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Abstract <p>Algorithms for calculating the spread of epidemics and analyzing the consequences of introducing or lifting restrictive measures based on an SIR model and the Hamilton–Jacobi–Bellman equations are considered. After studying the identifiability and sensitivity of SIR models, their well-posedness in the vicinity of the exact solution, and the convergence of numerical algorithms for solving direct and inverse problems, an optimal control problem is formulated. The results of numerical simulation showed that feedback control can help determine the vaccination policy. The use of physics-informed neural networks (PINNs) made it possible to reduce the calculation time by five times, which is important for promptly changing restrictive measures.</p>

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Differential Epidemic Models and Scenarios of Restrictive Measures

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • S. I. Kabanikhin,
  • O. I. Krivorotko,
  • A. V. Neverov

摘要

Abstract

Algorithms for calculating the spread of epidemics and analyzing the consequences of introducing or lifting restrictive measures based on an SIR model and the Hamilton–Jacobi–Bellman equations are considered. After studying the identifiability and sensitivity of SIR models, their well-posedness in the vicinity of the exact solution, and the convergence of numerical algorithms for solving direct and inverse problems, an optimal control problem is formulated. The results of numerical simulation showed that feedback control can help determine the vaccination policy. The use of physics-informed neural networks (PINNs) made it possible to reduce the calculation time by five times, which is important for promptly changing restrictive measures.