A SEIR Model to Control Varicella Transmission in Ghana

Thumbnail Image
Journal Title
Journal ISSN
Volume Title
In this thesis, a SEIR epidemiological model is formulated to help control the transmission of varicella, using clinical varicella data from Ghana Health Service. The thesis is based on the assumption that the population is constant with birth rate equals death rate. First it is shown that there exists a domain where the model is epidemiologically and mathematically well-posed as desired in any pop- ulation dynamics. Qualitative results show that the model has the disease-free equilibrium point which is locally asymptotically stable for R0 < 1 and unstable for R0 > 1. The Routh-Hurwitz criterion is used to show that the model has an endemic equilibrium point which is locally asymptotically stable when R0 > 1. The basic reproduction number for Ghana is found to be R0 = 1:2869, whiles the herd immunity threshold is found to be HI = 22:3%. Numerical simulation of the model, using MATLAB and a fouth order Runge-Kuta method suggests that one practical measure, to bring the transmission of the disease under control is early detection of the infectious, for isolated supervised treatment. It is concluded that vaccination is the most important factor to control the spread of varicella in case of an outbreak and that 22:3% of the susceptible population needs to be vaccinated in order to bring the disease under control.
A Thesis Submitted to the Department Of Mathematics, Kwame Nkrumah University of Science and Technology In Partial Fulfillment of the requirements for the Award of the Degree Of M.Phil Applied Mathematics.