Evaluations of Interventions Using Mathematical Models with Exponential and Non-exponential Distributions for Disease Stages: The Case of Ebola.

Many mathematical models for the disease transmission dynamics of Ebola have been developed and studied, particularly during and after the 2014 outbreak in West Africa. Most of these models are systems of ordinary differential equations (ODEs). One of the common assumptions made in these ODE models is that the duration of disease stages, such as latent and infectious periods, follows an exponential distribution. Gamma distributions have also been used in some of these models. It has been demonstrated that, when the models are used to evaluate disease control strategies such as quarantine or isolation, the models with exponential and Gamma distribution assumptions may generate contradictory results (Feng et al. in Bull Math Biol 69(5):1511-1536, 2007). Several Ebola models are considered in this paper with various stage distributions, including exponential, Gamma and arbitrary distributions. These models are used to evaluate control strategies such as isolation (or hospitalization) and timely burial and to identify potential discrepancies between the results from models with exponential and Gamma distributions.