A brief discussion about a predator-prey model including disease in predators with the delay effect

Abstract

Prey-predator interactions in an ecosystem are greatly influenced by the gestation delay and disease. To analyze the complex dynamics of the prey-predator interaction, we have proposed a three-tire delayed eco-epidemic model including disease in the predator population. During the study of this model, we establish the positivity and boundedness of the proposed model and also find all possible equilibrium points with their local and global stability condition in absence and presence of gestation delay. Analytical and numerical studies explain the existence of Transcritical and Hopf-bifurcations. Using sensitivity analysis, we examine the positive and negative impact of all model parameters and identify the most significant parameters. The main objective is to understand how disease and gestation delay influence the populations of this proposed model and also examine the combined effect of both gestation delay and disease infection rate. Furthermore, we incorporate the disease transmission delay and explore the combined effect of both gestation delay and disease transmission delay on the solutions of the proposed system. Numerically, we have demonstrated that the system experiences only steady and periodic behavior under the influence of gestation delay, but under the combined impact of both gestation delay and disease transmission delay, the system undergoes stable, one-periodic, two-periodic, and chaotic regimes.