The aim of this thesis is to investigate mathematical models for how the media can affect the spread of smoking. In Chapter 2, we review the basic SIR model for the spread of an infectious disease, because we model smoking as an infectious disease. The model contains three compartments: the susceptibles, the infectives and the recovereds. In this Chapter I used sensitivity analysis to analyse the endemic steady-state - this is new. In Chapter 3, we use the standard SIR model as the underlying model to construct the basic smoking PSQ model by adding relapse into the SIR model. The three compartments in this model are the potential smokers, the smokers and the quit smokers group. Relapse is important because one of the features of smoking is that it is easy for quit smoker to start smoking again they do not get lifelong immunity as in infectious diseases. In Chapter 4, we split the quit smokers group into two compartments: the temporarily and permanently quit smoking groups. In Chapter 5, we add the education and determination terms to the PSQ model from Chapter 3 to investigate how the media influences smoking. Similarly, in Chapter 6, we use Chapter 4 as the underlying model and add an education term into that model. The work presented in Chapter 5 and 6 is original work. In each of Chapters 2-6 we present sensitivity analysis of the endemic steady-state, this is rarely been done by others. Analysis of these models demonstrates that there are two steady states for each model. One is the eradicated steady state and the other is the endemic steady state. They are stable when the basic reproduction number is less than one and large than one respectively.