Predator-prey model with disease infection in both populations

Area of Science:

• Ecology
• Epidemiology
• Mathematical Biology

Background:

• Predator-prey dynamics are crucial for ecosystem stability.
• Disease transmission between species (spillover) can significantly alter ecological interactions.
• Previous models often focused on disease in a single population.

Purpose of the Study:

• To develop a predator-prey model incorporating disease in both populations.
• To investigate how cross-species disease transmission affects population dynamics and coexistence.
• To analyze the conditions under which disease can lead to extinction or eradication.

Main Methods:

• Mathematical modeling using differential equations.
• Local stability analysis of system equilibria.
• Derivation and analysis of threshold parameters (ecological threshold number, disease basic reproduction number).
• Analytical and numerical simulations.

Main Results:

• Identified coupled conditions determining ecosystem stability and disease endemicity.
• Demonstrated that disease can cause predator extinction even when coexistence is otherwise possible.
• Showed that predation on infected prey can lead to disease eradication, potentially resulting in disease-free periodic solutions.
• Observed complex dynamics including bistability and periodic oscillations in both disease-free and endemic states.

Conclusions:

• Disease in both predator and prey populations can have varied impacts, either promoting or impairing coexistence.
• The specific effects of disease depend heavily on the interplay of ecological and epidemiological factors.
• The model highlights the importance of considering inter-species disease dynamics for accurate ecological predictions.