The threshold dynamics of a discrete-time echinococcosis transmission model

Cuicui Li; Lin Zhou; Zhidong Teng; Buyu Wen

doi:10.3934/dcdsb.2020339

Article Contents

2021, Volume 26, Issue 10: 5197-5216. Doi: 10.3934/dcdsb.2020339

This issue Previous Article Next Article A posteriori error estimate of weak Galerkin fem for second order elliptic problem with mixed boundary condition

The threshold dynamics of a discrete-time echinococcosis transmission model

1.
College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, China
2.
School of Information Engineering, Eastern Liaoning University, Dandong 108001, China

^* Corresponding author: Zhidong Teng
^* Corresponding author: Zhidong Teng

Received: June 30, 2020

Revised: August 31, 2020

Early access: November 2020

Published: October 2021

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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Abstract

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.

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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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