Spread of infectious diseases: Effects of the treatment of population

TL;DR

This study introduces the SHIR model, a modified metapopulation SIR model with a latent period, analyzing how infectious disease spread is affected by individual travel restrictions during different infection stages.

Contribution

The paper presents the SHIR model with a latent period, highlighting differences in disease spread dynamics and final size distributions compared to traditional SIR models.

Findings

Final size distribution in Monte Carlo simulations is similar for SIR and SHIR models.

Reaction-diffusion systems show a discontinuous jump in SHIR model's final size distribution.

Discontinuous jump is an artifact due to termination condition, not an inherent model property.

Abstract

In a metapopulation network, infectious diseases spread widely because of the travel of individuals. In the present study, we consider a modified metapopulation Susceptible-Infected-Removed (SIR) model with a latent period, which we call the SHIR model. In the SHIR model, an infectious period is divided into two stages. In the first stage, which corresponds to the latent period, infectious individuals can travel. However, in the second stage, the same individuals cannot travel since they are seriously ill. Final size distributions of the metapopulation SIR and SHIR models are simulated with two different methods and compared. In Monte Carlo simulations, in which the population is treated as an integer, the distributions show similar behavior. However, in reaction-diffusion systems, in which the population is treated as a real number, the final size distribution of the SHIR model has a discontinuous jump, and that of the SIR model shows a continuous transition. The discontinuous jump is found to be an artifact that occurs owing to an inappropriate termination condition.