Algebraic Analysis of Social Networks for Bio-surveillance: The Cases of SARS-Beijing-2003 and AH1N1 Influenza-Mexico-2009

Algebraic analysis of social networks exhibited by SARS-Beijing-2003 and AH1N1 flu-Mexico-2009 was realized. The main tools were the Tune 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 Tune polynomial. The reduction of a given social network was described like an involution of the algebraic complexity of the associated Tune 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.