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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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    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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    Cited by:

    1. 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).
    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.

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