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Epidemiology and Networks

Ashrafi Amineh, Rasa | 2020

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 53885 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Haji Sadeghi, Mir Omid; Razvan, Mahammad Reza
  7. Abstract:
  8. Networks and the epidemiology of directly transmitted infectious diseases are fun-damentally linked. The foundations of epidemiology and early epidemiological models were based on population wide random-mixing, but in practice each individual has a finite set of contacts to whom they can pass infection; the ensemble of all such contacts forms a network. Knowledge of the structure of the network allows models to compute the epidemic dynamics at the population scale from the individual-level behaviour of infections.Motivated by the analysis of social networks, we study a model of random net-works that has both a given degree distribution and a tunable clustering coefficient.We consider two types of growth processes on these graphs: diffusion and symmet-ric threshold model. The diffusion process is inspired from epidemic models. It is characterized by an infection probability, each neighbor transmitting the epidemic independently. In the symmetric threshold process, the interactions are still local but the propagation rule is governed by a threshold (that might vary among the different nodes). As an example of symmetric threshold process, we study the con-tagion process which is a simple coordination game played on the network. Here we analyze the impact of clustering on the growth processes. For both diffusion and symmetric threshold models, we characterize conditions under which global cascades are possible and compute their size explicitly, as a function of the degree distribution and the clustering coefficient. We show the results on regular and power-law graphs with exponential cutoff and see the impact of clustering
  9. Keywords:
  10. Network ; Epidemiology ; Infectious Diseases ; Clustering Coefficient ; Random Graph ; Epidemic

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