The use of mathematics in understanding the dynamics of infectious and non-infectious diseases is a major area of research, worldwide. As we know, measles is one of the most contagious infectious diseases known to man; its prevalence is still prominent worldwide. However, most of the models on measles exclude consideration of the effects of vaccination on the dynamics of measles infection, though, it is a known fact that vaccination is the most effective means of preventing measles’ outbreak. This book presented background studies that had been carried out on dynamics of infectious diseases, especially measles, by some researchers and models presented in those research works was examined and extended to include new compartments. In addition to mathematical models and analysis contained in this book, a statistical analysis of measles data set was perused. This book will be useful to undergraduate and postgraduate students that are interested in mathematical modelling of infectious diseases in particular and biomathematics in general.