| Summary: | This thesis studies dynamics and control of epidemic spreading in complex networks especially scale-free networks. Four problems have been investigated which, to the best of our knowledge, have been largely missed in existing results. The four problems include
1) Effectiveness of imperfect targeted immunization. It is taken into account that protections in large-scale systems may not be perfect due to realistic constraints. Analytical and simulation results show that such protections cannot easily prevent an epidemic outbreak from happening yet can significantly reduce the infection size.
2) Effects of human behaviors of reducing social contacts when in face of a dangerous infectious disease. A few scenarios are studied. It is revealed that similar to that of the imperfect targeted protection, the fear factor-driven behaviors may not easily prevent the spreading from happening yet do help reduce the infection size.
3) Epidemic spreading in two interconnected networks. We show that interconnected systems have a lower epidemic thresholds compared to those of two isolated systems. When under infection with lower-than-threshold transmissibility, the average outbreak size (AOS) is also increased. The threshold and AOS are both sensitive to the interconnection pattern. When under infection with higher-than-threshold transmissibility, however, the infection size is not sensitive to the interconnection pattern. Such observation may help better understand the risks faced by newly-emerged integrated systems, e.g., smart grids.
4) Finally we extend our work to social complex systems to study the dynamics of the spreading of two competing ideas with neighborhood influences which may affect each other’s spreading. We show that compared to the case with only a single idea, dynamics of two competing ideas turns out to be much more complex. Depending on whether the neighborhood influences strictly prohibit the transmission of the competitor idea and their respective spreading rates, different final states may include exclusion, multiple coexistences, founder control, and many more.
We believe that the above studies provide useful insights into the effects of complex human behaviors and human society structures on the spreading and control of one or multiple infectious agents. Such knowledge would help better handle the infectious diseases in human society, digital viruses in computer and telecommunication systems, as well as the spreading of information/ideas/rumors in human communities, etc. General background and some future research topics are also discussed.
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