Stochastic Stability of the non linear epidemic model with temporary immunity

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Published: Sep 9, 2017

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Chahrazed Laid
Department of Mathematics, Faclty of Exacte sciences, University Constantine 1, Algeria.

Abstract

In this paper, addresses a time-delayed epidemiologic model by experi-
encing the disease; whenever the quarantine will return to the susceptible.
First, the equilibrium and global stabilities of the endemic equilibrium.
Second, Stochastic Stability. Finally, the equilibrium and stability of the
epidemic model with age.

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How to Cite
Laid, C. (2017). Stochastic Stability of the non linear epidemic model with temporary immunity. Journal of Global Research in Mathematical Archives(JGRMA), 4(8), 01–15. Retrieved from https://jgrma.com/index.php/jgrma/article/view/249
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Vol. 4 No. 8 (2017): August - 2017
Section
Research Paper
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References

Anderson R. M and Medley R M and Jhonson A K. A Preliminary Study of

the Transmission Dynamics of the Human Immunode ciency Virus (HIV),

the Causative Agent of AIDS. IMA. J. Math. Appl. Med. Biol 3, 229-

(1986) :

Abta A and Kaddar A and Talibi H. A. Global Stability for Delay SIR

and SEIR Epidemic Models With Saturated Incidence Rates. Electronic

Journal of Di¤erential Equations, 23,1-13.(2012):

Bailley. N.T.J. Some Stochastic Models for Small Epidemics in Large Pop-

ulation. Appl. Statist.13, 9-19.(1964) :

Bailley. N.T.J. The Mathematical Theory of Infection Diseases and its Ap-

plication. Applied Statistics, 26, N1, 85-87.(1977) :

Batiha, M. S. M. Noorani and I. Hashim. Numerical solutions of the non-

linear integro-di¤erential equations, Int. J. Open Probl. Compt. Math, 34-

(2008) :

Becker.N.G: The Uses of Epidemic Models. Biometrics 35, 295-305.

(1979).

Billard.L: A Stochastic General Epidemic in m Sub-Population. J. Appl.

Prob. 13, 567-572. (1976) :

Jinliang W, Xinxin Tian. Global Stabilty of a Delay Di¤erential Equation

Of Hepatitis B Virus Infection With Immune Response. Electronic Journal

of Di¤erential Equations,94,1-11. (2013).

Jin. Z, Zhien. M and Maoan. H. Globale stability of an SIRS epidemic

model with delay, Acta Matimatica Scientia. 26 B. 291-306.(2006) :

[10] Kuang Y. Delay-Di¤erential Equations with application in population bi-

ology. Academic Press, new york.(1993) :

Lounes. R and Arazoza. H. Modeling HIV Epidemic Under Contact

Tracing. The Cuban Case. Journal of theoritical Medecine Vol 2, 267-

(2000) :

Lounes. R, Arazoza. H. A Non-Linear Model for a Sexually Transmitted

Disease with contact tracing. IMA. J. MJath. Appl. Med. Biol.19, 221-

(2002) :

Lahrouz A and El Maroufy H. Qualitative Behaviour of a Model of an SIRS

Epidemic:Stability and Permanence. Applied Mathematics & Information

Sciences. An International Journal 5 (2), 220-238.(2011):

Luo Q and Mao X. Stochastic population dynamics under regime switching.

J. Math. Anal. Appl.334, 69-84.(2007)

Michael Steel J. Stochastic calculus and nantial applications. Springer-

Verlag. (2003) :

Naresh R, and Omar S. An epidemic model for the transmission dynamics

of HIV/AIDS and another infection. International Journal of Mathematical

Archive-1(3) ; 68-72. (2010) :

Perto. L. Di¤erential Equations and Dynamical Systems. 2nd edition,

Springer, New York.(1996) :

Ray Waston. A useful Random Time-Seal Transformation For The Stan-

dard Epidemic Model. J. Appl. Prob.17, 324-332. (1980) :

Ray Waston, 1980. On The Size Distribution For Some Epidemic Models.

J. Appl. Prob.17, 912-921.(1980) :

Robert N and May. Population Biology of infectious diseases I. Interna-

tional centre of theoritical physics.1-9. (1982) :

Ruoyan Sun. Global stability of the endemic equilibrium of multigroup

SIR models with nonlinear incidence. Computers and Mathematics with

Applications 60. 2286-2291. (2010) :

Takeuchi and W. Ma. Stability analysis on a delayed SIR epidemic model

with density dependent birth process, Dy-nam. Contin. Discrete Impuls.

Systems, 5 . 171-184.(1999):

Volodymyr Makarov, Denis Dragunov. A numeric-analytical method for

solving the Cauchy problem for ordinary diferential equations. Applied

Mathematics and Computation,1-26. (2010) :

[24] W. Ma, Y. Takeuchi, T. Hara and E. Beretta, Permanence of are SIR

epidemic model with distributed time delays, Tohoku Math. J. 54, 581-

(2002)

W. Wang, Global behavior of an SEIR epidemic model with time delay,

Appl. Math. Letters.15, 423-428.(2002).

Wen L and Yang X. Global stability of a delayed SIRS model with tempo-

rary immunity. Chaos, Solitons and Fractals 38, 221-226. (2008)

Xiao, L Chen and F. ven den Bosch, Dynamical behavior for a stage-

structured SIR infectious disease model, Nonlinear Anal. Real World Appl

,175-190.(2002).

Z. Ma, J. Liu and J. Li, Stability analysis for di¤erential infectivity epidemic

models, Nonlinear Anal. Real World Appl 4, 841-856. (2003).

Zhang F and Zhen Li and Zhang F. Global stability of an SIRepidemic

model with constant infectious period. Applied Mathematics and Compu-

tation 199, 285-291.(2008) :