Epidemic dynamics on random and scale-free networks

Abstract

Random networks were first used to model epidemic dynamics in the 1950s, but in the last decade it has been realized that scale-free networks more accurately represent the network structure of many real-world situations. Here we give an analytical and a Monte Carlo method for approximating the basic reproduction number R0 of an infectious agent on a network. We investigate how final epidemic size depends on R0 and on network density in random networks and in scale-free networks with a Pareto exponent of 3. Our results show that: (i) an epidemic on a random network has the same average final size as an epidemic in a well-mixed population with the same value of R0; (ii) an epidemic on a scale-free network has a larger average final size than in an equivalent well-mixed population if R0 1 ; (iii) an epidemic on a scale-free network spreads more rapidly than an epidemic on a random network or in a well-mixed population.©Australian Mathematical Society 2013.