Association Journal of CSIAM
Supervised by Ministry of Education of PRC
Sponsored by Xi'an Jiaotong University
ISSN 1005-3085  CN 61-1269/O1

Chinese Journal of Engineering Mathematics ›› 2017, Vol. 34 ›› Issue (4): 409-423.doi: 10.3969/j.issn.1005-3085.2017.04.008

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Global Dynamics for a Two-patch SIS Model with Time Delay and Transport-related Infection

LIU Jun-li1,   JIA Ying1,   ZHANG Tai-lei2   

  1. 1- School of Science, Xi'an Polytechnic University, Xi'an 710048
    2- School of Science, Chang'an University, Xi'an 710064
  • Received:2015-12-23 Accepted:2016-11-02 Online:2017-08-15 Published:2017-10-15
  • Supported by:
    The National Natural Science Foundation of China (11101323); the Fundamental Research Funds for the Central Universities (310812152002); the Natural Science Foundation of Shaanxi Province (11101323); the Natural Science Basic Research Plan in Shaanxi Province (2014JQ1038; 2014JQ1018); the Scientific Research Program Funded by Shaanxi Provincial Education Department (16JK1331).

Abstract: We formulate a delayed SIS model to describe the effect of transport-related infec-tion. The basic reproduction number is obtained. By the linearization method and comparison principle, it is proved that the disease-free equilibrium is globally asymptotically stable and the disease always dies out if the basic reproduction number is less than unity. While there exists a unique endemic equilibrium which is globally attractive and the disease persists if the basic reproduction number is greater than unity. The simulation results show the influence of travel rates on the disease spread. The dependence of the basic reproduction number on the travel rates during travel is also analyzed.

Key words: transport-related infection, basic reproduction number, uniform persistence, global dynamics, time delay

CLC Number: