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Asymptotic Stability in an Epidemic System
Author(s) -
Feng Youhe
Publication year - 1996
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/(sici)1099-1476(19960725)19:11<847::aid-mma797>3.0.co;2-h
Subject(s) - mathematics , exponential stability , banach space , stability (learning theory) , epidemic model , convergence (economics) , mathematical analysis , invariance principle , differential equation , pure mathematics , demography , population , linguistics , philosophy , physics , quantum mechanics , nonlinear system , machine learning , sociology , computer science , economics , economic growth
Using the invariance principle in a Banach space with less restriction, we discuss the asymptotic behaviour of an integro‐differential equation with infinite delay which is an infection disease model. It is proved that the equilibria are globally asymptotic stable if the parameters fit some relation and the integral kern satisfies a convergence condition.