Unpredictability in seasonal infectious diseases spread

TL;DR

This paper investigates the unpredictability in seasonal infectious disease spread using a SEIRS model, revealing bistable dynamics and tipping points that can lead from predictable to chaotic, unpredictable outbreaks.

Contribution

It introduces a bifurcation analysis of a seasonal SEIRS model, highlighting the prevalence of bistability and tipping points related to unpredictability in disease dynamics.

Findings

Over 70% of parameter space shows coexistence of periodic and chaotic attractors.

Chaotic attractors are generally preferred over periodic ones.

Tipping points can cause transitions from predictable to unpredictable disease spread.

Abstract

In this work, we study the unpredictability of seasonal infectious diseases considering a SEIRS model with seasonal forcing. To investigate the dynamical behaviour, we compute bifurcation diagrams type hysteresis and their respective Lyapunov exponents. Our results from bifurcations and the largest Lyapunov exponent show bistable dynamics for all the parameters of the model. Choosing the inverse of latent period as control parameter, over 70% of the interval comprises the coexistence of periodic and chaotic attractors, bistable dynamics. Despite the competition between these attractors, the chaotic ones are preferred. The bistability occurs in two wide regions. One of these regions is limited by periodic attractors, while periodic and chaotic attractors bound the other. As the boundary of the second bistable region is composed of periodic and chaotic attractors, it is possible to interpret these critical points as tipping points. In other words, depending on the latent period, a periodic attractor (predictability) can evolve to a chaotic attractor (unpredictability). Therefore, we show that unpredictability is associated with bistable dynamics preferably chaotic, and, furthermore, there is a tipping point associated with unpredictable dynamics.