Mitigation of epidemics in contact networks through optimal contact adaptation
This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preser...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-05-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1227 |
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| author | Mina Youssef Caterina Scoglio |
| author_facet | Mina Youssef Caterina Scoglio |
| author_sort | Mina Youssef |
| collection | DOAJ |
| description | This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights. |
| format | Article |
| id | doaj-art-8d9a6182085441e684691925464409ec |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-05-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-8d9a6182085441e684691925464409ec2025-01-24T02:26:20ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-05-011041227125110.3934/mbe.2013.10.1227Mitigation of epidemics in contact networks through optimal contact adaptationMina Youssef0Caterina Scoglio1K-State Epicenter, Department of Electrical and Computer Engineering, Kansas State University, 2061 Rathbone Hall, Manhattan, KS 66506-5204K-State Epicenter, Department of Electrical and Computer Engineering, Kansas State University, 2061 Rathbone Hall, Manhattan, KS 66506-5204This paper presents an optimal control problem formulation to minimize the total number of infection cases during the spread of susceptible-infected-recovered SIR epidemics in contact networks. In the new approach, contact weighted are reduced among nodes and a global minimum contact level is preserved in the network. In addition, the infection cost and the cost associated with the contact reduction are linearly combined in a single objective function. Hence, the optimal control formulation addresses the tradeoff between minimization of total infection cases and minimization of contact weights reduction. Using Pontryagin theorem, the obtained solution is a unique candidate representing the dynamical weighted contact network. To find the near-optimal solution in a decentralized way, we propose two heuristics based on Bang-Bang control function and on a piecewise nonlinear control function, respectively. We perform extensive simulations to evaluate the two heuristics on different networks. Our results show that the piecewise nonlinear control function outperforms the well-known Bang-Bang control function in minimizing both the total number of infection cases and the reduction of contact weights. Finally, our results show awareness of the infection level at which the mitigation strategies are effectively applied to the contact weights.https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1227spread of epidemicsnetwork-based approachbehavioral responses.adaptive contact networksoptimal control of epidemics |
| spellingShingle | Mina Youssef Caterina Scoglio Mitigation of epidemics in contact networks through optimal contact adaptation Mathematical Biosciences and Engineering spread of epidemics network-based approach behavioral responses. adaptive contact networks optimal control of epidemics |
| title | Mitigation of epidemics in contact networks through optimal contact adaptation |
| title_full | Mitigation of epidemics in contact networks through optimal contact adaptation |
| title_fullStr | Mitigation of epidemics in contact networks through optimal contact adaptation |
| title_full_unstemmed | Mitigation of epidemics in contact networks through optimal contact adaptation |
| title_short | Mitigation of epidemics in contact networks through optimal contact adaptation |
| title_sort | mitigation of epidemics in contact networks through optimal contact adaptation |
| topic | spread of epidemics network-based approach behavioral responses. adaptive contact networks optimal control of epidemics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2013.10.1227 |
| work_keys_str_mv | AT minayoussef mitigationofepidemicsincontactnetworksthroughoptimalcontactadaptation AT caterinascoglio mitigationofepidemicsincontactnetworksthroughoptimalcontactadaptation |