Stability Analysis of Deterministic Cholera Model

DIMI Jean Luc, BISSILA BISSILA, Theophile MAVOUNGOU

Abstract


In this paper, we study two models models for the dynamics spread and transmission of cholera.For these models Lyapounov functions are used to show that when the basic reproduction number is less than or equal to one, the disease free equilibrium is globally stable , and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

Keywords


Nonlinear epidemic model; Lyapounov function; asymptotic stability.

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References


J Arino, C. McCluskey and P. Van den Driessche Global results for an endemic model with vaccination that exhibits backward bifurcation Siam Journ. on applied Math., 64, 2003, 260-276.

B Buonomo, D.Lacitignola On the use of the geometric approach to global stability for three dimensional ODE systems : A bilinear case Journal of mathematical analysis and applications num. 348 (2008)255-266.

Y. Cheng and X. Yang On the global stability of SEIRS models in epidemiology Canadian Journ. Applied Math. quartely vol. 20, n2 pp 115-131.

J. L. DIMI Thése de l'Université de Metz (2006).

J. Muldowney Compound matrices and ordinary differential equations Rocky Mountains J. of Math.n20 ,pp 857-872.

P. Van den Driessche , J. Watmough reproduction numbers and sub-thresolds endemic equilibria for compartimental models of diseases transmission Math. Biosciences vol. 180, pp29-48.

C. Vargas-De- Leon Analysis of a model for dynamics of Hepatitis B with noncytolytic loss of infected cells World J. of Modelling and Simulation Vol 8, n4 pp 243-259.

J. Wang and C. Modmak Modelling cholera dynamics with controls Canadian Journ. Applied Math. quartely vol. 20, n3 pp 255.


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