A new view on migration processes between SIR centra: an account of the different dynamics of host and guest

TL;DR

This paper introduces a novel SIR epidemic model that separately analyzes host and guest migration, revealing that accounting for both significantly accelerates epidemic spread in a network of populations.

Contribution

It presents a new model distinguishing host and guest migrations, providing a more realistic depiction of epidemic dynamics across multiple centers.

Findings

Separately modeling host and guest migration alters epidemic spread predictions.

Guest susceptibles can become infected and influence the epidemic dynamics.

Accounting for both migration fluxes increases the speed of epidemic spread.

Abstract

We study an epidemic propagation between $M$ population centra. The novelty of the model is in analyzing the migration of host (remaining in the same centre) and guest (migrated to another centre) populations separately. Even in the simplest case $M=2$, this modification is justified because it gives a more realistic description of migration processes. This becomes evident in a purely migration model with vanishing epidemic parameters. It is important to account for a certain number of guest susceptible present in non-host cenrta because these susceptible may be infected and return to the host node as infectives. The flux of such infectives is not negligible and is comparable with the flux of host infectives migrated to other centra, because the return rate of a guest individual will, by nature, tend to be high. It is shown that taking account of both fluxes of infectives noticeably increases the speed of epidemic spread in a 1D lattice of identical SIR centra.