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Nontrivial periodic solution for a stochastic brucellosis model with application to Xinjiang, China

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  • Wang, Lei
  • Wang, Kai
  • Jiang, Daqing
  • Hayat, Tasawar

Abstract

Brucellosis is a kind of zoonotic disease caused by Gram-negative bacteria of the genus Brucella. In this paper, we propose a stochastic periodic brucellosis model by introducing the effect of environmental white noise on transmission dynamics of brucellosis. By Has’minskii theory of periodic solution and constructing a novel combination of Lyapunov functions, we establish the existence of nontrivial positive periodic solution if the condition R0S>1 holds. Based on the reported data of newly acute human brucellosis cases for each season from 2010 to 2014 in Xinjiang, numerical simulations have been performed to support our result and indicate that brucellosis in Xinjiang takes on the feature of long-term prevalence and cyclical fluctuation.

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  • Wang, Lei & Wang, Kai & Jiang, Daqing & Hayat, Tasawar, 2018. "Nontrivial periodic solution for a stochastic brucellosis model with application to Xinjiang, China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 522-537.
    • Handle: RePEc:eee:phsmap:v:510:y:2018:i:c:p:522-537
    DOI: 10.1016/j.physa.2018.06.061
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    References listed on IDEAS

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    1. Shufan Wang & Zhihui Ma, 2012. "Analysis of an Ecoepidemiological Model with Prey Refuges," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-16, November.
    2. Cai, Yongli & Jiao, Jianjun & Gui, Zhanji & Liu, Yuting & Wang, Weiming, 2018. "Environmental variability in a stochastic epidemic model," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 210-226.
    3. Liu, Qun & Jiang, Daqing & Shi, Ningzhong & Hayat, Tasawar, 2018. "Dynamics of a stochastic delayed SIR epidemic model with vaccination and double diseases driven by Lévy jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2010-2018.
    4. Guo, Wenjuan & Cai, Yongli & Zhang, Qimin & Wang, Weiming, 2018. "Stochastic persistence and stationary distribution in an SIS epidemic model with media coverage," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 2220-2236.
    5. Cai, Yongli & Kang, Yun & Wang, Weiming, 2017. "A stochastic SIRS epidemic model with nonlinear incidence rate," Applied Mathematics and Computation, Elsevier, vol. 305(C), pages 221-240.
    6. Carletti, M. & Burrage, K. & Burrage, P.M., 2004. "Numerical simulation of stochastic ordinary differential equations in biomathematical modelling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(2), pages 271-277.
    7. Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
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    Cited by:

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