Abstract
In this paper, we consider a SIR epidemic model with demographic effects. By carrying out a global analysis of the model and studying the locally stability of the equilibrium in this paper, and make some predictions implied by this model about some qualitative aspects of the spread of a disease, we show that the equilibrium of a SIR epidemic model is locally astatically stable.
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References
[1] Brauer, F dan Chavez, C.C. 2001. Mathematical Models in Population Biology and Epidemiology.NewYork:Springer-Verlag.
[2] Dickmann, O. dan Heesterbeek, J.A.P. 2000. Mathematical Epidemiology of Infectious Disease; Model Building, Analysis and Interpretation. England : Jhon Wiley and Sons . Ltd.
[3] D.G. Luenberger. 1979. Dynamic System; Theory, Models, & Applications, John Wiley & Sons, Canada.
[4] J.A. Yorke, W.P. London. 1973. Recurrent outbreaks of measles, chickenpox, and mumps II, AM. J. Epidemiol, 98, 469-482.
[5] Nurul, H. Analysis of disease-free equilibrium point for a SEIV epidemic model with nonlinear incidence rate. Makalah disampaikan pada Seminar Internasional Matematika dan Penerapannya Jurusan Matematika FMIPA UGM, Yogyakarta, 12 Oktober 2009.
[6] M. A. Titelbaulm, M. Edmunds. 1999. Immunization and Vaccine-Preventable Illness, Stat. Bull. Metrop. Insur. Co., 80, 13-20
[2] Dickmann, O. dan Heesterbeek, J.A.P. 2000. Mathematical Epidemiology of Infectious Disease; Model Building, Analysis and Interpretation. England : Jhon Wiley and Sons . Ltd.
[3] D.G. Luenberger. 1979. Dynamic System; Theory, Models, & Applications, John Wiley & Sons, Canada.
[4] J.A. Yorke, W.P. London. 1973. Recurrent outbreaks of measles, chickenpox, and mumps II, AM. J. Epidemiol, 98, 469-482.
[5] Nurul, H. Analysis of disease-free equilibrium point for a SEIV epidemic model with nonlinear incidence rate. Makalah disampaikan pada Seminar Internasional Matematika dan Penerapannya Jurusan Matematika FMIPA UGM, Yogyakarta, 12 Oktober 2009.
[6] M. A. Titelbaulm, M. Edmunds. 1999. Immunization and Vaccine-Preventable Illness, Stat. Bull. Metrop. Insur. Co., 80, 13-20