A modified Leslie-Gower predator-prey model with alternative food and selective predation of noninfected prey

Infectious diseases affect prey populations, and predators choosing susceptible prey may lead to the extinction of the prey population. We propose a mathematical model of prey-predator interaction with the prey population divided into two classes: susceptible and infected. The susceptible prey subpopulation becomes infected by direct contact with the infected prey subpopulation, and the predator consumes only susceptible prey. An analysis of the model enabled the establishment of thresholds for the spread of disease in the absence and presence of predators. In the absence of predators, we obtain the classic basic reproduction numberR(0), and in the presence of predators, we obtain a new thresholdR0P, which measures the effect of predators in the disease spread. Furthermore, these thresholds establish conditions for the existence and stability of biologically viable equilibrium points. Using numerical simulations, we determined the different biological characteristics of the model and illustrated the analytical results.

Automated summary

The model divides the prey population into susceptible and infected classes, with thresholds for disease spread and conditions for biological equilibrium points established through mathematical analysis. Numerical simulations are used to determine the biological characteristics of the model and illustrate the analytical results.