Finite horizon optimal control of reaction-diffusion SIV epidemic system with stochastic environment
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910304613433344 |
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| author | Wang, Zong |
| author_facet | Wang, Zong |
| contents | This contribution mainly focuses on the finite horizon optimal control problems of a susceptible-infected-vaccinated(SIV) epidemic system governed by reaction-diffusion equations and Markov switching. Stochastic dynamic programming is employed to find the optimal vaccination effort and economic return for a stochastic reaction diffusion SIV epidemic model. To achieve this, a key step is to show the existence and uniqueness of invariant measure for the model. Then, we obtained the necessary and sufficient conditions for the near-optimal control. Furthermore, we give an algorithm to approximate the Hamilton-Jacobi Bellman (HJB) equation. Finally, some numerical simulations are presented to confirm our analytic results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11744 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite horizon optimal control of reaction-diffusion SIV epidemic system with stochastic environment Wang, Zong Optimization and Control Dynamical Systems This contribution mainly focuses on the finite horizon optimal control problems of a susceptible-infected-vaccinated(SIV) epidemic system governed by reaction-diffusion equations and Markov switching. Stochastic dynamic programming is employed to find the optimal vaccination effort and economic return for a stochastic reaction diffusion SIV epidemic model. To achieve this, a key step is to show the existence and uniqueness of invariant measure for the model. Then, we obtained the necessary and sufficient conditions for the near-optimal control. Furthermore, we give an algorithm to approximate the Hamilton-Jacobi Bellman (HJB) equation. Finally, some numerical simulations are presented to confirm our analytic results. |
| title | Finite horizon optimal control of reaction-diffusion SIV epidemic system with stochastic environment |
| topic | Optimization and Control Dynamical Systems |
| url | https://arxiv.org/abs/2401.11744 |