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.

Abstract-The flow interior and exterior to a viscous liquid drop in steady motion in an unbounded quiescent fluid is investigated using the perturbation solution of Taylor and Acrivos (1964) to first order in the Reynolds number. New analytical results are derived for the detached wake behind the drop. It is found that as the viscosity of the drop tends to infinity the wake becomes attached to the surface of the drop and the results of Proudman and Pearson (1957) for a solid sphere are rederived.

No abstract

A singular perturbation solution is given for small Reynolds number flow past a spherical liquid drop. The interfacial tension required to maintain the drop in a spherical shape is calculated. When the interfacial tension gradient exceeds a critical value, a region of reversed flow occurs on the interface at the rear and the interior flow splits into two parts with reversed circulation at the rear. The magnitude of the interior fluid velocity is small, of order the Reynolds number. A thin transition layer attached to the drop at the rear occurs in the exterior flow. The effects could model the stagnant cap which forms as surfactant is added but the results apply however the variability in the interfacial tension might have been induced.

No abstract