IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v152y2018icp15-34.html
   My bibliography  Save this article

Stability and bifurcation in a vector-bias model of malaria transmission with delay

Author

Listed:
  • Li, Jinhui
  • Teng, Zhidong
  • Zhang, Long

Abstract

In this paper, we propose a new vector-bias model of malaria transmission with time delay. The basic reproduction number and the existence of equilibria are obtained. By using the linearization method and the theory of Hopf bifurcation, we study local stability and the existence of Hopf bifurcation. Furthermore, the direction and stability of the Hopf bifurcation are discussed by normal form method and center manifold theory. Finally, some numerical examples are given to illustrate the theoretical results and show that the delay destabilized the model and led to the occurrence of chaotic attractors.

Suggested Citation

  • Li, Jinhui & Teng, Zhidong & Zhang, Long, 2018. "Stability and bifurcation in a vector-bias model of malaria transmission with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 152(C), pages 15-34.
    • Handle: RePEc:eee:matcom:v:152:y:2018:i:c:p:15-34
    DOI: 10.1016/j.matcom.2018.04.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475418300958
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2018.04.009?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. Jeffrey Sachs & Pia Malaney, 2002. "The economic and social burden of malaria," Nature, Nature, vol. 415(6872), pages 680-685, February.
    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. Anatoliy Alabugin & Sergei Aliukov & Tatyana Khudyakova, 2022. "Review of Models for and Socioeconomic Approaches to the Formation of Foresight Control Mechanisms: A Genesis," Sustainability, MDPI, vol. 14(19), pages 1-19, September.
    2. Zheng, Tingting & Nie, Lin-Fei & Teng, Zhidong & Luo, Yantao, 2020. "Competitive exclusion in a multi-strain malaria transmission model with incubation period," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).

    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. Maximiliano Marzetti & Rok Spruk, 2023. "Long-Term Economic Effects of Populist Legal Reforms: Evidence from Argentina," Comparative Economic Studies, Palgrave Macmillan;Association for Comparative Economic Studies, vol. 65(1), pages 60-95, March.
    2. Rok Spruk & Mitja Kovac, 2018. "Inefficient Growth," Review of Economics and Institutions, Università di Perugia, vol. 9(2).
    3. Janz, Teresa & Augsburg, Britta & Gassmann, Franziska & Nimeh, Zina, 2023. "Leaving no one behind: Urban poverty traps in Sub-Saharan Africa," World Development, Elsevier, vol. 172(C).
    4. Anastasia Litina, 2016. "Natural land productivity, cooperation and comparative development," Journal of Economic Growth, Springer, vol. 21(4), pages 351-408, December.
    5. Christina Paxson & Norbert Schady, 2007. "Does Money Matter? The Effects of Cash Transfers on Child Health and Development in Rural Ecuador," Working Papers 145, Princeton University, Department of Economics, Center for Economic Policy Studies..
    6. Ng, Pin & Zhao, Xiaobing, 2011. "No matter how it is measured, income declines with global warming," Ecological Economics, Elsevier, vol. 70(5), pages 963-970, March.
    7. Carl-Johan Dalgaard & Holger Strulik, 2015. "The physiological foundations of the wealth of nations," Journal of Economic Growth, Springer, vol. 20(1), pages 37-73, March.
    8. Rodríguez-Pose, Andrés & Ketterer, Tobias, 2016. "Institutions vs. ‘First-Nature’ Geography – What Drives Economic Growth in Europe’s Regions?," CEPR Discussion Papers 11322, C.E.P.R. Discussion Papers.
    9. Maseland, Robbert, 2021. "Contingent determinants," Journal of Development Economics, Elsevier, vol. 151(C).
    10. Luiza M Karpavicius & Ariaster Chimeli, 2023. "Forest Protection and Human Health: The Case of Malaria in the Brazilian Amazon," Working Papers, Department of Economics 2023_08, University of São Paulo (FEA-USP), revised 26 Jul 2023.
    11. Elisa Sicuri & Silke Fernandes & Eusebio Macete & Raquel González & Ghyslain Mombo-Ngoma & Achille Massougbodgi & Salim Abdulla & August Kuwawenaruwa & Abraham Katana & Meghna Desai & Michel Cot & Mic, 2015. "Economic Evaluation of an Alternative Drug to Sulfadoxine-Pyrimethamine as Intermittent Preventive Treatment of Malaria in Pregnancy," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-23, April.
    12. Stephen Knowles & P. Dorian Owen, 2010. "Which Institutions are Good for Your Health? The Deep Determinants of Comparative Cross-country Health Status," Journal of Development Studies, Taylor & Francis Journals, vol. 46(4), pages 701-723.
    13. Federman, Maya & Levine, David I., 2005. "Industrialization and Infant Mortality," Center for International and Development Economics Research, Working Paper Series qt85j7s6s6, Center for International and Development Economics Research, Institute for Business and Economic Research, UC Berkeley.
    14. Guanchun Liu & Chien-Chiang Lee & Yuanyuan Liu, 2020. "Growth path heterogeneity across provincial economies in China: the role of geography versus institutions," Empirical Economics, Springer, vol. 59(2), pages 503-546, August.
    15. Cirera, Laia & Castelló, Judit Vall & Brew, Joe & Saúte, Francisco & Sicuri, Elisa, 2022. "The impact of a malaria elimination initiative on school outcomes: Evidence from Southern Mozambique," Economics & Human Biology, Elsevier, vol. 44(C).
    16. Erkan Gören, 2014. "The Biogeographic Origins of Novelty-Seeking Traits," Working Papers V-366-14, University of Oldenburg, Department of Economics, revised May 2014.
    17. Nathan Nunn & Diego Puga, 2012. "Ruggedness: The Blessing of Bad Geography in Africa," The Review of Economics and Statistics, MIT Press, vol. 94(1), pages 20-36, February.
    18. Paolo Buonanno & Ruben Durante & Giovanni Prarolo, 2013. "Rich Mines, Poor Institutions: Resource Curse and the Origins of the Sicilian Mafia," Working Papers hal-03460966, HAL.
    19. Samantha Rawlings, 2012. "Gender, race, and heterogeneous scarring and selection effects of epidemic malaria on human capital," Economics Discussion Papers em-dp2012-01, Department of Economics, University of Reading.
    20. Paolo Buonanno & Ruben Durante & Giovanni Prarolo & Paolo Vanin, 2015. "Poor Institutions, Rich Mines: Resource Curse in the Origins of the Sicilian Mafia," Economic Journal, Royal Economic Society, vol. 125(586), pages 175-202, August.

    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:152:y:2018:i:c:p:15-34. 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.