IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v203y2023icp250-270.html
   My bibliography  Save this article

Optimal control of dengue vector based on a reaction–diffusion model

Author

Listed:
  • Li, Yazhi
  • Wang, Yan
  • Liu, Lili

Abstract

In recent decades, the incidence rate of dengue fever has increased sharply in the world, which has caused a serious burden on society as a whole. Considering that using Wolbachia to inhibit the spread of dengue fever is an effective and sustainable mean, we try to explore the effect of the control measures by establishing a mathematical model. Due to the uneven distribution of mosquitoes in space, a reaction–diffusion model containing the wild mosquito population and the Wolbachia-infected mosquito population with control is established. Firstly, the dynamic behaviors of the uncontrolled model are analyzed. It is found that Wolbachia may completely invade the wild mosquito population or fail, which is mainly determined by the initial proportion of Wolbachia, and the diffusion has a negligible effect on the successful transmission of Wolbachia. Secondly, the optimal control strategies in the case of no diffusion and with diffusion are studied. The specific expression of optimal control is obtained. Thirdly, the results are verified and the influence of diffusion on the optimal control is discussed by numerical simulations. The results show that the implementation of control will cause Wolbachia to completely invade the wild mosquito population. The greater the control force, the shorter the time required for a complete invasion. The control force of diffusion system is much greater than that of non diffusion system. Finally, all the conclusions are showed and explained, and some discussions are given.

