Backward bifurcation and oscillations in a nested immuno-eco-epidemiological model

Area of Science:

• Mathematical Biology
• Ecology
• Epidemiology
• Immunology

Background:

• Competition between species can influence disease dynamics and population persistence.
• Stress-induced competition, where one species lowers another's immune response, is a critical but understudied ecological interaction.
• Existing models often simplify complex ecological and epidemiological interactions.

Purpose of the Study:

• To develop and analyze a novel partial differential equation (PDE) immuno-eco-epidemiological model incorporating stress-induced competition.
• To investigate the impact of stress-induced competition on disease dynamics, species coexistence, and population stability.
• To explore the utility of reduced ordinary differential equation (ODE) models for understanding complex PDE models.

Main Methods:

• Formulation of a partial differential equation (PDE) model for interacting species, one diseased and one competing.
• Reduction of the PDE model to a three-dimensional ordinary differential equation (ODE) model under specific assumptions (chronic disease, rapid within-host dynamics).
• Analysis of the ODE model for phenomena such as backward bifurcation and sustained oscillations.
• Comparison of ODE model findings with the behavior of the parent PDE model.

Main Results:

• The ODE model exhibits backward bifurcation and sustained oscillations, driven by stress-induced competition.
• Stress-induced competition enables the competing species to persist even when its invasion number is below one.
• In the PDE model, stress-induced competition destabilizes the coexistence equilibrium, leading to sustained oscillations.
• The simplified ODE model effectively detects backward bifurcation and oscillations present in the more complex PDE model.

Conclusions:

• Stress-induced competition is a significant factor that can alter ecological and epidemiological outcomes, promoting species coexistence and instability.
• Reduced ODE models can serve as valuable tools for analyzing and understanding complex PDE models in immuno-eco-epidemiology.
• Complex ecological systems with disease and competition can be effectively studied using simplified, well-designed ODE models.