STABILITE LOCALE ET GLOBALE D’UN MODELE EPIDEMIQUE NON LINEAIRE
Keywords:
Modéle epidémique, Nombre de reproduction basique, Stabilité globale, Stabilité asymptotiquement localeAbstract
Ce travail présente un modéle épidemiologique dans une population de taille totale N qui est divisées en trois sous populations épidémiologiques des personnes qui sont suseptibles, infectieux et ceux mis en quarantaines. Le modèle contient un point d’équilibre trivial et il existe aussi le poin non trivial. Nous avons etudier la stabilité global et local des deux points d’equilibres trivial et non trivial, aussi on a pu obtenir le nombre de reproduction basique.Downloads
References
Anderson. R. M &AL. (1986). A Preliminary Study of the Transmission Dynamics of the Human Immunodeficiency Virus (HIV), the Causative Agent of AIDS. IMA. J. Math. Appl. Med. Biol 3, p. 229-263.
Bailley . N.T.J.(1964). Some Stochastic Models for Small Epidemics in Large Population». Appl. Statist.13, p.9-19.
Bailley. N.T.J.1977. The Mathematical Theory of Infection Diseases and its Application», Applied Statistics, Vol. 26, No. 1, p. 85-87.
Bartlett, M.(1978). An Introduction to Stochastic Processes», 3rd ed. Cambridge University Press.
Isham. V. (1988). Mathematical Modeling of the Transmission Dynamics of HIV Infection and AIDS. J. R. Statist. Soc. A 151, Part 1, p5-30.
Isham. V. (1993). Stochastic Models For Epidemics with special References to AIDS. The Annals of Applied Probability. Vol3. N 1, p. 1-27.
Jin. Z, Zhien. M and Maoan, H. (2006). Globale stability of an SIRS epidemic model with delay, Acta Matimatica Scientia. 26 B. 291-306.
Lounes. R, Arazoza, H. (1995). A Two-Sex Model for the AIDS-Epidemic. Application to the Cuban National Programme on HIV-AIDS. Second Conference on Operation Research, Habana, 3-5 October1995, Cuba.
Lounes. R, Arazoza, H. (2000). Modeling HIV Epidemic Under Contact Tracing. The Cuban Case. Journal of theoritical Medecine Vol 2, p267-274(2000).
Lounes. R, Arazoza, H. (2002). A Non-Linear Model for a Sexually Transmitted Disease with contact tracing. IMA. J. MJath. Appl. Med. Biol. 19, 221-234..
Lounes. R, Arazoza, H. (2003). What percentage of the Cuban HIV-AIDS Epidemic is known? Rev Cubana. Med Trop ; 55(1):30-7
Perto. L. (1996). Differential Equations and Dynamical Systems. 2nd edition, Springer, New York.
Xiao. D and Ruan, S.(2007). Global analysis of an epidemic model with nonmonotone incidence rate, Math Bio, V208, No2. 419-429.
Lounes. R, Arazoza, H. (1995). A Two-Sex Model for the AIDS-Epidemic. Application to the Cuban National Programme on HIV-AIDS. Second Conference on Operation Research, Habana, 3-5 October1995, Cuba.
Lounes. R, Arazoza, H. (2000). Modeling HIV Epidemic Under Contact Tracing. The Cuban Case. Journal of theoritical Medecine Vol 2, p 267-274 (2000).
Lounes. R, Arazoza, H. (2002). A Non-Linear Model for a Sexually Transmitted Disease with contact tracing. IMA. J. MJath. Appl. Med. Biol. 19, p 221-234.
Lounes. R, Arazoza, H. (2003). What percentage of the Cuban HIV-AIDS Epidemic is known? Rev Cubana. Med Trop; 55(1). p30-37
Perto. L. (1996). Differential Equations and Dynamical Systems. 2nd edition, Springer, New York.
Serdal Pamuk, An application for linear and nonlinear heat equations by Adomian’s decomposition method, Appl. Math. Comput. 163 (2005), p 89-96.
Syed Tauseef Mohyud-Din, Mustafa Inc and Ebru Cavlak, On numerical solutions of two-dimensional Boussinesq equations by using Adomian decomposition and He’s homotopy perturbation method, Appl. Appl. Math. Special Issue1. (2010), p 1-11.
Xiao. D and Ruan, S.(2007). Global analysis of an epidemic model with nonmonotone incidence rate, Math Bio, V208, No2. P 419-429.
