Differential Epidemic Models and Scenarios of Restrictive Measures

• Published in: Computational mathematics and mathematical physics Vol. 65; no. 6; pp. 1300 - 1313
• Main Authors: Kabanikhin, S. I., Krivorotko, O. I., Neverov, A. V.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.06.2025; Springer Nature B.V
• Subjects: 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; Europe; China; epidemiology; Hamilton–Jacobi–Bellman equation; optimization; inverse problems; SIR models; optimal control; development scenarios
• ISSN: 0965-5425; 1555-6662
• DOI: 10.1134/S0965542525700459

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.