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Ebola virus disease is a lethal human and primate disease that currentlyrequires a particular attention from the international health authorities dueto important outbreaks in some Western African countries and isolated cases inthe United Kingdom, the USA and Spain. Regarding the emergency of thissituation, there is a need of development of decision tools, such asmathematical models, to assist the authorities to focus their efforts inimportant factors to eradicate Ebola. In this work, we propose a noveldeterministic spatial-temporal model, called Be-CoDiS (Between-CountriesDisease Spread), to study the evolution of human diseases within and betweencountries. The main interesting characteristics of Be-CoDiS are theconsideration of the movement of people between countries, the control measureeffects and the use of time dependent coefficients adapted to each country.First, we focus on the mathematical formulation of each component of the modeland explain how its parameters and inputs are obtained. Then, in order tovalidate our approach, we consider two numerical experiments regarding the2014-15 Ebola epidemic. The first one studies the ability of the model inpredicting the EVD evolution between countries starting from the index cases inGuinea in December 2013. The second one consists of forecasting the evolutionof the epidemic by using some recent data. The results obtained with Be-CoDiSare compared to real data and other models outputs found in the literature.Finally, a brief parameter sensitivity analysis is done. A free Matlab versionof Be-CoDiS is available at: http://www.mat.ucm.es/momat/software.htm

Be-CoDiS: A mathematical model to predict the risk of human diseases  spread between countries. Validation and application to the 2014-15 Ebola  Virus Disease epidemic