Lyapunov functional for virus infection model with diffusion and state-dependent delays

Area of Science:

• Mathematical modeling
• Virology
• Dynamical systems theory

Background:

• Virus dynamics are complex, influenced by factors like diffusion, time delays, and host-pathogen interactions.
• Understanding the stability of viral populations is crucial for predicting disease progression and developing interventions.
• Previous models often simplify these interactions, necessitating more comprehensive approaches.

Purpose of the Study:

• To investigate a virus dynamics model incorporating diffusion, state-dependent delays, and a general nonlinear functional response.
• To establish the stability of the interior equilibrium for this complex dynamical system.
• To extend the developed methodology to virus models with logistic growth rates.

Main Methods:

• Construction of the dynamical system on a nonlinear metric space.
• Application of a novel Lyapunov functional to rigorously prove the stability of the interior equilibrium.
• Extension of the analytical framework to accommodate logistic growth dynamics.

Main Results:

• The stability of the interior equilibrium for the proposed virus dynamics model was successfully established.
• A novel Lyapunov functional was developed and validated for stability analysis.
• The methodology was demonstrated to be applicable to virus models with logistic growth.

Conclusions:

• The study provides a robust mathematical framework for analyzing virus dynamics with complex features.
• The developed Lyapunov functional offers a powerful tool for stability assessment in related epidemiological models.
• The findings contribute to a deeper understanding of viral persistence and control strategies.