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

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  • 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
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    References listed on IDEAS

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    1. Jeffrey Sachs & Pia Malaney, 2002. "The economic and social burden of malaria," Nature, Nature, vol. 415(6872), pages 680-685, February.
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    1. Akın, E. & Yeni, G. & Konur, D. & Işık, S.R. & Işık, M.R., 2026. "An SEIR model on time scales with discrete applications to tuberculosis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 241(PA), pages 72-103.
    2. 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.
    3. 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).
    4. Seck, Rama & Ngom, Diene & Ivorra, Benjamin & Ramos, Angel M., 2025. "An age-structured mathematical model for studying Malaria transmission dynamics: Applications to some areas of Senegal," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 392-408.

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