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Global stability of an SIS epidemic model with delays
Author(s) -
Fushimi Kei,
Enatsu Yoichi,
Ishiwata Emiko
Publication year - 2018
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.5084
Subject(s) - mathematics , stability (learning theory) , stability theory , lyapunov function , epidemic model , discrete time and continuous time , lyapunov stability , exponential stability , control theory (sociology) , computer science , nonlinear system , control (management) , statistics , population , physics , demography , quantum mechanics , machine learning , artificial intelligence , sociology
In this paper, we consider the global dynamics of the S(E)IS model with delays denoting an incubation time. By constructing a Lyapunov functional, we prove stability of a disease‐free equilibrium E 0 under a condition different from that in the recent paper. Then we claim that R 0 ≤1 is a necessary and sufficient condition under which E 0 is globally asymptotically stable. We also propose a discrete model preserving positivity and global stability of the same equilibria as the continuous model with distributed delays, by means of discrete analogs of the Lyapunov functional.