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Ebola virus disease (EVD) can rapidly cause death to animals and people, for less than 1month. In addition, EVD can emerge in one region and spread to its neighbors in unprecedented durations. Such cases were reported in Guinea, Sierra Leone, and Liberia. Thus, by blocking free travelers, traders, and transporters, EVD has had also impacts on economies of those countries. In order to find effective strategies that aim to increase public knowledge about EVD and access to possible treatment while restricting movements of people coming from regions at high risk of infection, we analyze three different optimal control approaches associated with awareness campaigns, treatment, and travel-blocking operations that health policy-makers could follow in the war on EVD. Our study is based on the application of Pontryagin's maximum principle, in a multi-regional epidemic model we devise here for controlling the spread of EVD. The model is in the form of multi-differential systems that describe dynamics of susceptible, infected, and removed populations belonging to p different geographical domains with three control functions incorporated. The forward-backward sweep method with integrated progressive-regressive Runge-Kutta fourth-order schemes is followed for resolving the multi-points boundary value problems obtained. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In this paper, we propose a free final time optimal control approach applied to 4 ordinary differential equations which describe the tumor‐immune interactions after the injection of the bacillus Calmette‐Guérin (BCG) in the bladder of a hypothetical patient. The main goal of this optimal control strategy is to find the optimal dosage amount needed in each instillation of BCG for stimulating the immune‐system and then killing superficial bladder tumors and to determine the optimal duration of treatment, adequate for stopping the intravesical therapy with lesser side‐effects. For this, we introduce into the model of interest, a control function which represents the dose of BCG immunotherapy procedure and we formulate a minimization problem where the final time is considered free (nonfixed). The characterization of the sought optimal control noted u∗ is derived based on Pontryagin's maximum principle, while the formulation of the sought optimal final time noted t f i n a l ∗ is based on formulae of sensitivity which are obtained conditions from the derivative of the objective function with respect to t f i n a l ∗. We investigate the resolution of the free final time optimal control problem in 3 possible cases: (a) when t f i n a l ∗ is quadratic in the final gain function, (b) when the final gain function does not depend on t f i n a l ∗, and (c) when t f i n a l ∗ is linear in the final gain function. Finally, we obtain the sought optimal dose of BCG, and we conclude that in case (a), we obtain an optimal duration which is more beneficial regarding the activation of immune cells while cases (b) and (c) both provide an optimal duration which is more adequate for the minimization of the tumoral population. [ABSTRACT FROM AUTHOR]