Stability Analysis of an SIR Epidemic Model with Non-Linear Incidence Rate and Treatment

Olukayode Adebimpe^1*, Kehinde Adekunle Bashiru², Taiwo Adetola Ojurongbe²

¹Department of Industrial Mathematics, Landmark University, Omuaran, Nigeria.
²Department of Mathematical and Physical Science, Osun State University, Osogbo, Nigeria.

DOI: 10.4236/ojmsi.2015.33011                

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.

Keywords

SIR Epidemic Model, Basic Reproduction Number, Local Stability, Treatment, Saturated Incidence Rate

Conflicts of Interest

The authors declare no conflicts of interest.

References

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