Reduced modelling and optimal control of epidemiological individual‐based models with contact heterogeneity
Summary Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as they are able to take into account heterogeneity features, such as super‐spreaders, and describe the dynamics involved in small clusters. In r...
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| Published in | Optimal control applications & methods Vol. 45; no. 2; pp. 459 - 493 |
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| Main Authors | , , , , |
| Format | Journal Article |
| Language | English |
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01.03.2024
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| ISSN | 0143-2087 1099-1514 1099-1514 |
| DOI | 10.1002/oca.2970 |
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| Abstract | Summary
Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as they are able to take into account heterogeneity features, such as super‐spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are expensive to simulate and difficult to optimize, both in theory and in practice. By combining the reinforcement learning philosophy with reduced models, we propose a numerical approach to determine optimal health policies for a stochastic individual‐based model taking into account heterogeneity in the population. More precisely, we introduce a deterministic reduced population‐based model involving a neural network, designed to faithfully mimic the local dynamics of the more complex individual‐based model. Then the optimal control is determined by sequentially training the network until an optimal strategy for the population‐based model succeeds in also containing the epidemic when simulated on the individual‐based model. After describing the practical implementation of the method, several numerical tests are proposed to demonstrate its ability to determine controls for models with contact heterogeneity. |
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| AbstractList | Modelling epidemics using classical population-based models suffers from shortcomings that so-called individual-based models are able to overcome, as they are able to take into account heterogeneity features, such as super-spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are expensive to simulate and difficult to optimize, both in theory and in practice.By combining the reinforcement learning philosophy with reduced models, we propose a nu- merical approach to determine optimal health policies for a stochastic individual-based model taking into account heterogeneity in the population. More precisely, we introduce a deterministic reduced population-based model involving a neural network, designed to faithfully mimic the local dynamics of the more complex individual-based model. Then the optimal control is determined by sequentially training the network until an optimal strategy for the population-based model succeeds in also containing the epidemic when simulated on the individual-based model.After describing the practical implementation of the method, several numerical tests are pro- posed to demonstrate its ability to determine controls for models with contact heterogeneity. Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as they are able to take into account heterogeneity features, such as super‐spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are expensive to simulate and difficult to optimize, both in theory and in practice. By combining the reinforcement learning philosophy with reduced models, we propose a numerical approach to determine optimal health policies for a stochastic individual‐based model taking into account heterogeneity in the population. More precisely, we introduce a deterministic reduced population‐based model involving a neural network, designed to faithfully mimic the local dynamics of the more complex individual‐based model. Then the optimal control is determined by sequentially training the network until an optimal strategy for the population‐based model succeeds in also containing the epidemic when simulated on the individual‐based model. After describing the practical implementation of the method, several numerical tests are proposed to demonstrate its ability to determine controls for models with contact heterogeneity. Summary Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as they are able to take into account heterogeneity features, such as super‐spreaders, and describe the dynamics involved in small clusters. In return, such models often involve large graphs which are expensive to simulate and difficult to optimize, both in theory and in practice. By combining the reinforcement learning philosophy with reduced models, we propose a numerical approach to determine optimal health policies for a stochastic individual‐based model taking into account heterogeneity in the population. More precisely, we introduce a deterministic reduced population‐based model involving a neural network, designed to faithfully mimic the local dynamics of the more complex individual‐based model. Then the optimal control is determined by sequentially training the network until an optimal strategy for the population‐based model succeeds in also containing the epidemic when simulated on the individual‐based model. After describing the practical implementation of the method, several numerical tests are proposed to demonstrate its ability to determine controls for models with contact heterogeneity. |
| Author | Courtès, C. Franck, E. Navoret, L. Lutz, K. Privat, Y. |
| Author_xml | – sequence: 1 givenname: C. surname: Courtès fullname: Courtès, C. organization: Université de Strasbourg – sequence: 2 givenname: E. surname: Franck fullname: Franck, E. organization: IRMA, Université de Strasbourg – sequence: 3 givenname: K. surname: Lutz fullname: Lutz, K. organization: Ecole Centrale de Lyon – sequence: 4 givenname: L. surname: Navoret fullname: Navoret, L. organization: Université de Strasbourg – sequence: 5 givenname: Y. orcidid: 0000-0002-2039-7223 surname: Privat fullname: Privat, Y. email: yannick.privat@unistra.fr organization: Institut Universitaire de France (IUF) |
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| Keywords | Individual-based models Super-spreaders Reduced models Neural network Optimal control |
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Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as... Modelling epidemics using classical population‐based models suffers from shortcomings that so‐called individual‐based models are able to overcome, as they are... Modelling epidemics using classical population-based models suffers from shortcomings that so-called individual-based models are able to overcome, as they are... |
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| SubjectTerms | Computer Science Epidemics Heterogeneity individual‐based models Machine Learning Mathematical models Mathematics Modeling and Simulation Modelling neural network Neural networks Optimal control Optimization Optimization and Control reduced models super‐spreaders |
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| Title | Reduced modelling and optimal control of epidemiological individual‐based models with contact heterogeneity |
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