OJMSi  Vol.3 No.3 , July 2015
Stability Analysis of an SIR Epidemic Model with Non-Linear Incidence Rate and Treatment
ABSTRACT
We consider a SIR epidemic model with saturated incidence rate and treatment. We show that if the basic reproduction number, R0 is less than unity and the disease free equilibrium is locally asymptotically stable. Moreover, we show that if R0 > 1, the endemic equilibrium is locally asymptotically stable. In the end, we give some numerical results to compare our model with existing model and to show the effect of the treatment term on the model.

Cite this paper
Adebimpe, O. , Bashiru, K. and Ojurongbe, T. (2015) Stability Analysis of an SIR Epidemic Model with Non-Linear Incidence Rate and Treatment. Open Journal of Modelling and Simulation, 3, 104-110. doi: 10.4236/ojmsi.2015.33011.
References
[1]   Bernouilli, D. (1760) Essai d’une nouvelle analyse de la mortalite causse par la petite verole et des avantages de l’innoculation pour al prevenir. In Memoires de Mathematiques et de Physique. Academic Royale Des Science, Paris, 1-45.

[2]   Hethcote, H.W. (2000) The Mathematics of Infectious Disease. SIAM Review, 42, 599-653.
http://dx.doi.org/10.1137/S0036144500371907

[3]   Capasso, V. and Serio, G. (1978) A Generalization of the Kermack-Mckendrick Deterministic Epidemic Model. Mathematical Biosciences, 42, 41-61.
http://dx.doi.org/10.1016/0025-5564(78)90006-8

[4]   Ruan, S. and Wang, W. (2003) Dynamical Behavior of an Epidemic Model with a Nonlinear Incidence Rate. Journal of Differential Equations, 188, 135-163.
http://dx.doi.org/10.1016/S0022-0396(02)00089-X

[5]   van den Driessche, P. and Watmough, J. (2000) A Simple SIS Epidemic Model with a Backward Bifurcation. Journal of Mathematical Biology, 40, 525-540.
http://dx.doi.org/10.1007/s002850000032

[6]   Xiao, D.M. and Ruan, S.G. (2005) Global Analysis of an Epidemic Model with a Nonlinear Incidence Rate. Preprint.

[7]   Jasmine, D.E.C. and Amirtharaj, H. (2014) A Modified SIR Epidemic Model with Immigration and Generalized Saturated Incidence Rate Function. International Journal of Science and Research, 3, 440-443.

[8]   Chauchan, S., Misra O.P. and Dhar, J. (2014) Stability Analysis of SIR Model with Vaccination. American Journal of Computational and Applied Mathematics, 4, 17-23.

[9]   Kaddar, A. (2010) Stability Analysis in a Delayed SIR Epidemic Model with a Saturated Incidence Rate. Nonlinear Analysis: Modelling and Control, 15, 299-306.

[10]   Pathak, S., Maiti, A. and Samanta, G.P. (2010) Rich Dynamics of an SIR Epidemic Model. Nonlinear Analysis: Modelling and Control, 15, 71-81.

 
 
Top