Global Journal of Pure and Applied Mathematics. ISSN 0973-1768 Volume 16, Number 4 (2020), pp. 588-604 c Research India Publications http://www.ripublication.com/gjpam.htm Mathematical Modelling of Transmission Dynamics of Hepatitis B Virus Incorporating Moderation of Human Activities In Uganda Sr Justine Babirye *1 , George Kimathi 1 , and Sr Agnes Njeri 3 1,2 Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Box 62157-00200, Nairobi-Kenya. 3 Director Centre for Leadership Mgt., Tangaza University College, Nairobi, Kenya. Abstract Hepatitis B is among the dangerous diseases that threaten the lives of many people in the world because it causes cirrhosis and liver cancer. Moderating human activities that lead to its transmission is one way of preventing this deadly disease. In this study,Hepatitis B model for moderation of human activities that lead to transmission dynamics has been formulated and analysed. The threshold value for Hepatitis B transmission was determined using next generation matrix. Jacobian matrix was used to determine local stability of disease free equilibrium point which is stable. The study established the endemic equilibrium point and its local stability was analysed using the Routh-Hurwitz theorem, and was asymptotically stable. We determined the most sensitivity parameter contribution using sensitivity analysis on the threshold value for HBV spread. Numerical simulation was also established and it was found out that Hepatitis B transmission can be reduced from the population through moderation of human activities that contribute towards the increased transmission of Hepatitis B virus. Keywords: Modelling, Hepatitis B Virus disease, equilibrium point, Local stability, Reproductive number,Numerical simulation. * Corresponding author’s e-mail: babsjustine@gmail.com