Kinetics of distribution of infections in networks

SummaryWe develop a model for disease spreading in networks in a manner similar to the kinetics of crystallization of undercooled melts. The same kind of equations can be used in ecology and in sociology studies. For instance, they control the spread of gossip among the population. The time t dependence of the overall fraction α(t) of an infected network mass (individuals) affected by the disease is represented by an S-shaped curve. The derivative, i.e. the time dependence of intensity W(t) with which the epidemic evolves, is a bell-shaped curve. In essence, an analytical solution is offered describing the kinetics of spread of information along a (d-dimensional) network.