Loading [Contrib]/a11y/accessibility-menu.js
Search Advanced

Mathematical Biosciences and Engineering

2011, Volume 8, Issue 1: 183-197. doi: 10.3934/mbe.2011.8.183
Previous Article Next Article

A note on the use of optimal control on a discrete time model of influenza dynamics

  • 1.
    Program in Computational Science, The University of Texas at El Paso, El Paso, TX 79968-0514
  • 2.
    Mathematical, Computational and Modeling Sciences Center, School of Human Evolution and Social Change, Arizona State University, Tempe, AZ 85287
  • 3.
    Program in Computational Science, Department of Mathematical Sciences, The University of Texas at El Paso, El Paso, TX 79968-0514
  • 4.
    Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287
  • Received: 01 June 2010 Accepted: 29 June 2018 Published: 01 January 2011

  • MSC : Primary: 92B05, 49K21, 93C55; Secondary: 92D40.

  • A discrete time Susceptible - Asymptomatic - Infectious - Treated - Recovered (SAITR) model is introduced in the context of influenza transmission. We evaluate the potential effect of control measures such as social distancing and antiviral treatment on the dynamics of a single outbreak. Optimal control theory is applied to identify the best way of reducing morbidity and mortality at a minimal cost. The problem is solved by using a discrete version of Pontryagin's maximum principle. Numerical results show that dual strategies have stronger impact in the reduction of the final epidemic size.

    Citation: Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics[J]. Mathematical Biosciences and Engineering, 2011, 8(1): 183-197. doi: 10.3934/mbe.2011.8.183

    Related Papers:

    [1] Olivia Prosper, Omar Saucedo, Doria Thompson, Griselle Torres-Garcia, Xiaohong Wang, Carlos Castillo-Chavez . Modeling control strategies for concurrent epidemics of seasonal and pandemic H1N1 influenza. Mathematical Biosciences and Engineering, 2011, 8(1): 141-170. doi: 10.3934/mbe.2011.8.141
    [2] Eunha Shim . Optimal strategies of social distancing and vaccination against seasonal influenza. Mathematical Biosciences and Engineering, 2013, 10(5&6): 1615-1634. doi: 10.3934/mbe.2013.10.1615
    [3] Sherry Towers, Katia Vogt Geisse, Chia-Chun Tsai, Qing Han, Zhilan Feng . The impact of school closures on pandemic influenza: Assessing potential repercussions using a seasonal SIR model. Mathematical Biosciences and Engineering, 2012, 9(2): 413-430. doi: 10.3934/mbe.2012.9.413
    [4] Keguo Ren, Xining Li, Qimin Zhang . Near-optimal control and threshold behavior of an avian influenza model with spatial diffusion on complex networks. Mathematical Biosciences and Engineering, 2021, 18(5): 6452-6483. doi: 10.3934/mbe.2021321
    [5] Majid Jaberi-Douraki, Seyed M. Moghadas . Optimal control of vaccination dynamics during an influenza epidemic. Mathematical Biosciences and Engineering, 2014, 11(5): 1045-1063. doi: 10.3934/mbe.2014.11.1045
    [6] Xiaomeng Wang, Xue Wang, Xinzhu Guan, Yun Xu, Kangwei Xu, Qiang Gao, Rong Cai, Yongli Cai . The impact of ambient air pollution on an influenza model with partial immunity and vaccination. Mathematical Biosciences and Engineering, 2023, 20(6): 10284-10303. doi: 10.3934/mbe.2023451
    [7] Tom Reichert . Pandemic mitigation: Bringing it home. Mathematical Biosciences and Engineering, 2011, 8(1): 65-76. doi: 10.3934/mbe.2011.8.65
    [8] B. M. Adams, H. T. Banks, Hee-Dae Kwon, Hien T. Tran . Dynamic Multidrug Therapies for HIV: Optimal and STI Control Approaches. Mathematical Biosciences and Engineering, 2004, 1(2): 223-241. doi: 10.3934/mbe.2004.1.223
    [9] Junyoung Jang, Kihoon Jang, Hee-Dae Kwon, Jeehyun Lee . Feedback control of an HBV model based on ensemble kalman filter and differential evolution. Mathematical Biosciences and Engineering, 2018, 15(3): 667-691. doi: 10.3934/mbe.2018030
    [10] Guodong Li, Wenjie Li, Ying Zhang, Yajuan Guan . Sliding dynamics and bifurcations of a human influenza system under logistic source and broken line control strategy. Mathematical Biosciences and Engineering, 2023, 20(4): 6800-6837. doi: 10.3934/mbe.2023293
  • A discrete time Susceptible - Asymptomatic - Infectious - Treated - Recovered (SAITR) model is introduced in the context of influenza transmission. We evaluate the potential effect of control measures such as social distancing and antiviral treatment on the dynamics of a single outbreak. Optimal control theory is applied to identify the best way of reducing morbidity and mortality at a minimal cost. The problem is solved by using a discrete version of Pontryagin's maximum principle. Numerical results show that dual strategies have stronger impact in the reduction of the final epidemic size.


