Optimal Vaccination Strategy in the Stochastic Epidemic Limited-Treatment Model.

Area of Science:

• Epidemiology
• Mathematical Biology
• Public Health

Background:

• The SIR (Susceptible-Infectious-Recovered) model is a fundamental tool for understanding infectious disease dynamics.
• Stochastic variations and the interplay of vaccination and treatment significantly impact epidemic trajectories.
• Optimizing public health interventions requires robust mathematical frameworks.

Purpose of the Study:

• To analyze the stochastic SIR epidemic model incorporating vaccination and limited treatment.
• To develop and propose a method for determining an optimal vaccination strategy.
• To minimize a defined cost functional related to disease control and resource allocation.

Main Methods:

• Stochastic differential equations to model epidemic dynamics.
• Optimal control theory to derive vaccination strategies.
• Numerical simulations to evaluate the proposed method.

Main Results:

• The study presents a novel method for calculating optimal vaccination policies.
• The proposed strategy effectively balances disease suppression with intervention costs.
• Sensitivity analysis demonstrates the robustness of the optimal strategy under varying parameters.

Conclusions:

• The developed method provides a valuable tool for public health decision-making.
• Optimizing vaccination strategies is crucial for managing stochastic epidemics efficiently.
• Further research can extend this approach to more complex epidemiological models.