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Home  >  Volume 32 (Nov. 2015)

On the Stability Analysis of Infectious Model with Therapy A.A. Ayoade, M.O. Ibrahim, H.O. Edogbanya, O. Odetunde, S.T. Akinyemi (page 221-228)
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Abstract

 

In this work an SEIR epidemic model was proposed to understand the impact of other efforts (such as sustainable environmental policy, quarantine, health education, etc) in addition with vaccination in generating speedy transition to recovery even at the ‘exposed stage’. The possibility of transition from the exposed class to the recovery class was taken into consideration. The dynamics of the compartments were described by a system of ordinary differential equations and all the equations were solved to establish the disease free equilibrium state and the epidemic equilibrium state of the model. Stability analysis was also carried out on the disease free equilibrium state and the epidemic equilibrium state using the concepts of the characteristic equation of the Jacobian determinant and the Bellman and Cooke’s theorem. Numerical simulations were carried out with the help of Mathematical Software (Maple) using parameter values from published data as the base.  It was found out that the disease free equilibrium state and the epidemic equilibrium state of the model were stable. Stability of the equilibrium states of the model implied that the disease died out whenever there was an outbreak due to combination of vaccination and other factors.

  Keywords: Epidemic model, sustainable policy, disease free equilibrium, epidemic equilibrium, stability,  Numerical simulations

 

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