Almost periodic solutions for a SVIR epidemic model with relapse

Area of Science:

• Epidemiology
• Mathematical Biology
• Dynamical Systems

Background:

• Understanding infectious disease dynamics is crucial for public health interventions.
• Nonautonomous models capture time-varying environmental factors influencing disease spread.
• Relapse (recurrence) is a key factor in many infectious diseases, yet often simplified in models.

Purpose of the Study:

• To develop and analyze a nonautonomous SVIR (Susceptible-Vaccinated-Infected-Recovered) epidemic model incorporating a relapse rate.
• To investigate the existence, uniqueness, and global attractivity of almost periodic solutions.
• To assess the necessity of including relapse rates and the impact of vaccination and relapse on disease control.

Main Methods:

• Mathematical modeling using a system of ordinary differential equations.
• Proof of system permanence.
• Construction of a Lyapunov function to establish the existence and uniqueness of a globally attractive almost periodic solution.
• Numerical simulations to validate theoretical results and explore parameter influences.

Main Results:

• The nonautonomous SVIR model with relapse is shown to be permanent.
• A unique, globally attractive, almost periodic solution exists for the system.
• Analysis confirms the significance of incorporating relapse rates into epidemic models.
• Numerical simulations demonstrate the impact of vaccination and relapse rates on disease dynamics.

Conclusions:

• The study provides a rigorous mathematical framework for understanding infectious diseases with relapse.
• Increasing vaccination rates and decreasing disease recurrence rates are essential strategies for effective epidemic control.
• The findings highlight the importance of considering disease-specific factors like relapse in epidemiological modeling.