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Global dynamics of an epidemic model with relapse and nonlinear incidence
Author(s) -
Chen Yuming,
Li Jianquan,
Zou Shaofen
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.5439
Subject(s) - epidemic model , mathematics , basic reproduction number , lemma (botany) , invariant (physics) , lyapunov function , nonlinear system , basis (linear algebra) , incidence (geometry) , mathematical economics , demography , mathematical physics , population , biology , ecology , physics , poaceae , geometry , quantum mechanics , sociology
On the basis of a basic SIR epidemic model, we propose and study an epidemic model with nonlinear incidence. The model also incorporates many features of the recovered such as relapse and with/without immunity. A threshold dynamics is established, which is completely determined by the basic reproduction number. The global stability of the disease‐free equilibrium is proved by means of the fluctuation lemma. To prove the global stability of the endemic equilibrium, we need some novel techniques including the transformation of variables, the construction of a new type of Lyapunov functions, and the seeking of an appropriate positively invariant set of the model.