Chaos in disease outbreaks among prey

Abstract

Epidemics are highly unpredictable, and so are real-world population dynamics. In this paper, we examine a dynamical model of an ecosystem with one predator and two prey species of which one carries a disease. We find that the system behaves chaotically for a wide range of parameters. Using the allometric mass scaling of animal and disease lifetimes, we predict chaos if (a) the disease is infectious enough to persist, and (b) it affects the larger prey species. This provides another example of chaos in a Lotka-Volterra system and a possible explanation for the apparent randomness of epizootic outbreaks.

The Chaotic Behavior of the Spread of Infection During the COVID-19 Pandemic in the United States and Globally

“…The study indicated that chaos mostly occurs when the disease spreads into more prey species. Interestingly, the study verified chaotic behavior in a relatively minimal eco-epidemiological system [13].…”

“…Sun et al [12] proposed a susceptible-infectious-recovered-susceptible (SIRS) model, and demonstrated the model's chaotic properties based on LE indices. Eilersen et al [13] described an ecoepidemiological model with a two-prey one-predator ecosystem, where one carries a disease. To assess whether the dynamic model is chaotic, the study determined the LE.…”

Epidemiologically and Socio-economically Optimal Policies via Bayesian Optimization

“…testing and quarantining models to be checked for false positive and missed detection rates. Lastly, non-linear systems with negative feedback loops such as epidemiological models, are known to exhibit chaotic behavior (Bolker 1993;Eilersen et al 2020). It is interesting how techniques like ESOP can be adapted to handle such systems.…”

Demand–capacity modelling and COVID‐19 disease: identifying themes for future NHS planning

“…COVID‐19 will do this even if its incidence becomes low and it does not markedly increase the mean demand; even at low incidence it will affect variability of demand. The mathematical proof of this lies in an equation called the ‘logistic map’ (Appendix 1), which is widely used to model population growth [16,17], synonymous with disease spread, for viral populations [https://arxiv.org/ftp/arxiv/papers/2003/2003.05681.pdf]. Although the initial growth/spread of virus is initially exponential, the logistic map shows that later, population size/infection rates become cyclical.…”

“…COVID-19 will do this even if its incidence becomes low and it does not markedly increase the mean demand; even at low incidence it will affect variability of demand. The mathematical proof of this lies in an equation called the 'logistic map' (Appendix 1), which is widely used to model population growth [16,17], synonymous with disease spread, for viral populations Although the initial growth/spread of virus is initially exponential, the logistic map shows that later, population size/infection rates become cyclical. This variability is greatly affected by very small changes in the underlying growth rate (infectivity, or r or R0 value) that do not themselves change the mean, and in turn this is reflected in demand on services overall (Fig.…”