Mathematical Modeling of an Eco-epidemiological Prey-predator System: Impact of Time Delay and Nonlinear Harvesting

• Published in: International journal of applied and computational mathematics Vol. 11; no. 5
• Main Authors: Raw, S. N., Sahu, S. R.
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.10.2025; Springer Nature B.V
• Subjects: Applications of Mathematics; Computational Science and Engineering; Disease control; Fisheries; Infections; Mathematical analysis; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Nuclear Energy; Operations Research/Decision Theory; Original Paper; Predator-prey simulation; Predators; Theoretical; Time lag; Chaos; 34D45; 24K23; 92D25; 34C23; Incubation delay; Asymptotically stable; Chilika lake; Intra-specific competition
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-01953-3

In this paper, we investigate an eco-epidemiological prey-predator model with delay in which the prey population is affected by an infectious disease. The prey is divided into two subclasses: susceptible and infected, both subject to a Michaelis–Menten type harvesting function. A time delay is included to capture the incubation period, reflecting that disease transmission doesn’t happen instantly. We analyze comprehensive mathematical analyses such as the existence and uniqueness of solutions, positivity and boundedness of the system, the existence and stability of equilibria, and the direction of bifurcating periodic solutions. A disease-free equilibrium exists and is shown to be globally stable. A longer delay may prevent infected prey from becoming infectious, indicating a positive role of incubation delay in disease control. Our results reveal that low predator density is insufficient to suppress the progression of infection, while a high infection rate significantly reduces the growth of the susceptible prey population. A high infection rate among prey leads to predator extinction. The analysis suggests that over harvesting of healthy prey and low harvesting of infected prey contribute to fisheries decline and ecosystem degradation. Numerical simulations support the analytical results and demonstrate that the chaotic dynamics can be regulated by increasing the delay parameter.