Modeling Importations and Exportations of Infectious Diseases via Travelers

This paper is an attempt to estimate the risk of infection importation and exportation by travelers. Two countries are considered: one disease-free country and one visited or source country with a running endemic or epidemic infectious disease. Two models are considered. In the first model (disease importation), susceptible individuals travel from their disease-free home country to the endemic country and come back after some weeks. The risk of infection spreading in their home country is then estimated supposing the visitors are submitted to the same force of infection as the local population but do not contribute to it. In the second model (disease exportation), it is calculated the probability that an individual from the endemic (or epidemic) country travels to a disease-free country in the condition of latent infected and eventually introduces the infection there. The input of both models is the force of infection at the visited/source country, assumed known. The models are deterministic, but a preliminary stochastic formulation is presented as an appendix. The models are exemplified with two distinct real situations: the risk of dengue importation from Thailand to Europe and the risk of Ebola exportation from Liberia to the USA.