Kestabilan Model Epidemi Dengan Laju Insidensi Jenuh

Roni Tri Putra, Quinoza Guvil -

Abstract


In this paper, it will be studied stability for a SEIR epidemic model with infectious force in latent, infected and immune period with saturated incidence. From the model it will be found investigated the existence and uniqueness solution  of points its equilibrium. Existence solution of points equilibrium proved by show its differential equations system of equilibrium continue, and uniqueness solution of points equilibrium proved by show its differential equation system of equilibrium differentiable continue.


Keywords


stability, equilibrium points, saturated incidence

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References


Anton H, dan Rorres,C.,2004. Aljabar Linear Elementer Versi Aplikasi, Edisi Kedelapan, alih bahasa oleh Indriasari,R dan Harmaen,I., Erlangga, Jakarta.

Arrowsmith, D.R. dan Place, C.M., 1992, Dynamical System Differential Equation, Maps and Chaotic Behaviour, Chapman & Hall Mathematic, London.

Bazaraa, M.S., Sheraly, H.D, and Shetty, C.M., Nonlinear Programming Theory and Algorithms, John Wiley & Sons, Inc, New York, 1993.

Becerra, M.V., 2008. La Salle’s Invariant Set Theory, http://www.personal.rdg.ac.uk/~shs99vmb/notes/anc/lecture3.pdf

Boyd, Stephen, 2008, Basic Lyapunov Theory, Stanford University, http://www.stanford.edu/class/ee363/lyap.pdf

Capazzo, V., Mathematical Structures of Epidemic Systems, Springer-Verlag, Heidelberg, 2008.

Chong, K.P and Stainslow, H.Z., An Introduction to Optimization, John Wiley & Sons, University of New Hampshire, 1984.

Debarre, F., SIR Models of Epidemics, Theoretical Biology.

Gantmacher, F.R., 1959, The Theory of Matrices, Chelsea Publishing Company, New York.

Hanh, Wolfgang, 1967, Stability of Motion, Springer – Verlag, New York.

Hirsch, M.W., dan Smith, Monotone Dynamical Systems, University of California, Berkeley, 2004.

Iwami. S, Takeuchi, Y., dan Liu, X., 2007. Avian – human Influenza Epidemic Model, Mathematical Biosciences 2007, hal 1-25.

Feng J., dan Hadeler,K.P., Qualitative Behaviour of Some Simple Networks, Mathematical Gen. 1996, hal 5019-5033.

Kocak, H. dan Hole, J.K., 1991, Dynamic and Bifurcation, Springer – Verlag, New York.

Leon, J.S., Aljabar Linear dan Aplikasinya, Edisi Kelima, Alih bahasa olehBondan,A. Erlangga, Jakarta, 1998.

Luenberger, G.D., 1979, Introduction to Dynamic System Theory, Models & Aplication, John Wiley & Sons, New York.

Ngwenga, O., The Role of IncidenceFunctions on the Dynamics of SEIR Model, African Institute for Mathematical Science (AIMS), 2009.

Olsder, G.J., 1994, Mathematical System Theory, Delftse Uitgevers Maatschappij, Netherlands.

Perko L., 1991, Differential Equations and Dynamical Systems, Springer – Verlag, New York.

Ross, S.L., Differential Equations, edition, John Wiley & Sons, University of New Hampshire, 1984.

Verhultz, Ferdinand, 1990, Nonlinear Differential Equations and Dynamical Systems, Springer – Verlag, Berlin.

Wiggins S, 1990, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer – Verlag, New York




DOI: http://dx.doi.org/10.30630/jipr.13.1.64

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