Epidemic oscillations: Interaction between delays and seasonality

TL;DR

This paper develops a generalized SIRS epidemic model incorporating realistic infection and immunity durations, revealing how delays and seasonal factors induce transitions between steady and oscillatory disease dynamics.

Contribution

It introduces a comprehensive SIRS model with distributed delays for infection and immunity, analyzing how these factors interact with seasonality to produce complex epidemic oscillations.

Findings

Delays in infection and immunity durations can cause epidemic oscillations.

Seasonality interacts with delays to induce transitions between endemic and oscillating states.

The model captures more realistic epidemic behaviors than traditional constant-rate models.

Abstract

Traditional epidemic models consider that individual processes occur at constant rates. That is, an infected individual has a constant probability per unit time of recovering from infection after contagion. This assumption certainly fails for almost all infectious diseases, in which the infection time usually follows a probability distribution more or less spread around a mean value. We show a general treatment for an SIRS model in which both the infected and the immune phases admit such a description. The general behavior of the system shows transitions between endemic and oscillating situations that could be relevant in many real scenarios. The interaction with the other main source of oscillations, seasonality, is also discussed.