A New Diffusion Process to Epidemic Data

摘要

In this paper, a new non-homogeneous diffusion process is introduced, which is a combination between a Gompertz-type and a log-normal diffusion process, so that the mean function is a mixture between Gompertz and exponential curves. The main innovation of the process is that the trend, after reaches a bound, changes to be increasing or decreasing to zero, a situation that is not provided by the previous models. After building the model, a comprehensive study of its main characteristics is presented. Our goal is to use the process with preditive purpose, so how to get the estimations of the parameters of the process and theirs characteristics functions is presented in this paper. Finally, the potential of the new process to model epidemic data are illustrated by means of an application to simulated data.