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This study introduces a structured SIR model for comparing vaccination strategies. It demonstrates how different dosing schedules significantly alter disease progression and identifies optimal vaccination controls using cost functions.

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Public Health

Background:

  • Infectious disease modeling is crucial for understanding transmission dynamics.
  • Vaccination strategies are key interventions but require careful planning.
  • Optimizing vaccination requires robust analytical frameworks.

Purpose of the Study:

  • To develop a modeling framework for evaluating diverse vaccination strategies.
  • To identify optimal vaccination controls based on defined cost functions.
  • To analyze the impact of vaccination timing and population targeting.

Main Methods:

  • Utilized a structured compartmental Susceptible-Infectious-Recovered (SIR) model.
  • Incorporated vaccination strategies dosed by age, time, and population proportion.
  • Introduced cost functions to define and optimize vaccination strategies.
  • Applied mathematical analysis to ensure the existence of optimal controls.

Main Results:

  • Demonstrated that vaccination prescription significantly influences disease evolution.
  • Established Lipschitz continuous dependence of costs on control parameters.
  • Confirmed the existence of optimal vaccination strategies.
  • Suggested methods like steepest descent for finding optimal controls.

Conclusions:

  • The proposed SIR modeling framework effectively compares vaccination strategies.
  • Optimal vaccination controls can be rigorously identified and sought.
  • This work provides a foundation for evidence-based public health vaccination policies.