IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v228y2025icp1-22.html
   My bibliography  Save this article

Nonstandard finite difference schemes for some epidemic optimal control problems

Author

Listed:
  • Ouemba Tassé, Arsène J.
  • Kubalasa, Vuyiswa B.
  • Tsanou, Berge
  • Lubuma, Jean M.-S,

Abstract

We construct and analyse nonstandard finite difference (NSFD) schemes for two epidemic optimal control problems. Firstly, we consider the well-known MSEIR system that can be used to model childhood diseases such as the measles, with the vaccination as a control intervention. The second optimal control problem is related to the 2014–2016 West Africa Ebola Virus Disease (EVD) outbreak, that came with the unprecedented challenge of the disease spreading simultaneously in three different countries, namely Guinea, Liberia and Sierra Leone, where it was difficult to control the considerable migrations and travels of people inbound and outbound. We develop an extended SEIRD metapopulation model modified by the addition of compartments of quarantined and isolated individuals. The control parameters are the exit screening of travelers and the vaccination of the susceptible individuals. For the two optimal control problems, we provide the results on: (i) the (global) stability of the disease-free and/or endemic equilibria of the state variable systems; (ii) the positivity and boundedness of solutions of the state variables systems; (iii) the existence, uniqueness and characterization of the optimal control solutions that minimizes the cost functional. On the other hand: (iv) we design Euler-based nonstandard finite difference versions of the Forward-Backward Sweep Method (NSFD-FBSM) that are dynamically consistent with the state variable systems; (v) we provide numerical simulations that support the theory and show the superiority of the nonstandard approach over the classical FBSM. The numerical simulations suggest that significantly increasing the coverage of the vaccine with its implementation for adults as well is essential if the recurrence of measles outbreaks is to be stopped in South Africa. They also show that the optimal control vaccination for the 2014-2016 EVD is more efficient than the exit screening intervention.

Suggested Citation

  • Ouemba Tassé, Arsène J. & Kubalasa, Vuyiswa B. & Tsanou, Berge & Lubuma, Jean M.-S,, 2025. "Nonstandard finite difference schemes for some epidemic optimal control problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 228(C), pages 1-22.
    • Handle: RePEc:eee:matcom:v:228:y:2025:i:c:p:1-22
    DOI: 10.1016/j.matcom.2024.08.028
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475424003380
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2024.08.028?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. Michael McAsey & Libin Mou & Weimin Han, 2012. "Convergence of the forward-backward sweep method in optimal control," Computational Optimization and Applications, Springer, vol. 53(1), pages 207-226, September.
    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. Alessandro Ramponi & Maria Elisabetta Tessitore, 2024. "Optimal Social and Vaccination Control in the SVIR Epidemic Model," Mathematics, MDPI, vol. 12(7), pages 1-17, March.
    2. Niyirora, Jerome & Zhuang, Jun, 2017. "Fluid approximations and control of queues in emergency departments," European Journal of Operational Research, Elsevier, vol. 261(3), pages 1110-1124.
    3. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Epidemics and macroeconomic outcomes: Social distancing intensity and duration," Journal of Mathematical Economics, Elsevier, vol. 93(C).
    4. Liu, Fangzhou & Zhang, Zengjie & Buss, Martin, 2019. "Robust optimal control of deterministic information epidemics with noisy transition rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 577-587.
    5. Akinlotan, Morenikeji Deborah & Mallet, Daniel G. & Araujo, Robyn P., 2020. "An optimal control model of the treatment of chronic Chlamydia trachomatis infection using a combination treatment with antibiotic and tryptophan," Applied Mathematics and Computation, Elsevier, vol. 375(C).
    6. Torre, Davide La & Liuzzi, Danilo & Marsiglio, Simone, 2021. "Transboundary pollution externalities: Think globally, act locally?," Journal of Mathematical Economics, Elsevier, vol. 96(C).
    7. Tian, Xiaohong & Xu, Rui & Lin, Jiazhe, 2019. "Mathematical analysis of a cholera infection model with vaccination strategy," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 517-535.
    8. Xavier Brusset & Aida Jebali & Davide Torre & Danilo Liuzzi, 2025. "Production optimization in the time of pandemic: an SIS-based optimal control model with protection effort and cost minimization," Annals of Operations Research, Springer, vol. 344(1), pages 79-102, January.
    9. Alessandro Ramponi & Maria Elisabetta Tessitore, 2022. "The economic cost of social distancing during a pandemic: an optimal control approach in the SVIR model," Papers 2208.04908, arXiv.org.
    10. La Torre, Davide & Liuzzi, Danilo & Marsiglio, Simone, 2015. "Pollution diffusion and abatement activities across space and over time," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 48-63.
    11. Wang, Jinling & Jiang, Haijun & Hu, Cheng & Yu, Zhiyong & Li, Jiarong, 2021. "Stability and Hopf bifurcation analysis of multi-lingual rumor spreading model with nonlinear inhibition mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    12. Bruno Buonomo, 2015. "Modeling ITNs Usage: Optimal Promotion Programs Versus Pure Voluntary Adoptions," Mathematics, MDPI, vol. 3(4), pages 1-14, December.
    13. Eunok Jung & Aurelio A de los Reyes V & Kurt Jan A Pumares & Yangjin Kim, 2019. "Strategies in regulating glioblastoma signaling pathways and anti-invasion therapy," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-34, April.
    14. Soukaina, Ben Rhila & Imane, Agmour & Mostafa, Rachik & Naceur, Achtaich & Youssef, El Foutayeni, 2022. "Optimal control of a phytoplankton-zooplankton spatiotemporal discrete bioeconomic model," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    15. Liu, Yujing & Ding, Li & An, Xuming & Hu, Ping & Du, Fuying, 2020. "Epidemic spreading on midscopic multi-layer network with optimal control mechanism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    16. Jerome Niyirora & Jamol Pender, 2016. "Optimal staffing in nonstationary service centers with constraints," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(8), pages 615-630, December.

    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:matcom:v:228:y:2025:i:c:p:1-22. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.