Dynamical analysis of an age-structured multi-group SIVS epidemic model

Area of Science:

• Epidemiology
• Mathematical Biology
• Disease Modeling

Background:

• Host heterogeneities like space, gender, and age significantly influence disease mechanisms and transmission.
• Understanding these factors is crucial for developing effective disease control strategies.

Purpose of the Study:

• To propose a multi-group Susceptible-Infected-Vaccinated-Susceptible (SIVS) epidemic model incorporating inter-group, intra-group, and age structures.
• To analyze the threshold dynamics of the proposed model.

Main Methods:

• Utilized renewal equations to derive the basic reproduction number as the spectral radius of the next-generation operator.
• Applied integral semigroup theory and Lyapunov methods to analyze the system's stability.
• Established the existence and uniqueness of the endemic equilibrium under specific parameter assumptions.

Main Results:

• The basic reproduction number was successfully obtained for the multi-group SIVS model.
• The existence and uniqueness of the endemic equilibrium were proven.
• Demonstrated that the system's threshold dynamics are entirely governed by the basic reproduction number.

Conclusions:

• Host heterogeneities are fundamental to understanding disease transmission.
• The developed multi-group SIVS model provides a robust framework for analyzing epidemic dynamics.
• The basic reproduction number serves as a critical threshold parameter for disease persistence.