Differential Epidemic Models and Scenarios of Restrictive Measures
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 t...
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| Published in | Computational mathematics and mathematical physics Vol. 65; no. 6; pp. 1300 - 1313 |
|---|---|
| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
Moscow
Pleiades Publishing
01.06.2025
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0965-5425 1555-6662 |
| DOI | 10.1134/S0965542525700459 |
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| 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. |
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| AbstractList | 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. |
| Author | Krivorotko, O. I. Kabanikhin, S. I. Neverov, A. V. |
| Author_xml | – sequence: 1 givenname: S. I. surname: Kabanikhin fullname: Kabanikhin, S. I. organization: Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences – sequence: 2 givenname: O. I. surname: Krivorotko fullname: Krivorotko, O. I. email: krivorotko.olya@mail.ru organization: Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences – sequence: 3 givenname: A. V. surname: Neverov fullname: Neverov, A. V. organization: Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences |
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| Keywords | epidemiology Hamilton–Jacobi–Bellman equation optimization inverse problems SIR models optimal control development scenarios |
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| SubjectTerms | Algorithms Computational Mathematics and Numerical Analysis Coronaviruses COVID-19 vaccines Epidemics Exact solutions Feedback control Immunization Infections Infectious diseases Influenza Inverse problems Mathematical models Mathematics Mathematics and Statistics Neural networks Numerical analysis Optimal control Ordinary Differential Equation Ordinary differential equations Pandemics Public health Quarantine Simulation Social distancing |
| Title | Differential Epidemic Models and Scenarios of Restrictive Measures |
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