Journal of Modern Mathematics and Statistics

Year: 2019
Volume: 13
Issue: 2
Page No. 28 - 39

Biufrcation Analysis on Infection Disease Treatment by Compartment Models

Authors : TadesseLamessa

References

Anderson, R. and R. May, 1991. Infectious Diseases of Humans: Dynamics and Control. Oxford University Press, Oxford.

Beretta, E. and Y. Takeuchi, 1995. Global stability of an SIR epidemic model with time delays. J. Math. Biol., 33: 250-260.
CrossRef  |  Direct Link  |  

Beretta, E. and Y. Takeuchi, 1997. Convergence results in SIR epidemic models with varying population sizes. Nonlinear Anal., 28: 1909-1921.
CrossRef  |  Direct Link  |  

Beretta, E., T. Hara, W. Ma and Y. Takeuchi, 2001. Global asymptotic stability of an SIR epidemic model with distributed time delay. Nonlinear Anal. Theor. Meth. Appl., 47: 4107-4115.
CrossRef  |  Direct Link  |  

Bogdanov, R., 1981. Bifurcations of a limit cycle for a family of vector fields on the plan. Selecta Math. Soviet., 1: 373-388.

Bogdanov, R., 1981. Versal deformations of a singular point on the plan in the case of zero Eigen-values. Selecta Math. Soviet., 1: 389-421.

Brauer, F. and P. van den Driessche, 2001. Models for transmission of disease with immigration of infectives. Math. Biosci., 171: 143-154.
PubMed  |  Direct Link  |  

Capasso, V. and G. Serio, 1978. A generalization of the Kermack-McKendrick deterministic epidemic model. Math. Biosci., 42: 43-61.
CrossRef  |  Direct Link  |  

Derrick, W.R. and P. Van Den Driessche, 1993. A disease transmission model in a nonconstant population. J. Math. Bio., 31: 495-512.
CrossRef  |  PubMed  |  Direct Link  |  

Diekmann, O. and M. Kretzschmar, 1991. Patterns in the effects of infectious diseases on population growth. J. Math. Bio., 29: 539-570.
PubMed  |  Direct Link  |  

Earn, D.J., P. Rohani, B.M. Bolker and B.T. Grenfell, 2000. A simple model for complex dynamical transitions in epidemics. Sci., 287: 667-670.
CrossRef  |  PubMed  |  Direct Link  |  

Feng, Z. and H.R. Thieme, 1995. Recurrent outbreaks of childhood diseases revisited: The impact of isolation. Math. Biosci., 128: 93-130.
PubMed  |  Direct Link  |  

Feng, Z. and H.R. Thieme, 1995. Recurrent outbreaks of childhood diseases revisited: The impact of isolation. Math. Biosci., 128: 93-130.
PubMed  |  Direct Link  |  

Hethcote, H.W. and D.W. Tudor, 1980. Integral equation models for endemic infectious diseases. J. Math. Bio., 9: 37-47.
CrossRef  |  Direct Link  |  

Hethcote, H.W. and P. Van den Driessche, 1991. Some epidemiological models with nonlinear incidence. J. Math. Bio., 29: 271-287.
CrossRef  |  PubMed  |  Direct Link  |  

Hethcote, H.W. and P. Van den Driessche, 1991. Some epidemiological models with nonlinear incidence. J. Math. Bio., 29: 271-287.
CrossRef  |  PubMed  |  Direct Link  |  

Hethcote, H.W. and S.A. Levin, 1989. Periodicity in Epidemiological Models. In: Applied Mathematical Biology, Levin, S.A., T.G. Hallam and L.J. Gross (Eds.). Springer, New York, USA., pp: 193-211.

Hethcote, H.W., H.W. Stech and P. Van Den Driessche, 1981. Nonlinear oscillations in epidemic models. SIAM. J. Appl. Math., 40: 1-9.
CrossRef  |  Direct Link  |  

Hyman, J.M. and J. Li, 1998. Modeling the effectiveness of isolation strategies in preventing STD epidemics. SIAM. J. Appl. Math., 58: 912-925.
Direct Link  |  

Hyman, J.M. and J. Li, 1998. Modeling the effectiveness of isolation strategies in preventing STD epidemics. SIAM. J. Appl. Math., 58: 912-925.
Direct Link  |  

Kermack, W.O. and A.G. McKendrick, 1927. Contribution to the mathematical theory of epidemics, part I. Proc. R. Soc. London Ser. A, 115: 700-721.
CrossRef  |  Direct Link  |  

Liu, W.M., H.W. Hethcote and S.A. Levin, 1987. Dynamical behavior of epidemiological models with nonlinear incidence rates. J. Math. Bio., 25: 359-380.
PubMed  |  Direct Link  |  

Ma, W., M. Song and Y. Takeuchi, 2004. Global stability of an SIR epidemicmodel with time delay. Appl. Math. Lett., 17: 1141-1145.
Direct Link  |  

Ma, W., Y. Takeuchi, T. Hara and E. Beretta, 2002. Permanence of an SIR epidemic model with distributed time delays. Tohoku Math. J. Second Ser., 54: 581-591.
CrossRef  |  Direct Link  |  

Ma, W., Y. Takeuchi, T. Hara and E. Beretta, 2002. Permanence of an SIR epidemic model with distributed time delays. Tohoku Math. J. Second Ser., 54: 581-591.
CrossRef  |  Direct Link  |  

Ruan, S. and W. Wang, 2003. Dynamical behavior of an epidemic model with a nonlinear incidence rate. J. Differ. Equations, 188: 135-163.
CrossRef  |  Direct Link  |  

Xiao, D. and S. Ruan, 2007. Global analysis of an epidemic model with nonmonotone incidence rate. Math. Biosci., 208: 419-429.
CrossRef  |  PubMed  |  Direct Link  |  

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