Optimal control metapopulation models for the West Africa Ebola epidemic and their nonstandard finite difference discretizations

The 2014-2016 Ebola Virus disease (EVD) outbreak came with an unprecedented challenge. It simultaneously arose in three different countries with considerable inbound and outbound travels. This led the World Health Organization (WHO) to suggest implementing exit screening of travelers at their borders. In addition to this measure, some countries accounted for entry screening and/or vaccination to curb the disease. In this paper, we consider two optimal controls for patch models in which other interventions supplement exit screening. The first problem is defined through the exit and entry screenings of travelers. The second involves the combination of exit screening and vaccination interventions. We prove the well-posedness of both optimal control problems. For each problem, we construct a new Nonstandard Finite Difference Forward-Backward-Sweep-Method, which preserves the dynamics of the continuous model. Numerical simulations that support the theory are provided. They also suggest that vaccination alone is effective in reducing the disease burden.