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Home  >  Transactions OF NAMP VOL1

32. On The Reproduction Number of Vaccination Model by A.A. Ayoade, M.O. Ibrahim, O. Odetunde, S.T. Akinyemi Transactions Vol 1, (Nov. 2015), pp 291 – 300
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Abstract

In this work, an SEIR epidemic model was developed to investigate the efficacy of vaccination on the control of epidemic diseases. The dynamics of the compartments were described by a system of ordinary differential equations and the resulting differential equations were analyzed for existence and uniqueness of solution and were found to have a feasible solution. The equations were solved for both the disease free and the endemic equilibrium states. The analysis for stability was done for disease free equilibrium state. We used the method of characteristic equation of the Jacobian determinant to show the local asymptotic stability (LAS) of the model at the disease free equilibrium state.

We also established that the disease free equilibrium state for the model was globally asymptotically stable (GAS) whenever the effective reproduction number R0< 1.Numerical simulations were carried out with the help of Mathematical Software(Maple) using parameter values from published data as the base


Keywords: Existence of solution, stability analysis, disease free equilibrium state, epidemic equilibrium state, reproduction number, local asymptotic stability (LAS), global asymptotic stability (GAS), Numerical simulation

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