Abstract
An SIQ epidemic model with isolation and nonlinear incidence rate is studied. We have obtained a threshold value R and shown that there is only a disease free equilibrium point when R < 1 , and there is also an endemic equilibrium point if R > 1. With the help of Liapunov function, we have shown that disease free- and endemic equilibrium point is globally stable.
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References
Hethcote, H.W., van den Driessche: Some epidemiological models with nonlinear incidence rate. J. Math. Biol. 29, 271–287 (1991)
Li, M.Y., Muldowney, J.S.: Global stability of the SEIR model in epidemiology. Math. Biosci. 125, 155–164 (1995)
Ruan, S., Wang, W.: Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Diff. Equa. 188, 135–163 (2003)
Korobeinikov, A., Maini, P.K.: Nonlinear incidence and stability of infectious disease models. Math. Medicine and Biology 22, 113–128 (2005)
Kyrychko, Y.N., Blyuss, K.B.: Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear Analysis: Real world Applications 6, 495–507 (2005)
Feng, Z.L., Thieme, H.R.: Recurrent outbreaks of childhood diseases revisited: The impace of isolation. Math. Biosci. 128, 93–130 (1995)
Gerberry, D.J., Milner, F.A.: An SEIQR model for childhood diseases. Mathematical Biology 59, 535–561 (2009)
Castillo-Chavez, C., Castillo-Garsow, C.W., Yakubu, A.A.: Matheamtical models of isolation and quarantine. JAMA 290, 2876–2877 (2003)
Xiao, D., Ruan, S.: Global analysis of an epidemic model with nonmonotone incidence rate. Math. Biosci. 208, 419–429 (2007)
Chinviriyasit, S., Chinviriyasit, W.: Global stability of an SIQ epidemic model. Kasetsart J., (Nat. Sci.) 41, 225–228 (2007)
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Yang, X., Li, F., Cheng, Y. (2012). Global Stability Analysis on the Dynamics of an SIQ Model with Nonlinear Incidence Rate. In: Jin, D., Lin, S. (eds) Advances in Future Computer and Control Systems. Advances in Intelligent and Soft Computing, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29390-0_89
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DOI: https://doi.org/10.1007/978-3-642-29390-0_89
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