Epidemic Dynamics Modelling and Analysis for the Respiratory Infectious Diseases: Control, Prevention and Treatment

The goal of this thesis is to develop and analyze mathematical models of respiratory infection diseases, particularly MERS-CoV and influenza, that affect the Middle East daily, and through the Hajj Mass Gathering, to aid in understanding of how these diseases can be spread, and how they may be controlled through public health mitigation. The thesis work employs deterministic and stochastic models of disease transmission between humans and between animals and humans in different settings. We also include analysis of disease spread in a network, and using metapopulation models. We concentrate on the creation and use of models either as criteria for evaluation or as a way of understanding the epidemiological processes with theoretical findings using the following considerations: 1) Developing and checking hypotheses; evaluating quantitative assumptions; measuring sensitivity to changes in model parameters; assessing process conditions from data. 2) Evaluating and contrasting the efficacy of different public health interventions. 3) Interpreting mathematical results to the biological questions. 4) Evaluating the basic reproduction number $ R_{0} $ to provide the early estimates of epidemiological thresholds. 5) Investigating the local and global stability for the equilibrium points