Eco-epidemiological model in the interaction betwen Pelecanidae and Tilapia

Abstract

Eco-epidemiology is the study that combines a model of disease spread with how the interaction between two or more species modelled together. In this article, an eco-epidemiological model is constructed to describe the interactions between Tilapia and Pelecanidae with infection in Pelecanidae. Poisoning (botulism) in the Tilapia population is caused by an infection of the Vibrio Vulnificus bacterium that can be transmitted to Pelecanidae through predation. A five-dimensional of ordinary nonlinear differential equations formed by dividing the whole population into bacterial populations (Vibrio Vulnificus), susceptible and infected prey (Tilapia) populations, susceptible and infected predator (Pelecanidae) populations. The infection process in Tilapia is modelled with the Holling-Type II response function. Mathematical analysis regarding the existence of the equilibrium points and the local stability criteria conducted analytically and numerically. Numerical simulations are given to show how disease factors in the prey population can influence predator and prey interactions.