Graph theoretic applications to disease models

Disease models formulated based on a mass action principle assume a homogeneousmixing of particles of substances or humans. For these diseases, this assumptionis reasonable and good as there is an abundance of everyday situations whereindividuals are exposed to such infections through random mixing such as at airports,workplace, shops, drinking holes, and in classrooms. The standard epidemiologicalmodels have to take into account for heterogeneity in sexual activities and mixing patterns.Random interactions between humans is at odds with everyday intuition andexperience as well as empirical reports on human sexual behavior. This contempt anddisregard of complex patterns and structures of intimate contacts, whose heterogeneityis apparent due to the selective nature of humans, by standard epidemiologicalmodels,has often resulted in models whose inaccuracies are overwhelming. In this chapter, weconsider the application of graph theoretic approaches, to model heterogeneity. Wereview, a few studies, on the nature of empirical sexual patterns in societies and introducea simple graph model for (sexual) networks.