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A simple mathematical model for Ebola in Africa
Authors:T Berge
Institution:1. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa;2. Department of Mathematics and Computer Sciences, University of Dschang, Dschang, Cameroon
Abstract:We deal with the following question: Can the consumption of contaminated bush meat, the funeral practices and the environmental contamination explain the recurrence and persistence of Ebola virus 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 absence of the Ebola virus shedding in the environment. For the sub-model without the provision of Ebola viruses, the disease dies out or stabilizes globally at an endemic equilibrium. At the endemic level, the number of infectious is larger for the full model than for the sub-model without provision of Ebola viruses. We design a nonstandard finite difference scheme, which preserves the dynamics of the model. Numerical simulations are provided.
Keywords:Ebola  environmental transmission  dynamical system  NSFD scheme  stability
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