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Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold

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  • Wei Zhang
  • Juan Zhang
  • Yong-Ping Wu
  • Li Li

Abstract

As we all know, bacteria is different from virus which with certain types can be killed by the immune cells in the body. The brucellosis, a bacterial disease, can invade the body by indirect transmission from environment, which has not been researched by combining with immune cells. Considering the effects of immune cells, we put a minimum infection dose of brucellosis invading into the dairy cows as an immunological threshold and get a switch model. In this paper, we accomplish a thorough dynamics analysis of a switch model. On the one hand, we can get a disease-free and bacteria-free steady state and up to three endemic steady states which may be thoroughly analyzed in different cases of a minimum infection dose in a switch model. On the other hand, we calculate the basic reproduction number and know that the disease-free and bacteria-free steady state is a global stability when , and the one of the endemic steady state is a conditionally global stability when . We find that different amounts of may lead to different steady states of brucellosis, and considering the effects of immunology is more serious in mathematics and biology.

Suggested Citation

  • Wei Zhang & Juan Zhang & Yong-Ping Wu & Li Li, 2019. "Dynamical Analysis of the SEIB Model for Brucellosis Transmission to the Dairy Cows with Immunological Threshold," Complexity, Hindawi, vol. 2019, pages 1-13, May.
    • Handle: RePEc:hin:complx:6526589
    DOI: 10.1155/2019/6526589
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    1. Sharomi, Oluwaseun Y. & Safi, Mohammad A. & Gumel, Abba B. & Gerberry, David J., 2017. "Exogenous re-infection does not always cause backward bifurcation in TB transmission dynamics," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 322-335.
    2. Zhan, Xiu-Xiu & Liu, Chuang & Zhou, Ge & Zhang, Zi-Ke & Sun, Gui-Quan & Zhu, Jonathan J.H. & Jin, Zhen, 2018. "Coupling dynamics of epidemic spreading and information diffusion on complex networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 437-448.
    3. Li, Li & Zhang, Jie & Liu, Chen & Zhang, Hong-Tao & Wang, Yi & Wang, Zhen, 2019. "Analysis of transmission dynamics for Zika virus on networks," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 566-577.
    4. Li, Li, 2015. "Patch invasion in a spatial epidemic model," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 342-349.
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    Cited by:

    1. Jiaming Guo & Xiaofeng Luo & Juan Zhang & Mingtao Li, 2022. "A Mathematical Model for Ovine Brucellosis during Dynamic Transportation of Sheep, and Its Applications in Jalaid Banner and Ulanhot City," Mathematics, MDPI, vol. 10(19), pages 1-26, September.
    2. Cyrille Kenne & Gisèle Mophou & René Dorville & Pascal Zongo, 2022. "A Model for Brucellosis Disease Incorporating Age of Infection and Waning Immunity," Mathematics, MDPI, vol. 10(4), pages 1-19, February.

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