and find that underlying network structure is crucial for disease transmission. Further numerical simulations reveal that infection during travel has the potential to change the stability of disease-free equilibrium from stable to unstable. The coupling strength and transmission coefficients are also very crucial in disease propagation. Different exit screening scenarios indicate that the patch with the highest prevalence may have adverse effects but other patches will be benefited from exit screening. Furthermore, while studying the multi-strain dynamics, it is observed that two co-circulating strains will not persist simultaneously in the community but only one of the strains may persist in the long run. Transmission coefficients corresponding to the second strain are very crucial and show threshold like behavior with respect to the equilibrium density of the second strain.