IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v256y2015icp131-147.html
   My bibliography  Save this article

Transmission dynamics and optimal control of measles epidemics

Author

Listed:
  • Pang, Liuyong
  • Ruan, Shigui
  • Liu, Sanhong
  • Zhao, Zhong
  • Zhang, Xinan

Abstract

Based on the mechanism and characteristics of measles transmission, we propose a susceptible-exposed-infectious-recovered (SEIR) measles epidemic model with vaccination and investigate the effect of vaccination in controlling the spread of measles. We obtain two critical threshold values, μc1 and μc2, of the vaccine coverage ratio. Measles will be extinct when the vaccination ratio μ>μc1, endemic when μc2<μ<μc1, and outbreak periodically when μ<μc2. In addition, we apply the optimal control theory to obtain an optimal vaccination strategy μ∗(t) and give some numerical simulations for those theoretical findings. Finally, we use our model to simulate the data of measles cases in the U.S. from 1951 to 1962 and design a control strategy.

Suggested Citation

  • Pang, Liuyong & Ruan, Shigui & Liu, Sanhong & Zhao, Zhong & Zhang, Xinan, 2015. "Transmission dynamics and optimal control of measles epidemics," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 131-147.
    • Handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:131-147
    DOI: 10.1016/j.amc.2014.12.096
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314017573
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.12.096?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Matthew J. Ferrari & Rebecca F. Grais & Nita Bharti & Andrew J. K. Conlan & Ottar N. Bjørnstad & Lara J. Wolfson & Philippe J. Guerin & Ali Djibo & Bryan T. Grenfell, 2008. "The dynamics of measles in sub-Saharan Africa," Nature, Nature, vol. 451(7179), pages 679-684, February.
    2. Xia, Cheng-yi & Wang, Zhen & Sanz, Joaquin & Meloni, Sandro & Moreno, Yamir, 2013. "Effects of delayed recovery and nonuniform transmission on the spreading of diseases in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1577-1585.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Pang, Liuyong & Zhao, Zhong & Song, Xinyu, 2016. "Cost-effectiveness analysis of optimal strategy for tumor treatment," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 293-301.
    2. Nudee, K. & Chinviriyasit, S. & Chinviriyasit, W., 2019. "The effect of backward bifurcation in controlling measles transmission by vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 400-412.
    3. Li, Can & Guo, Zun-Guang & Zhang, Zhi-Yu, 2017. "Transmission dynamics of a brucellosis model: Basic reproduction number and global analysis," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 161-172.
    4. Kimberly M. Thompson, 2016. "Evolution and Use of Dynamic Transmission Models for Measles and Rubella Risk and Policy Analysis," Risk Analysis, John Wiley & Sons, vol. 36(7), pages 1383-1403, July.
    5. Juliet Nakakawa & Joseph Y. T. Mugisha & Michael W. Shaw & William Tinzaara & Eldad Karamura, 2017. "Banana Xanthomonas Wilt Infection: The Role of Debudding and Roguing as Control Options within a Mixed Cultivar Plantation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-13, December.
    6. Xu, Rui & Wang, Zhili & Zhang, Fengqin, 2015. "Global stability and Hopf bifurcations of an SEIR epidemiological model with logistic growth and time delay," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 332-342.
    7. Madhu, Kalyanasundaram & Al-arydah, Mo’tassem, 2021. "Optimal vaccine for human papillomavirus and age-difference between partners," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 325-346.
    8. Abdelaziz, Mahmoud A.M. & Ismail, Ahmad Izani & Abdullah, Farah A. & Mohd, Mohd Hafiz, 2020. "Codimension one and two bifurcations of a discrete-time fractional-order SEIR measles epidemic model with constant vaccination," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Mingdong Lyu & Kuofu Liu & Randolph W. Hall, 2024. "Spatial Interaction Analysis of Infectious Disease Import and Export between Regions," IJERPH, MDPI, vol. 21(5), pages 1-19, May.
    10. Ali Khaleel Dhaiban & Baydaa Khalaf Jabbar, 2021. "An optimal control model of COVID-19 pandemic: a comparative study of five countries," OPSEARCH, Springer;Operational Research Society of India, vol. 58(4), pages 790-809, December.
    11. Farman, Muhammad & Xu, Changjin & Shehzad, Aamir & Akgul, Ali, 2024. "Modeling and dynamics of measles via fractional differential operator of singular and non-singular kernels," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 461-488.
