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Algebraic analysis of social networks for bio-surveillance: the cases of SARS-Beijing-2003 and AH1N1 influenza-Mexico-2009.
(SPRINGER-VERLAG BERLIN, 2011-01-01) Hincapié D; Ospina J; Hincapié D; Ospina J; Universidad EAFIT. Departamento de Ciencias; Lógica y Computación
Algebraic analysis of social networks exhibited by SARS-Beijing-2003 and AH1N1 flu-Mexico-2009 was realized. The main tools were the Tutte polynomials and Maple package Graph-Theory. The topological structures like graphs and networks were represented by invariant polynomials. The evolution of a given social network was represented like an evolution of the algebraic complexity of the corresponding Tutte polynomial. The reduction of a given social network was described like an involution of the algebraic complexity of the associated Tutte polynomial. The outbreaks of SARS and AH1N1 Flu were considered like represented by a reduction of previously existing contact networks via the control measures executed by health authorities. From Tutte polynomials were derived numerical indicators about efficiency of control measures.