Modelling of rubella dynamics in the presence of vaccination and treatment
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Date
2015
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Publisher
University of Dar es Salaam
Abstract
The speed at which rubella spread and its serious effects in the public health underscores the needs for this study. The main objective of the study is to assess the effect of vaccination and treatment on the transmission of rubella. In this dissertation, a basic rubella model is formulated and extended to incorporate vaccination and treatment. In extended model, six classes of human population are considered namely; susceptibles, vaccinated, exposed, infectives, treated and recovered. The basic and effective reproduction numbers are computed by using next generation operator method. The stabilities of disease free and endemic equilibrium points are analysed by using Centre manifold theory. The results reveal that the disease free equilibrium is locally and globally asymptotically stable whenever the effective reproduction number is less than one. It is also revealed that the endemic equilibrium is locally asymptotically stable when the effective reproduction number is greater than one but when the effective reproduction number is equal to one, forward bifurcation occurs. Sensitivity analysis and numerical simulation are carried out to illustrate the analytical results and test the effect of certain parameters. It is shown that the contact rate of infected individuals with susceptibles is the most sensitive parameter while rate of amount of individuals from the exposed state to infectious state is the least. The numerical results indicate that the number of infected population decreases while recovered individuals increase. This implies that using vaccination and treatment together can reduce the rubella infection from the community.
Description
Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF QR189.5.R8M63)
Keywords
Rubella, Rubella vaccines, Mathematical models
Citation
Moh’d, K.A.(2015) Modelling of rubella dynamics in the presence of vaccination and treatment, Master dissertation, University of Dar es Salaam, Dar es Salaam