We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contaminationexplaintherecurrenceandpersistenceofEbolavirus disease outbreaks in Africa? We develop an SIR-type model which, incorporates both the direct and indirect transmissions in such a manner that there is a provision of Ebola viruses. We prove that the full model has one (endemic) equilibrium which is locally asymptotically stable whereas, it is globally asymptotically stable in the absenceoftheEbolavirussheddingintheenvironment.ForthesubmodelwithouttheprovisionofEbolaviruses,thediseasediesoutor stabilizes globally at an endemic equilibrium. At the endemic level, thenumberofinfectiousislargerforthefullmodelthanforthesubmodel without provision of Ebola viruses. We design a nonstandard finitedifferencescheme,whichpreservesthedynamicsofthemodel. Numericalsimulationsareprovided.
