Controlling infectious diseases: the decisive phase effect on a seasonal vaccination strategy

TL;DR

This paper investigates how phase control of seasonal vaccination strategies can suppress chaotic dynamics in epidemic models, potentially leading to more predictable disease outbreaks.

Contribution

It introduces a phase control method applied to the seasonally forced SIR model to effectively suppress chaos through weak perturbations.

Findings

Phase difference significantly influences chaos control effectiveness.

Numerical simulations demonstrate chaos suppression with phase adjustments.

Control strategy offers a new approach to managing epidemic unpredictability.

Abstract

The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that, under seasonal variation, the incidence rates of some endemic infectious diseases fluctuate dramatically and the dynamics is often characterized by chaotic oscillations in the absence of specific vaccination programs. In fact, the existence of chaotic behavior has been precisely stated in the literature as a noticeable feature in the dynamics of the classical Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However, in the context of epidemiology, chaos is often regarded as an undesirable phenomenon associated with the unpredictability of infectious diseases. As a consequence, the problem of converting chaotic motions into regular motions becomes particularly relevant. In this article, we consider the phase control technique applied to the seasonally forced SIR epidemic model to suppress chaos. Interestingly, this method of controlling chaos takes on a clear meaning as a weak perturbation on a seasonal vaccination strategy. Numerical simulations show that the phase difference between the two periodic forces - contact rate and vaccination - plays a very important role in controlling chaos.