Stochastic Optimal Control of an Epidemic Under Partial Information
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912267015028736 |
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| author | Njiasse, Ibrahim Mbouandi Kamkumo, Florent Ouabo Wunderlich, Ralf |
| author_facet | Njiasse, Ibrahim Mbouandi Kamkumo, Florent Ouabo Wunderlich, Ralf |
| contents | In this paper, we address a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the state dynamics of the epidemic, we apply filtering arguments to transform the partially observable stochastic optimal control problem into an optimal control problem with complete information. This transformed problem is treated as a Markov decision process. The associated Bellman equation is solved numerically using optimal quantization methods for approximating the expectations involved to mitigate the curse of dimensionality. We implement two approaches, the first involves state discretization coupled with linear interpolation of the value function at non-grid points. The second utilizes a parametrization of the value function with educated ansatz functions. Extensive numerical experiments are presented to demonstrate the efficacy of both methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06804 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stochastic Optimal Control of an Epidemic Under Partial Information Njiasse, Ibrahim Mbouandi Kamkumo, Florent Ouabo Wunderlich, Ralf Optimization and Control 93E20, 92D30, 90C40, 92-10, 90-80 In this paper, we address a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the state dynamics of the epidemic, we apply filtering arguments to transform the partially observable stochastic optimal control problem into an optimal control problem with complete information. This transformed problem is treated as a Markov decision process. The associated Bellman equation is solved numerically using optimal quantization methods for approximating the expectations involved to mitigate the curse of dimensionality. We implement two approaches, the first involves state discretization coupled with linear interpolation of the value function at non-grid points. The second utilizes a parametrization of the value function with educated ansatz functions. Extensive numerical experiments are presented to demonstrate the efficacy of both methods. |
| title | Stochastic Optimal Control of an Epidemic Under Partial Information |
| topic | Optimization and Control 93E20, 92D30, 90C40, 92-10, 90-80 |
| url | https://arxiv.org/abs/2503.06804 |