  • This article has been cited by:

    1. Naveed Chehrazi, Lauren E Cipriano, Eva E. Enns, Dynamics of Drug Resistance: Optimal Control of an Infectious Disease, 2017, 1556-5068, 10.2139/ssrn.2927549
    2. Anuj Kumar, Prashant K. Srivastava, Yueping Dong, Yasuhiro Takeuchi, Optimal control of infectious disease: Information-induced vaccination and limited treatment, 2020, 542, 03784371, 123196, 10.1016/j.physa.2019.123196
    3. Eunha Shim, Optimal strategies of social distancing and vaccination against seasonal influenza, 2013, 10, 1551-0018, 1615, 10.3934/mbe.2013.10.1615
    4. Anuj Kumar, Prashant K Srivastava, Anuradha Yadav, Delayed information induces oscillations in a dynamical model for infectious disease, 2019, 12, 1793-5245, 1950020, 10.1142/S1793524519500207
    5. Paula Andrea Gonzalez Parra, Martine Ceberio, Sunmi Lee, Carlos Castillo-Chavez, 2014, Chapter 33, 978-3-319-01567-5, 231, 10.1007/978-3-319-01568-2_33
    6. Juan Jose Fallas-Monge, Jeffry Chavarria-Molina, Geisel Alpizar-Brenes, 2016, Combinatorial metaheuristics applied to infectious disease models, 978-1-4673-9578-6, 1, 10.1109/CONCAPAN.2016.7942337
    7. Seoyun Choe, Sunmi Lee, Modeling optimal treatment strategies in a heterogeneous mixing model, 2015, 12, 1742-4682, 10.1186/s12976-015-0026-x
    8. Naveed Chehrazi, Lauren E. Cipriano, Eva A. Enns, Dynamics of Drug Resistance: Optimal Control of an Infectious Disease, 2019, 67, 0030-364X, 619, 10.1287/opre.2018.1817
    9. Thao Dang, Tommaso Dreossi, Carla Piazza, 2015, Chapter 4, 978-3-319-27655-7, 67, 10.1007/978-3-319-27656-4_4
    10. Geisel Alpízar, Luis F. Gordillo, Disease Spread in Coupled Populations: Minimizing Response Strategies Costs in Discrete Time Models, 2013, 2013, 1026-0226, 1, 10.1155/2013/681689
    11. Baojun Song, Zhilan Feng, Gerardo Chowell, From the guest editors, 2013, 10, 1551-0018, 10.3934/mbe.2013.10.5i
    12. Josephine Mauskopf, Leslie Blake, Amanda Eiden, Craig Roberts, Tianyan Hu, Mawuli Nyaku, Economic Evaluation of Vaccination Programs: A Guide for Selecting Modeling Approaches, 2022, 25, 10983015, 810, 10.1016/j.jval.2021.10.017
    13. Vijay Pal Bajiya, Sarita Bugalia, Jai Prakash Tripathi, Maia Martcheva, Deciphering the transmission dynamics of COVID-19 in India: optimal control and cost effective analysis, 2022, 16, 1751-3758, 665, 10.1080/17513758.2022.2116493
    14. Carlos Castillo-Chavez, Sunmi Lee, 2015, Chapter 85, 978-3-540-70528-4, 427, 10.1007/978-3-540-70529-1_85
    15. Anuj Kumar, Yasuhiro Takeuchi, Prashant K Srivastava, Stability switches, periodic oscillations and global stability in an infectious disease model with multiple time delays, 2023, 20, 1551-0018, 11000, 10.3934/mbe.2023487
  • Reader Comments
  • © 2011 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
3.9

Metrics

Article views(3052) PDF downloads(516) Cited by(15)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog