A metapopulation model with exit screening measure for the 2014-2016 West Africa Ebola virus outbreak.

We construct a new metapopulation model for the transmission dynamics and control of the Ebola Virus Disease (EVD) in an environment characterized by considerable migrations and travels of people. It is an extended SEIR model modified by the addition of Quarantine and Isolated compartments to account for travelers who undergo the exit screening. The model is well-fitted by using the reported cases from the neighboring countries Guinea, Liberia and Sierra Leone where the 2014-2016 Ebola outbreak simultaneously arose. We show that the unique disease-free equilibrium (DFE) of the model is unstable or locally asymptotically stable (LAS) depending on whether the control reproduction number is larger or less than unity. In the latter case, we prove that the DFE is globally asymptotically stable (GAS) provided that the exit screening is 100% negative. We also prove the GAS of the DFE by introducing more explicit thresholds, thanks to which the existence of at least one boundary equilibrium is established. We design two new nonstandard finite difference (NSFD) schemes, which preserve the dynamics of the continuous model. Numerical simulations that support the theory highlight that exit screening is useful to mitigate the infection. They also suggest that the disease is controlled or the explicit threshold is less than unity provided that the migration and the exit screening parameters are above a critical value.