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Threshold conditions for a discrete nonautonomous SIRS model
Author(s) -
Zhang Tailei,
Liu Junli,
Teng Zhidong
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3186
Subject(s) - mathematics , persistence (discontinuity) , scheme (mathematics) , epidemic model , calculus (dental) , mathematical analysis , demography , medicine , population , geotechnical engineering , dentistry , sociology , engineering
Abstract In this paper, a discrete nonautonomous SIRS epidemic model is studied. The model is constructed by applying a nonstandard finite difference scheme. Under weaker assumptions, the sufficient and necessary conditions on the permanence and strong persistence of the disease and the sufficient condition on the extinction of the disease are established. In order to illustrate our theoretical analysis, some numerical simulations are included in the end. Copyright © 2014 John Wiley & Sons, Ltd.