Modeling and Control of Measles Transmission in Ghana

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In this study, the Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model is formulated to determine the transmission of measles in Ghana. The model assumes that individuals are equally likely to be infected by the infectious individuals in a case of contact except those who are immune. The undetected individuals are those contributing to the disease transmission in a population. The numerical and qualitative analyses of the model were performed and different state variables were determined. Qualitative results show that the model has the disease-free equilibrium which is locally asymptotically stable for R0 < 1 and unstable for R0 > 1. Simulation of different epidemiological classes revealed that most of the individuals undergoing treatment join the recovered class. It is observed that if the proportion of the population that is immune exceeds the herd immunity level for the disease, then the disease can no longer persist in a population. Thus, if this level of immunity can be exceeded by means of mass vaccination, then the disease can be eliminated.
A thesis submitted to the Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, in partial fulfilment of the requirements for the award of the Degree of Master of Philosophy, 2012