    12. Fu, Xinjie & Wang, JinRong, 2022. "Dynamic stability and optimal control of SISqIqRS epidemic network," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    13. Jose Diamantino Hernández Guillén & Ángel Martín del Rey & Roberto Casado Vara, 2020. "On the Optimal Control of a Malware Propagation Model," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    14. Yujiang Liu & Shujing Gao & Di Chen & Bing Liu, 2024. "Modeling the Transmission Dynamics and Optimal Control Strategy for Huanglongbing," Mathematics, MDPI, vol. 12(17), pages 1-23, August.
    15. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    16. Berhe, Hailay Weldegiorgis & Makinde, Oluwole Daniel & Theuri, David Mwangi, 2019. "Co-dynamics of measles and dysentery diarrhea diseases with optimal control and cost-effectiveness analysis," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 903-921.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Basnarkov, Lasko, 2021. "SEAIR Epidemic spreading model of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Almiala, Into & Aalto, Henrik & Kuikka, Vesa, 2023. "Influence spreading model for partial breakthrough effects on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    3. Wang, Juan & Li, Chao & Xia, Chengyi, 2018. "Improved centrality indicators to characterize the nodal spreading capability in complex networks," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 388-400.
    4. Wang, Zhishuang & Guo, Quantong & Sun, Shiwen & Xia, Chengyi, 2019. "The impact of awareness diffusion on SIR-like epidemics in multiplex networks," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 134-147.
    5. Jijun Zhao & Xinmin Li, 2016. "Determinants of the Transmission Variation of Hand, Foot and Mouth Disease in China," PLOS ONE, Public Library of Science, vol. 11(10), pages 1-14, October.
    6. Yang, Han-Xin & Tang, Ming & Wang, Zhen, 2018. "Suppressing epidemic spreading by risk-averse migration in dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 347-352.
    7. Hu, Xin & Wang, Zhishuang & Sun, Qingyi & Chen, Jiaxing & Zhao, Dawei & Xia, Chengyi, 2024. "Coupled propagation between one communicable disease and related two types of information on multiplex networks with simplicial complexes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 645(C).
    8. Zhang, Gui-Qing & Hu, Tao-Ping & Yu, Zi, 2016. "An improved fitness evaluation mechanism with noise in prisoner’s dilemma game," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 31-36.
    9. Li, Chao & Wang, Li & Sun, Shiwen & Xia, Chengyi, 2018. "Identification of influential spreaders based on classified neighbors in real-world complex networks," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 512-523.
    10. van de Water, Antoinette & Henley, Michelle & Bates, Lucy & Slotow, Rob, 2022. "The value of elephants: A pluralist approach," Ecosystem Services, Elsevier, vol. 58(C).
    11. Chen, Jian & Yang, Lu-Xing & Yang, Xiaofan & Tang, Yuan Yan, 2020. "Cost-effective anti-rumor message-pushing schemes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    12. Huang, Qiangjuan & Zhao, Chengli & Zhang, Xue & Yi, Dongyun, 2017. "Locating the source of spreading in temporal networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 434-444.
    13. Jian Yang & Shuying Bai & Zhao Qu & Hui Chang, 2017. "Investigation on law and economics of listed companies’ financing preference based on complex network theory," PLOS ONE, Public Library of Science, vol. 12(3), pages 1-17, March.
    14. Yi-Ling, Wang & Gui-Qing, Zhang, 2013. "Optimal convergence in fame game with familiarity," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 222-226.
    15. Wang, Xin-Wei & Chen, Zhen & Han, Chao, 2016. "Scheduling for single agile satellite, redundant targets problem using complex networks theory," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 125-132.
    16. Xie, Youxiang & Wang, Linjun & Deng, Qicheng & Wu, Zhengjia, 2017. "The dynamics of an impulsive predator–prey model with communicable disease in the prey species only," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 320-335.
    17. Zhang, Yan, 2013. "The impact of other-regarding tendencies on the spatial vaccination game," Chaos, Solitons & Fractals, Elsevier, vol. 56(C), pages 209-215.
    18. Xiang, Zhongyi & Tang, Sanyi & Xiang, Changcheng & Wu, Jianhong, 2015. "On impulsive pest control using integrated intervention strategies," Applied Mathematics and Computation, Elsevier, vol. 269(C), pages 930-946.
    19. Zhu, Linhe & Huang, Xiaoyuan, 2021. "Modeling the dynamics of multi-cluster information propagation in presence of time delay," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    20. Wayne M. Getz & Jean-Paul Gonzalez & Richard Salter & James Bangura & Colin Carlson & Moinya Coomber & Eric Dougherty & David Kargbo & Nathan D. Wolfe & Nadia Wauquier, 2015. "Tactics and Strategies for Managing Ebola Outbreaks and the Salience of Immunization," Post-Print hal-01214432, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:256:y:2015:i:c:p:131-147. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.