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Home  >  Volume 36 (no2)

On the Effect of poliomyelitis and immunity in poliovirus epidemiology and the Role of Vaccine. by H.A Gazali and M.M. Altine (pages 121-130)
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Abstract

In this paper, we studied the mathematical modeling of the effect of poliomyelitis and immunity in poliovirus epidemiology. It centers on the application of mathematics as a tool in explaining the dynamics of poliovirus transmission. The study is based on understanding the role of Vaccine. This work focuses on rate of Vaccine and the Chronicle stage of the virus tested for the existence and uniqueness of solution for the model using the Lipchitz condition to ascertain the efficacy of the model and proceeded to determine both the Disease Free Equilibrium (DFE) and the Endemic Equilibrium (EE) for the system of equations. We have seen that the system equations has a Unique solution. The local stability of the (DFE) of the model was obtained using the Variational Matrix Criteria while the stability of (EE) was analyzed. The reproduction number was calculated and simulated. We demonstrated that the disease will die out if the basic reproductive numbers for the disease-free equilibrium R0< 1. This is the case of a disease free state, with no infection in the population. Otherwise, the disease may become endemic if the basic reproductive number R0 is bigger than unity (i.e R0> 1). The basic reproduction number at both the disease Free State and the endemic state were obtained and the result shows stability in the role of Vaccine as a means of reducing the spread of the disease in the society.

Keywords: poliovirus, DFE, EE, Symptoms, model, stability

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