Neural nets for modelling of scenarios and control of epidemics
Keywords: neural network, forecasting, control infectious disease, mathematical modeling, differential equation
TL;DR: The work considers application of physically informed neural nets to numerical analysis of epidemics, effects of introduction and ending of restrictive measures in SIR models and control in form of Hamilton-Jacobi-Bellman (HJB) equation.
Abstract: The work considers application of physically informed neural nets to numerical analysis of epidemics, effects of introduction and ending of restrictive measures in SIR models and control in form of Hamilton-Jacobi-Bellman (HJB) equation.
Control problems for ordinary differential equations describe epidemic, social and other physics processes. We propose several scenarios of possible epidemic outcome and formulate of the optimal control problem. The usage of physically informed neural nets substantially decreases necessary man-hours to present characteristics of a differential equation, and total computational time, if according to hardware (GPUs) is available.
The proposed deep learning algorithm is compared to classical collocation approach. It is used in the most numerically challenging part of the problem, the nonlinear HJB partial differential equation, while classical methods are applied to main ODE part of SIR-based model.
Numerical results show substantial effect of induced control in decrease of total number of infected and time of active spread of epidemic.
This work is supported by the Government research assignment for Sobolev Institute of Mathematics SB RAS, project FWNF-2024-0002.
Submission Number: 35
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