Mathematical Modeling of the Epidemiology of Varicella

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In this thesis a modified SIR mathematical model on the spread of Varicella (Chickenpox) in Ghana was developed. Here the population is divided into three compartments: the susceptibles, the infectives, and the recovered. The resulting system of non-linear differential equations was analysed, thus in respect of the stability of the equilibrium points. The model focuses on the spread of the disease at the initial stages of the infection when the infected persons are absent and when they are present taking into consideration birth rate and natural death rate. The study is based on the assumption that the population of Ghana is constant, and the natural death rate was assumed to be equal to the birth rate. We then determine how the various compartments react to increasing proportion of persons at the initial stages of their infection. We perform sensitivity analysis on the already estimated model parameters to determine their effect on the reproductive number and at what values of the reproductive number are the disease free and endemic equilibra stable.
A thesis submitted to the Board of Postgraduate Studies, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the award of the Degree of Master of Philosophy