August 28, 2008 17:47 World Scientific Book - 9in x 6in ws-book9x6 Chapter 1 Interplay of network state and topology in epidemic dynamics Thilo Gross Max-Planck Institute for the Physics of Complex Systems, N¨ othnitzer Straße 38, 01187 Dresden, Germany 1.1 Introduction Throughout history epidemic diseases have been a constant threat to hu- mans (Cartwright, 1972; Oldstone, 1998). There is evidence that even our earliest ancestors suffered from disease-related mortality (Hart, 1983). Many of the old diseases have by now become harmless childhood mal- adies or have disappeared entirely. However, as humankind prospered and spread out new epidemic diseases continued to arrive in the human popu- lation (Karlen, 1995). The extend to which epidemic diseases have shaped our culture and politics can be guessed from religious texts, which contain numerous references to epidemics and rules for their avoidance. In the 20th century we have witnessed a brief episode in which it seemed that mankind was about to win the struggle and free itself from epidemics. The widespread use of antibiotics drove many infectious diseases back to hiding places in remote locations and animal populations (so-called disease vectors ). Some sources hold that the second world war was the first major war in history in which far more lives were lost due to fighting than epi- demics (Karlen, 1995). But, even when the belief that biomedical progress would conquer epidemics was still widespread, there was evidence to the contrary: In the 1950 new hemorrhagic fevers appeared in several parts of the world (Daubney et al., 1993). The subsequent decades brought Legion- 1