A delayed prey-predator system with parasitic infection

Area of Science:

• Mathematical Biology
• Ecology
• Epidemiology

Background:

• Parasitic infections can significantly alter host population dynamics.
• Prey-predator interactions are fundamental ecological processes.
• Functional responses describe predator feeding rates based on prey availability.

Purpose of the Study:

• To analyze a mathematical model of a prey-predator system with parasitic infection.
• To investigate the impact of parasite infection on both prey and predator populations.
• To determine the criteria for population persistence and extinction within this system.

Main Methods:

• Development of a mathematical model for the prey-predator system.
• Analysis of population persistence and extinction criteria.
• Investigation of the stability of the interior equilibrium point.
• Incorporation and analysis of time delay in the system dynamics.
• Verification of results through computer simulations.

Main Results:

• Derived criteria for the persistence and extinction of prey and predator populations.
• Discussed the stability of the interior equilibrium point.
• Identified the destabilizing effect of time delay on the system.
• Predator functional response modeled as a weighted sum of prey abundances.

Conclusions:

• Parasitic infection influences prey-predator dynamics.
• Time delays can introduce instability into ecological models.
• The model provides insights into the complex interactions within infected ecosystems.