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Stochastic asymptotic analysis of a multi-host model with vector transmission

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  • Acuña-Zegarra, Manuel Adrian
  • Díaz-Infante, Saúl

Abstract

We present a stochastic epidemic model with vectorial transmission and multi-host structure. To include environmental noise, we stochastically perturb biting rates with general state functional intensities. So, we derive a stochastic differential equation (SDE) which describes a vector disease with two types of hosts – humans and animals – and give conditions to assure disease extinction and persistence. Finally, via numerical experiments, we extend and illustrate our results using literature parameters for Chagas.

Suggested Citation

  • Acuña-Zegarra, Manuel Adrian & Díaz-Infante, Saúl, 2018. "Stochastic asymptotic analysis of a multi-host model with vector transmission," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 243-260.
    • Handle: RePEc:eee:phsmap:v:510:y:2018:i:c:p:243-260
    DOI: 10.1016/j.physa.2018.06.105
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    References listed on IDEAS

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    1. Cao, Boqiang & Shan, Meijing & Zhang, Qimin & Wang, Weiming, 2017. "A stochastic SIS epidemic model with vaccination," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 127-143.
    2. Liu, Yuting & Shan, Meijing & Lian, Xinze & Wang, Weiming, 2016. "Stochastic extinction and persistence of a parasite–host epidemiological model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 586-602.
    3. 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.
    4. Liu, Qun & Chen, Qingmei, 2016. "Dynamics of a stochastic SIR epidemic model with saturated incidence," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 155-166.
    5. Greenhalgh, D. & Liang, Y. & Mao, X., 2016. "SDE SIS epidemic model with demographic stochasticity and varying population size," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 218-238.
    6. 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.
    7. Wei, Fengying & Liu, Jiamin, 2017. "Long-time behavior of a stochastic epidemic model with varying population size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 146-153.
    8. Yongli Cai & Xixi Wang & Weiming Wang & Min Zhao, 2013. "Stochastic Dynamics of an SIRS Epidemic Model with Ratio-Dependent Incidence Rate," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, June.
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