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Home  >  Transasctions of NAMP VOL2

18. Analysis of a Seirs Epidemic Model with Saturated Incidence Rate Considering the Initial State of the Diseases BY M.K. Kolawole and M.O. Olayiwola Transactions of NAMP Volume2,(November, 2016), pp 171 – 180
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In this work, a Susceptible-Exposed-Infected-Recovered-Susceptible (SEIR) epidemic model with saturated incidence rate is investigated. We established the disease-free equilibrium and endemic equilibrium states of the model and analyses for the local and global stabilities of the disease free equilibrium using matrix and Lyapnnov function methods respectively when the basic reproduction number,  Ro < 1 were also studied. We proved that when Ro > 1  the endemic state is locally asymptotically stable. The studied can be viewed as an extension of the work of Kuniya and Nakata to include saturated incidence rate. The effect of initial state of the disease was also studied. At the end, initial state of the disease knowledge play a vital role in disease eradication.Some numerical results were presented to compare our results with existing results.

Keywords: Reproductive Number, SEIRS, Saturated Incidence Rate