Spread of Infectious Diseases with a Latent Period

TL;DR

This paper introduces the SIIR model, a modified metapopulation SIR model that incorporates a latent period with two infectious stages, leading to more accurate epidemic spread predictions.

Contribution

The paper proposes a novel SIIR model with two infectious stages, capturing the effects of a latent period on disease dynamics in complex networks.

Findings

Discontinuous final size distribution observed.

Infected stage spreads disease similarly to seriously ill stage.

Effective recovery rate is reduced due to the latent period.

Abstract

Infectious diseases spread through human networks. Susceptible-Infected-Removed (SIR) model is one of the epidemic models to describe infection dynamics on a complex network connecting individuals. In the metapopulation SIR model, each node represents a population (group) which has many individuals. In this paper, we propose a modified metapopulation SIR model in which a latent period is taken into account. We call it SIIR model. We divide the infection period into two stages: an infected stage, which is the same as the previous model, and a seriously ill stage, in which individuals are infected and cannot move to the other populations. The two infectious stages in our modified metapopulation SIR model produce a discontinuous final size distribution. Individuals in the infected stage spread the disease like individuals in the seriously ill stage and never recover directly, which makes an effective recovery rate smaller than the given recovery rate.