Suggested Citation

  • Li, Yazhi & Wang, Yan & Liu, Lili, 2023. "Optimal control of dengue vector based on a reaction–diffusion model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 250-270.
    • Handle: RePEc:eee:matcom:v:203:y:2023:i:c:p:250-270
    DOI: 10.1016/j.matcom.2022.06.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422002968
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.06.026?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. Emily Waltz, 2016. "US reviews plan to infect mosquitoes with bacteria to stop disease," Nature, Nature, vol. 533(7604), pages 450-451, May.
    2. T. Walker & P. H. Johnson & L. A. Moreira & I. Iturbe-Ormaetxe & F. D. Frentiu & C. J. McMeniman & Y. S. Leong & Y. Dong & J. Axford & P. Kriesner & A. L. Lloyd & S. A. Ritchie & S. L. O’Neill & A. A., 2011. "The wMel Wolbachia strain blocks dengue and invades caged Aedes aegypti populations," Nature, Nature, vol. 476(7361), pages 450-453, August.
    3. Brito da Cruz, Artur M.C. & Rodrigues, Helena Sofia, 2021. "Personal protective strategies for dengue disease: Simulations in two coexisting virus serotypes scenarios," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 254-267.
    4. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2021. "Optimal Control of Dengue Transmission with Vaccination," Mathematics, MDPI, vol. 9(15), pages 1-33, August.
    5. Li, Yazhi & Liu, Xianning, 2020. "Modeling and control of mosquito-borne diseases with Wolbachia and insecticides," Theoretical Population Biology, Elsevier, vol. 132(C), pages 82-91.
    6. Saha, Sangeeta & Samanta, Guruprasad, 2022. "Analysis of a host–vector dynamics of a dengue disease model with optimal vector control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 31-55.
    7. A. A. Hoffmann & B. L. Montgomery & J. Popovici & I. Iturbe-Ormaetxe & P. H. Johnson & F. Muzzi & M. Greenfield & M. Durkan & Y. S. Leong & Y. Dong & H. Cook & J. Axford & A. G. Callahan & N. Kenny & , 2011. "Successful establishment of Wolbachia in Aedes populations to suppress dengue transmission," Nature, Nature, vol. 476(7361), pages 454-457, August.
    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. Auliya A. Suwantika & Angga P. Kautsar & Woro Supadmi & Neily Zakiyah & Rizky Abdulah & Mohammad Ali & Maarten J. Postma, 2020. "Cost-Effectiveness of Dengue Vaccination in Indonesia: Considering Integrated Programs with Wolbachia -Infected Mosquitos and Health Education," IJERPH, MDPI, vol. 17(12), pages 1-15, June.
    2. Xingtong Liu & Yuanshun Tan & Bo Zheng, 2022. "Dynamic Behavior of an Interactive Mosquito Model under Stochastic Interference," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    3. Kristina K. Gonzales & Immo A. Hansen, 2016. "Artificial Diets for Mosquitoes," IJERPH, MDPI, vol. 13(12), pages 1-13, December.
    4. Tiago França Melo De Lima & Raquel Martins Lana & Tiago Garcia De Senna Carneiro & Cláudia Torres Codeço & Gabriel Souza Machado & Lucas Saraiva Ferreira & Líliam César De Castro Medeiros & Clodoveu A, 2016. "DengueME: A Tool for the Modeling and Simulation of Dengue Spatiotemporal Dynamics," IJERPH, MDPI, vol. 13(9), pages 1-21, September.
    5. Vanessa M. Macias & Johanna R. Ohm & Jason L. Rasgon, 2017. "Gene Drive for Mosquito Control: Where Did It Come from and Where Are We Headed?," IJERPH, MDPI, vol. 14(9), pages 1-30, September.
    6. Heverton Leandro Carneiro Dutra & Lilha Maria Barbosa dos Santos & Eric Pearce Caragata & Jéssica Barreto Lopes Silva & Daniel Antunes Maciel Villela & Rafael Maciel-de-Freitas & Luciano Andrade Morei, 2015. "From Lab to Field: The Influence of Urban Landscapes on the Invasive Potential of Wolbachia in Brazilian Aedes aegypti Mosquitoes," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 9(4), pages 1-22, April.
    7. Zhongcai Zhu & Yantao Shi & Rong Yan & Linchao Hu, 2022. "Periodic Orbits of a Mosquito Suppression Model Based on Sterile Mosquitoes," Mathematics, MDPI, vol. 10(3), pages 1-21, January.
    8. Turelli, Michael & Barton, Nicholas H., 2017. "Deploying dengue-suppressing Wolbachia : Robust models predict slow but effective spatial spread in Aedes aegypti," Theoretical Population Biology, Elsevier, vol. 115(C), pages 45-60.
    9. Lijie Chang & Yantao Shi & Bo Zheng, 2021. "Existence and Uniqueness of Nontrivial Periodic Solutions to a Discrete Switching Model," Mathematics, MDPI, vol. 9(19), pages 1-13, September.
    10. Abidemi, Afeez & Ackora-Prah, Joseph & Fatoyinbo, Hammed Olawale & Asamoah, Joshua Kiddy K., 2022. "Lyapunov stability analysis and optimization measures for a dengue disease transmission model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 602(C).
    11. Martin Foureaux Koppensteiner & Lívia Menezes, 2024. "Maternal Dengue and Health Outcomes of Children," American Economic Journal: Applied Economics, American Economic Association, vol. 16(2), pages 530-553, April.
    12. Philipp Walch & Petr Broz, 2024. "Viral-bacterial co-infections screen in vitro reveals molecular processes affecting pathogen proliferation and host cell viability," Nature Communications, Nature, vol. 15(1), pages 1-16, December.
    13. Saha, Pritam & Sikdar, Gopal Chandra & Ghosh, Jayanta Kumar & Ghosh, Uttam, 2023. "Disease dynamics and optimal control strategies of a two serotypes dengue model with co-infection," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 209(C), pages 16-43.
    14. Anusit Chamnan & Puntani Pongsumpun & I-Ming Tang & Napasool Wongvanich, 2022. "Effect of a Vaccination against the Dengue Fever Epidemic in an Age Structure Population: From the Perspective of the Local and Global Stability Analysis," Mathematics, MDPI, vol. 10(6), pages 1-25, March.
    15. Slavenko, Alex & Ross, Perran A & Mata, Luis & Hoffmann, Ary A & Umina, Paul A, 2024. "Modelling the spread of a novel endosymbiont infection in field populations of an aphid pest," Ecological Modelling, Elsevier, vol. 497(C).
    16. Linda O'Connor & Catherine Plichart & Ayo Cheong Sang & Corey L Brelsfoard & Hervé C Bossin & Stephen L Dobson, 2012. "Open Release of Male Mosquitoes Infected with a Wolbachia Biopesticide: Field Performance and Infection Containment," PLOS Neglected Tropical Diseases, Public Library of Science, vol. 6(11), pages 1-7, November.
    17. Saha, Sangeeta & Samanta, Guruprasad, 2022. "Analysis of a host–vector dynamics of a dengue disease model with optimal vector control strategy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 31-55.
    18. Pérez-Estigarribia, Pastor E. & Bliman, Pierre-Alexandre & Schaerer, Christian E., 2020. "A class of fast–slow models for adaptive resistance evolution," Theoretical Population Biology, Elsevier, vol. 135(C), pages 32-48.
    19. Jabili Angina & Anish Bachhu & Eesha Talati & Rishi Talati & Jan Rychtář & Dewey Taylor, 2022. "Game-Theoretical Model of the Voluntary Use of Insect Repellents to Prevent Zika Fever," Dynamic Games and Applications, Springer, vol. 12(1), pages 133-146, March.
    20. Yijie Li & Zhiming Guo, 2022. "Wolbachia Invasion Dynamics by Integrodifference Equations," Mathematics, MDPI, vol. 10(22), pages 1-13, November.

    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:203:y:2023:i:c:p:250-270. 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.