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Stability and backward bifurcation on a cholera epidemic model with saturated recovery rate
Author(s) -
Zhou Xueyong,
Shi Xiangyun,
Cui Jingan
Publication year - 2016
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.4053
Subject(s) - cholera , bifurcation , mathematics , basic reproduction number , bistability , transcritical bifurcation , stability (learning theory) , mathematical economics , bifurcation diagram , demography , nonlinear system , biology , computer science , virology , physics , population , sociology , quantum mechanics , machine learning
In this paper, a cholera epidemic model with saturated recovery rate is studied. Backward bifurcation leading to bistability possibly occurs, and global dynamics are shown by compound matrices and geometric approaches. Numerical simulations are presented to illustrate the results. Our results suggest that the basic reproduction number itself is not enough to describe whether cholera will prevail or not when the resources for treatment of infectives are limited and suggest that we should pay more attention to the initial state of cholera. Copyright © 2016 John Wiley & Sons, Ltd.