Mathematical Modelling Of Epidemic Dynamics And Epidemic Controls On Complex Social Networks

In this thesis,the epidemic dynamics and epidemic controls are studied using the combination of mathematical models and complex social network.Firstly,the compart-mental epidemic models are formulated and analysed by some essential mathematical tools.Two control strategies:vaccination and quarantine are added up to the standard S EIR epidemic models.The sufficient conditions of existence and uniqueness of solution are verified and basic reproduction number(R0)of each model is derived.Accordingly,local stability and global stability are also adjudicated through the basic reproduction number.If R0<1,the disease will no longer spread among population.In contrast,the disease will emerge and remain in population if Ro>1.The latter case can cause wide-range damages and it should be defended by some optimal levels of vaccination and quarantine.Increasing in vaccination and quarantine rates is able to reduce Ro and reduce the infection.Secondly,network algorithm and C++ programming are developed.Prop-erties of generated network and its distribution are observed.Simulation on computer-generated network taking into account a heterogeneously distributed population is car-ried out to predict how the disease spreads and how effective control strategies are.A multi-group SEIR epidemic model and a network with community structure organised by modularity are incorporated together.Different levels of vaccination are investigat-ed.Statistical methodologies are employed in data analyses after obtaining simulation results.It is expected that the conceptual and theoretical contributions of this thesis can be further extended for vaccine development,preventing pandemonium,controlling eco-nomic fluctuation and drawing public policies when there is an epidemic outbreak.