A mathematical model with isolation for the dynamics of Ebola virus

In the absence of valid medicine and vaccine, isolation strategy is an important measure against Ebola virus outbreaks. In this paper, we present a deterministic compartmental model for assessing the impact of isolation to contain Ebola virus. The model includes the demographic effects, the latent undetectable and latent detectable compartments with isolation of infectious individuals. We study the outbreak of Ebola occurred in Sierra Leone. The numerical simulation shows that the isolation of latent detectable and infectious individuals is the most effective in curtailing the virus. Then, we present an optimal control problems subject to the model with the aim to derive the optimal isolation strategies. For each strategy, we study a specific objective in order to minimize not only the number of latent detectable and infected individuals but also the cost associated with the isolation program.