Some threshold and stability results for epidemic models with a density-dependent death rate

Area of Science:

• Epidemiology
• Mathematical Biology
• Ecology

Background:

• Classical epidemic models often assume constant birth, death, and contact rates, irrespective of population size.
• These assumptions may not hold true for diseases in animal and insect populations where resource competition influences death rates.

Purpose of the Study:

• To investigate two epidemic models incorporating density-dependent death rates.
• To analyze the equilibrium levels of disease incidence and their stability.
• To provide biological interpretations and numerical simulations for these models.

Main Methods:

• Development and analysis of two mathematical models for infectious disease dynamics.
• Determination of equilibrium states for disease incidence.
• Stability analysis of these equilibrium states using perturbation methods.
• Numerical simulations to illustrate model behavior.

Main Results:

• Identified equilibrium levels of disease incidence in density-dependent models.
• Assessed the stability of these equilibrium points.
• Demonstrated the influence of density dependence on disease dynamics through simulations.

Conclusions:

• Density-dependent death rates significantly alter epidemic dynamics compared to classical models.
• The stability of disease equilibria is sensitive to population density.
• These models offer a more realistic framework for studying infectious diseases in ecologically relevant populations.