This paper introduces a new class of accelerated failure-time regression models derived from an equation satisfied by a group of diffusion processes. Several new models are derived. The most general model, which we call the generalized Hernes model, has three shape parameters, in addition to parameters that represent covariant effects on the acceleration of diffusion. This model includes as special cases the log-logistic model, the logistic model, the models that we call the extended Hernes model and the generalized logistic model. The extended Hernes model has two shape parameters and is a regression-extension for the Hernes model. The generalized logistic model also has two shape parameters and is an extension for the log-logistic and logistic models based on the Box-Cox transformation. An application to simulated data on information diffusion through networks shows that some of these models fit the data much better than well-known accelerated failure-time regression models, such as those in the generalized gamma family. The analysis focuses on the effects on information travel time through networks of such structural characteristics as global network density, local network density, number of bridges, and egocentric network expansiveness. It also provides some new substantive insights into diffusion through networks.

>