Résumé
Network theory has been applied to many aspects of biosciences, including epidemiology. Most epidemiological models in networks, however, have used the standard assumption of either susceptible or infected individuals. In some cases (e.g. the spread of Phytophthora ramorum in plant tradenetworks), acontinuum in the infection status of nodes can better capture the reality of epidemics in networks. In this paper, a Susceptible-Infected-Susceptible model alongacontinuum in the infection status (SISc) is presented, using as a case study directednetworks and two parameters governing the epidemic process (probability of infection persistence (pp) and of infection transmission (pt)). The previously empirically reported linear epidemic threshold in a plot of pp as a function of pt (Pautasso and Jeger, 2008) [29] is derived analytically. Also the previously observed negative correlation between the epidemic threshold and the correlation between links in and out of nodes (Moslonka-Lefebvre et al., 2009) [30] is justified analytically. A simple algorithm to calculate the threshold conditions is introduced. Additionally, acontrol strategy based on targeting market hierarchical categories such as producers, wholesalers and retailers is presented and applied to a realistic reconstruction of the UK horticultural tradenetwork. Finally, various applications (e.g., seed exchange networks, food trade, spread of ideas) and potential refinements of the SISc model are discussed.