Advanced Applied Statistics: Mathematical Modelling

This book is about modeling of infectious diseases which are normally recurrent. The human immunodeficiency virus (HIV) pandemic presents a massive challenge to the control of recurrent diseases like tuberculosis (TB) at all levels. Tuberculosis is also one of the most common causes of morbidity and one of the leading causes of mortality in people living with HIV/AIDS (PLWHA). In this book, various mathematical models that capture the role played by HIV/AIDS in accelerating the infection and hence spread of Tuberculosis. We looked at TB progression among people with HIV and those without. The model is formulated for TB/HIV negative individuals as well as for TB/HIV positive people. The model was developed using the first order partial differential Mackendrick-Von Foster equation. Further, different epidemiological techniques to estimate parameters in the model are surveyed. These parameters were estimated through extraction of relevant information from data available in other literature. Simulation was done using Matlab and Graphs produced for easy understanding of the text.