Threshold dynamics of a delayed nonlocal reaction-diffusion cholera model
Revisit of the Peierls-Nabarro model for edge dislocations in Hilbert space
The threshold dynamics of a discrete-time echinococcosis transmission model
Cuicui Li 1, , Lin Zhou 1, , Zhidong Teng 1,, and Buyu Wen 1,2,
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
School of Information Engineering, Eastern Liaoning University, Dandong 108001, China
* Corresponding author: Zhidong Teng
Received July 2020 Revised September 2020 Published November 2020
Fund Project: 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)
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.
Keywords: Echinococcosis, discrete-time model, basic reproduction number, equilibrium, stability, permanence.
Mathematics Subject Classification: Primary: 92D30, 39A60; Secondary: 39A30.
Citation: Cuicui Li, Lin Zhou, Zhidong Teng, Buyu Wen. The threshold dynamics of a discrete-time echinococcosis transmission model. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020339
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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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Cuicui Li Lin Zhou Zhidong Teng Buyu Wen