A class of diffusive delayed viral infection models with general incidence function and cellular proliferation

Area of Science:

• Mathematical Biology
• Virology
• Epidemiology

Background:

• Infectious diseases caused by viruses such as hepatitis B virus (HBV) and hepatitis C virus (HCV) pose significant public health challenges.
• Mathematical modeling is essential for understanding virus dynamics and developing effective control strategies.

Purpose of the Study:

• To propose and analyze a novel three-dimensional mathematical model for virus dynamics.
• To incorporate key biological factors like absorption, cell proliferation, time delay, and a generalized incidence rate.
• To investigate the global asymptotic stability of the model's equilibria.

Main Methods:

• Construction of a Reaction-Diffusion-Ordinary Differential Equation model.
• Utilizing Lyapunov functionals to establish threshold dynamics.
• Analysis of local asymptotic stability.
• Proving boundedness, positivity, existence, and uniqueness of solutions for the initial and boundary value problem.
• Numerical simulations in one-dimensional space to illustrate theoretical findings.

Main Results:

• The model exhibits threshold dynamics determined by the basic reproduction number ($R$₀).
• If $R$₀ < 1, the uninfected equilibrium is globally asymptotically stable.
• If $R$₀ > 1, under certain conditions, the infected equilibrium is globally asymptotically stable.
• The existence, uniqueness, positivity, and boundedness of solutions were rigorously proven.

Conclusions:

• The developed mathematical model provides a robust framework for studying virus dynamics.
• The threshold dynamics identified are critical for predicting disease persistence or eradication.
• The findings generalize and improve upon existing results in viral dynamics modeling.