Infectious Disease Induces Emergent Oscillations, Extinction and Changes in Community Persistence in a Food Chain

Food webs have been extensively studied from both ecological and mathematical aspects.

However, most of the models studied in this area do not capture the effects of infectious diseases simultaneously.

Recently, the idea of including an infectious disease in a food web model has been investigated.

We study and simulate a small food chain consisting of only prey, predators, and apex predators governed by the generalized Lotka-Volterra equations, and we implement the Susceptible-Infected-Recovered (SIR) model on only one of the species at a time in the food chain.

To study the effects of an infectious disease on the food chain, we introduce a new parameter that increases the predation rate by a factor of $w$ and decreases the hunting rate by a factor of $1/w$ for infected species.

When the infectious disease is present in predators, we observe that predators do not become extinct under any set of parameters; however, an oscillation in their population size occurs under some circumstances, which we do not observe in ordinary SIR or the generalized Lotka-Volterra equations alone.

When an infectious disease is present in apex predators, oscillations in the population size do not happen; but if the set of parameters is in a specific range the apex predators may become extinct.

Furthermore, the chance of survival of the community, known as community persistence, increases for the predators and decreases for the apex predators.