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A control theory approach to optimal pandemic mitigation.

Prakhar Godara1, Stephan Herminghaus1, Knut M Heidemann1

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Summary

This study identifies optimal pandemic control strategies using control theory within SIR models. It balances herd immunity goals with minimizing societal costs and healthcare system capacity constraints.

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Control Theory

Background:

  • Homogeneous susceptible-infected-recovered (SIR) models are foundational for understanding infectious disease dynamics.
  • Societal control measures (e.g., lockdowns, social distancing) significantly impact pandemic spread but incur costs.
  • Public health systems have limited capacity, necessitating constraints on infection levels.

Purpose of the Study:

  • To identify optimal pandemic mitigation strategies using a control theory approach.
  • To derive conditions for achieving herd immunity while minimizing societal control costs.
  • To analyze strategies under public health system capacity constraints and consider immune response decay.

Main Methods:

  • Application of control theory to homogeneous SIR models.
  • Derivation of optimality conditions using variational methods.
  • Numerical verification of derived strategies for various cost functions.
  • Inclusion and analysis of immune response decay post-recovery.

Main Results:

  • General conditions for optimal herd immunity strategies were derived.
  • Minimization of societal control costs was achieved under capacity constraints.
  • The feasibility of herd immunity strategies is affected by immune response decay.
  • Variational and numerical methods confirmed the derived optimal strategies.

Conclusions:

  • Control theory provides a robust framework for optimizing pandemic mitigation.
  • Balancing herd immunity, societal costs, and healthcare capacity is crucial for effective pandemic response.
  • Immune response decay poses challenges for long-term herd immunity strategies.