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The threshold dynamics of a discrete-time echinococcosis transmission model

  • * Corresponding author: Zhidong Teng

    * Corresponding author: Zhidong Teng 
Research of Zhidong Teng was supported by the NSF of China (Grant No. 11771373, 11861065) and the NSF of Xinjiang, China (Grant No. 2016D03022), Research of Buyu Wen was supported by the Doctoral Research Start-up Fund of Eastern Liaoning University of Liaoning, China(Grant No. 2019BS023)
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  • In this paper, based on the transmission mechanism of echinococcosis in China, we propose a discrete-time dynamical model for the transmission of echinococcosis. The research results indicate that transmission dynamics of this discrete-time model are determined by basic reproduction number $ R_{0} $. It is shown that when $ R_{0}\leq1 $ then the disease-free equilibrium is globally asymptotically stable and when $ R_{0}>1 $ then the model is permanent while the disease-free equilibrium is unstable. Finally, on the basis of the theoretical results established in this paper, we come up with some specific measures to control the transmission of echinococcosis.

    Mathematics Subject Classification: Primary: 92D30, 39A60; Secondary: 39A30.


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  • Figure 1.  Numerical simulations of solution $ (S_D(t),I_D(t),S_L(t), $ $ I_L(t),x(t),S_H(t),E_H(t),I_H(t)) $ with initial value $ (S_{D}(0),I_{D}(0), $ $ S_{L}(0),I_{L}(0),x(0),S_{H}(0),E_{H}(0),I_{H}(0)) = (2\times10^6,8\times10^5, $ $ 8.4\times10^8, 5.7\times10^7, 1.44\times10^7, 3\times10^7, 9\times10^3, 8\times10^4), (5\times10^4, 4\times10^6, 0.1\times10^8, 1\times10^8, 3\times10^7, 5\times10^6, 1\times10^3, 1\times10^5), (0.4\times10^6, 2\times10^6, 1.2\times10^8, 2.2\times10^8, 1\times10^7, 1.5\times10^7, 7\times10^3, 6\times10^4) $, respectively

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