Threshold dynamics and optimal control on an age-structured SIRS epidemic model with vaccination
1School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, China.
Mathematical Biosciences and Engineering : MBE
|November 24, 2021
Summary
This study introduces vaccination control into an age-structured SIRS model, analyzing disease dynamics and stability. Optimal vaccination strategies were determined using Hamilton-Jacobi-Bellman equations for effective disease management.
Area of Science:
- Epidemiology
- Mathematical Biology
- Control Theory
Background:
- Infectious disease modeling is crucial for public health.
- Age-structured models provide a more realistic representation of disease transmission.
- Vaccination is a key intervention for controlling epidemics.
Purpose of the Study:
- To analyze the global stability of equilibria in an age-structured SIRS model with vaccination.
- To derive an optimal vaccination control strategy using dynamic programming.
- To investigate the impact of vaccination on disease dynamics.
Main Methods:
- Development of an age-structured SIRS epidemiological model.
- Application of iterative methods to determine the global stability of endemic equilibrium.
- Utilizing the Hamilton-Jacobi-Bellman (HJB) equation and Bellman's principle of optimality.
- Proving the existence of viscosity solutions for the HJB equation.
Main Results:
- The basic reproduction number ($R_0$) was determined.
- Conditions for the global asymptotic stability of disease-free and endemic equilibria were established based on $R_0$.
- An optimal vaccination control strategy was derived.
- Numerical simulations validated the analytical findings.
Conclusions:
- Vaccination significantly impacts disease dynamics and stability in age-structured populations.
- The derived optimal control strategy offers a framework for effective vaccination campaigns.
- Mathematical modeling provides valuable insights into infectious disease management.
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