Contacts between infected and susceptible individuals within a population form a network of interactions. The topology, or structure of this network can affect the pattern and rate of disease spread throughout a population. This description of a network of interactions between individuals within a population contrasts with the more common assumption used in disease modeling that populations are fully mixed, and thus an individual is equally likely to infect any other individual in the same population. Newman (2002) used a network approach (and moment generating functions) to analytically solve SIR models, to determine epidemic thresholds by which the disease will spread through the population if a given transmissibility is reached, and to get the average outbreak size for any transmissibility value and network configuration (determined by degree distribution). Additionally, the author used simulations to demonstrate the analytic results of the above models held in more complicated networks that had variable infectiveness times and correlated transmission probabilities across all pairs of individuals. This approach was also applied to a bipartite network describing sexually transmitted disease between men and women. These models showed that a small number of highly connected individuals in the network can have a disproportionate effect on the spread of a disease through a population, and thus preventative measures targeted at these most connected individuals may be more effective than measures targeting the whole population.
Newman, M. E. J. Spread of epidemic disease on networks. Phys. Rev. E 66, 016128 (2002).