Deterministic and stochastic analysis of an eco-epidemiological model

Area of Science:

• Ecology
• Epidemiology
• Mathematical Biology

Background:

• Chronic wasting disease (CWD) is a contagious prion disease affecting deer family members.
• CWD poses a significant threat to ecosystem stability where deer populations are abundant.

Purpose of the Study:

• To develop and analyze a mathematical eco-epidemic model for CWD transmission in deer.
• To investigate the stability and dynamics of CWD spread using mathematical approaches.

Main Methods:

• The study employs a deterministic eco-epidemic model to simulate CWD dynamics.
• Mathematical techniques including stability analysis, Lyapunov functions, and bifurcation theory are utilized.
• Stochastic stability is explored by introducing white noise into the model.

Main Results:

• The model's boundedness was established, and its equilibria were analyzed for stability.
• Conditions for disease persistence and the global stability of the endemic equilibrium were determined.
• Hopf-bifurcation was analyzed, and numerical simulations validated the model's robustness against stochastic perturbations.

Conclusions:

• The deterministic eco-epidemic model provides a robust framework for understanding CWD dynamics.
• The model's stability analysis offers insights into disease persistence and spread within deer populations.
• Stochastic perturbations do not significantly alter the core dynamics predicted by the deterministic model.