An age-structured model for coupling within-host and between-host dynamics in environmentally-driven infectious...

Area of Science:

• Mathematical epidemiology
• Infectious disease modeling
• Age-structured population dynamics

Background:

• Environmentally-driven infectious diseases require models integrating within-host and between-host dynamics.
• Existing models often simplify or isolate these crucial components.
• Age structure significantly impacts disease transmission patterns.

Purpose of the Study:

• To develop and analyze a novel age-structured epidemic model coupling fast within-host and slow between-host dynamics.
• To investigate the complex dynamical behaviors arising from this coupling.
• To establish conditions for disease persistence and eradication.

Main Methods:

• A mixed system of ordinary and partial differential equations.
• Analysis of isolated fast and slow subsystems.
• Investigation of the coupled slow system's equilibria and stability.
• Derivation of the basic reproduction number (R₀).
• Numerical simulations to validate analytical findings.

Main Results:

• The isolated slow system exhibits a globally asymptotically stable disease-free equilibrium when R₀ ≤ 1 and a locally asymptotically stable endemic equilibrium when R₀ > 1.
• The coupled slow system can possess two positive equilibria when R₀ < 1 and a unique endemic equilibrium when R₀ > 1.
• Stability analysis reveals conditions for local asymptotic stability of equilibria in the coupled system.
• Numerical examples suggest that certain analytical conditions may not be necessary in practice.
• The coupled system demonstrates richer dynamical behaviors compared to the isolated slow system.

Conclusions:

• The integration of within-host and between-host dynamics in an age-structured model leads to significantly more complex epidemiological outcomes.
• The basic reproduction number (R₀) remains a critical determinant of disease persistence.
• The study highlights the importance of considering coupled dynamics and age structure for accurate disease forecasting and control.