Open AccessGlobal stability of a network-based sis epidemic model with a general nonlinear incidence rate
Author(s) -
Shouying Huang,
Jifa Jiang
Publication year - 2016
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2016016
Subject(s) - epidemic model , stability theory , nonlinear system , mathematics , stability (learning theory) , degree (music) , incidence (geometry) , birth–death process , exponential stability , mathematical optimization , control theory (sociology) , computer science , population , control (management) , demography , physics , geometry , quantum mechanics , machine learning , sociology , acoustics , artificial intelligence
In this paper, we develop and analyze an SIS epidemic model with a general nonlinear incidence rate, as well as degree-dependent birth and natural death, on heterogeneous networks. We analytically derive the epidemic threshold R0 which completely governs the disease dynamics: when R0 < 1, the disease-free equilibrium is globally asymptotically stable, i.e., the disease will die out; when R0 > 1, the disease is permanent. It is interesting that the threshold value R0 bears no relation to the functional form of the nonlinear incidence rate and degree-dependent birth. Furthermore, by applying an iteration scheme and the theory of cooperative system respectively, we obtain sufficient conditions under which the endemic equilibrium is globally asymptotically stable. Our results improve and generalize some known results. To illustrate the theoretical results, the corresponding numerical simulations are also given.