MODELING HEPATITIS B VIRUS TRANSMISSION WITH FRACTIONAL ORDER DIFFERENTIAL EQUATIONS AND VACCINATION IN ETHIOPIA

Abstract

In this thesis a deterministic mathematical model of HBV dynamics with vaccination is developed. The model is also extended in to fractional order to consider memory ef- fect. We formulated and analyzed a deterministic model and the model considers two age structure; children(aged 14 years) and adult(aged > 14 years). The qualitative analysis of both models were performed. Basic reproduction number of the models were determined. Local and global stability for both disease free and endemic equilibrium points were determined. Sensitivity analysis was done by using normalized forward sen- sitivity index approach. Numerical simulation of deterministic model were performed to study the e ects of newborn vaccine immediately after birth, vaccination of children and adult vaccination and to compare their e ects on dynamics of HB disease. Com- parison result between vaccination shows that increasing newborn vaccine immediately after birth is the best to eliminate hepatitis B virus disease. Also numerical simulation of the extended fractional order model were done to investigate the e ect of memory on hepatitis B disease dynamics by varying order of derivatives. It was observed that num- ber of infective population decreases faster and evenfall to zero overtime for model with memory than memory-less model. Therefore, we come to the conclusion that increasing new born vaccine immediately after birth is very important to eliminate hepatitis B virus disease.