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Multigroup deterministic and stochastic SEIRI epidemic models with nonlinear incidence rates and distributed delays: A stability analysis
Author(s) -
Zhang Hong,
Xia Juan,
Georgescu Paul
Publication year - 2017
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.4453
Subject(s) - mathematics , invariance principle , stability (learning theory) , lyapunov function , epidemic model , nonlinear system , white noise , control theory (sociology) , statistics , computer science , control (management) , population , philosophy , linguistics , physics , demography , quantum mechanics , machine learning , artificial intelligence , sociology
In this paper, we investigate the dynamics of a multigroup disease propagation model with distributed delays and nonlinear incidence rates, which accounts for the relapse of recovered individuals. The main concern is the stability of the equilibria, sufficient conditions for global stability being obtained by applying Lyapunov‐LaSalle invariance principle and using Lyapunov functionals, which are constructed using their single‐group counterparts. The situation in which the deterministic model is subject to perturbations of white noise type is also investigated from a stability viewpoint.