IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i13p2069-d1427167.html
   My bibliography  Save this article

Time-Delay Dynamic Model and Cost-Effectiveness Analysis of Major Emergent Infectious Diseases with Transportation-Related Infection and Entry-Exit Screening

Author

Listed:
  • Yi Xie

    (School of Information and Mathematics, Yangtze University, Jingzhou 434023, China)

  • Ziheng Zhang

    (School of Environment, Education & Development (SEED), The University of Manchester, Manchester M139PL, UK)

  • Yan Wu

    (College of Applied Sciences, Beijing University of Technology, Beijing 100124, China)

  • Shuang Li

    (College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China)

  • Liuyong Pang

    (School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China)

  • Yong Li

    (School of Information and Mathematics, Yangtze University, Jingzhou 434023, China)

Abstract

We analyze a time-delayed SIQR model that considers transportation-related infection and entry–exit screening. This model aims to determine the measures for preventing and controlling major emergent infectious diseases and the associated costs. We calculate the basic reproduction number ( R 0 ) and prove that the disease-free equilibrium is locally and globally asymptotically stable. We collect COVID-19 infection data from two regions in the United States in 2020 for data fitting, obtain a set of optimal parameter values, and find that transportation-related infection rates increase the basic reproduction number, enhancing the impact on disease spread. Entry–exit screening effectively suppresses the spread of disease by reducing the basic reproduction number. Furthermore, we investigate the influence of the incubation period on disease and find that a shorter incubation period results in a shorter duration but a larger scale of infection and that the peaks are reduced. We conduct a sensitivity analysis of the R 0 and propose three measures to prevent the spread of new infectious diseases based on the most sensitive parameters: wearing masks, implementing urban closures, and administering medication to sick but not yet hospitalized patients promptly. In the case of COVID-19, optimal control effectively controls the development and deterioration of the disease. Finally, several control measures are compared through cost-effectiveness analysis, and the results show that wearing masks is the most cost-effective measure.

Suggested Citation

  • Yi Xie & Ziheng Zhang & Yan Wu & Shuang Li & Liuyong Pang & Yong Li, 2024. "Time-Delay Dynamic Model and Cost-Effectiveness Analysis of Major Emergent Infectious Diseases with Transportation-Related Infection and Entry-Exit Screening," Mathematics, MDPI, vol. 12(13), pages 1-25, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:13:p:2069-:d:1427167
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/13/2069/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/13/2069/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Liu, Wenbin & Zheng, Qiben, 2015. "A stochastic SIS epidemic model incorporating media coverage in a two patch setting," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 160-168.
    2. 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.
    3. Julien Arino & P. van den Driessche, 2003. "A multi-city epidemic model," Mathematical Population Studies, Taylor & Francis Journals, vol. 10(3), pages 175-193.
    4. Dong, Yueping & Huang, Gang & Miyazaki, Rinko & Takeuchi, Yasuhiro, 2015. "Dynamics in a tumor immune system with time delays," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 99-113.
    5. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    Full references (including those not matched with items on IDEAS)

    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. Wanduku, Divine, 2017. "Complete global analysis of a two-scale network SIRS epidemic dynamic model with distributed delay and random perturbations," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 49-76.
    2. Liu, Xiangdong & Li, Qingze & Pan, Jianxin, 2018. "A deterministic and stochastic model for the system dynamics of tumor–immune responses to chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 500(C), pages 162-176.
    3. Andrea Di Liddo, 2018. "Price and Treatment Decisions in Epidemics: A Differential Game Approach," Mathematics, MDPI, vol. 6(10), pages 1-19, October.
    4. Pablo D. Fajgelbaum & Amit Khandelwal & Wookun Kim & Cristiano Mantovani & Edouard Schaal, 2021. "Optimal Lockdown in a Commuting Network," American Economic Review: Insights, American Economic Association, vol. 3(4), pages 503-522, December.
    5. Constanza Fosco, 2012. "Spatial Difusion and Commuting Flows," Documentos de Trabajo en Economia y Ciencia Regional 30, Universidad Catolica del Norte, Chile, Department of Economics, revised Sep 2012.
    6. Wang, Qi & Xiang, Kainan & Zhu, Chunhui & Zou, Lang, 2023. "Stochastic SEIR epidemic models with virus mutation and logistic growth of susceptible populations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 289-309.
    7. Zhang, Yan & Fan, Kuangang & Gao, Shujing & Liu, Yingfen & Chen, Shihua, 2019. "Ergodic stationary distribution of a stochastic SIRS epidemic model incorporating media coverage and saturated incidence rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 671-685.
    8. Jiang, Jiehui & Ma, Jie, 2023. "Dynamic analysis of pandemic cross-regional transmission considering quarantine strategies in the context of limited medical resources," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    9. Abbasi, Zohreh & Zamani, Iman & Mehra, Amir Hossein Amiri & Shafieirad, Mohsen & Ibeas, Asier, 2020. "Optimal Control Design of Impulsive SQEIAR Epidemic Models with Application to COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Zhao, Danling & Sun, Jianbin & Tan, Yuejin & Wu, Jianhong & Dou, Yajie, 2018. "An extended SEIR model considering homepage effect for the information propagation of online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 1019-1031.
    11. Saket Saurabh & Ayush Trivedi & Nithilaksh P. Lokesh & Bhagyashree Gaikwad, 2020. "Sustaining the economy under partial lockdown: A pandemic centric approach," Papers 2005.08273, arXiv.org.
    12. Dzyubak, Larysa & Dzyubak, Oleksandr & Awrejcewicz, Jan, 2023. "Nonlinear multiscale diffusion cancer invasion model with memory of states," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    13. Wang, Jianrong & Liu, Maoxing & Li, Youwen, 2013. "Analysis of epidemic models with demographics in metapopulation networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1621-1630.
    14. Andrea Di Liddo, 2016. "Optimal Control and Treatment of Infectious Diseases. The Case of Huge Treatment Costs," Mathematics, MDPI, vol. 4(2), pages 1-27, April.
    15. Sheryl Le Chang & Mahendra Piraveenan & Mikhail Prokopenko, 2019. "The Effects of Imitation Dynamics on Vaccination Behaviours in SIR-Network Model," IJERPH, MDPI, vol. 16(14), pages 1-31, July.
    16. Mahajan, Shveta & Kumar, Deepak & Verma, Atul Kumar & Sharma, Natasha, 2023. "Dynamic analysis of modified SEIR epidemic model with time delay in geographical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 629(C).
    17. Tri Nguyen-Huu & Pierre Auger & Ali Moussaoui, 2023. "On Incidence-Dependent Management Strategies against an SEIRS Epidemic: Extinction of the Epidemic Using Allee Effect," Mathematics, MDPI, vol. 11(13), pages 1-25, June.
    18. Duan, Wei-Long & Lin, Ling, 2021. "Noise and delay enhanced stability in tumor-immune responses to chemotherapy system," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    19. Liu, Shasha & Yamamoto, Toshiyuki, 2022. "Role of stay-at-home requests and travel restrictions in preventing the spread of COVID-19 in Japan," Transportation Research Part A: Policy and Practice, Elsevier, vol. 159(C), pages 1-16.
    20. Jiang, Jiehui & Ma, Jie & Chen, Xiaojing, 2024. "Multi-regional collaborative mechanisms in emergency resource reserve and pre-dispatch design," International Journal of Production Economics, Elsevier, vol. 270(C).

    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:gam:jmathe:v:12:y:2024:i:13:p:2069-:d:1427167. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.