Untangling the Interplay between Epidemic Spread and Transmission Network Dynamics
Evolution in the numbers of susceptible, primarily and latently infected individuals is shown in panel A, their average number of contacts per person during the epidemic is presented in panel B. The dotted, light colored curves correspond to the results of 20 agent-based simulations. The solid lines are the result of the numerical solution of the set of partial differential equations. A logarithmic scale was chosen to present the different orders of magnitude in the size of the epidemic subgroups. The epidemics take place on a scale free network with an average degree = 1.6 into which individuals are born at a rate of = 0.02 p.a. and die at a rate of = 0.015 p.a.. The epidemic parameters are chosen in accordance with the infectious profile of HIV , i.e., transmission rates in the stages of primary and latent infection are = 2.76 p.a. and = 0.1 p.a., respectively, with rates of progression of = 4.1 p.a. and = 0.12 p.a.. Epidemics are initiated with 10 infected individuals in an otherwise susceptible population (i.e., = 9, = 1, = 9990). Links between susceptible and infected hosts, as well as their contact behavior, are initially uncorrelated, i.e. , . Panels C and D show the evolution of the probability generating functions and distributions in the number of contacts over 20 years of the epidemic for individuals newly entering the population (, ) as well as in susceptible, primarily and latently infected individuals (, , ). The contour plots of the PGFs interpolate from 0 (dark colors) to 1 (light colors) in steps of 0.1.