Analytical Study of Optimal Control Intervention Strategies for Ebola Epidemic Model

A SEIR type model for the spread of Ebola epidemic in a population of constant size is considered. In order to control the spread of infection and prevent such epidemics, we add to the model four bounded controls. Three of them represent the efforts that reduce the contact between the susceptible and infectious individuals, between the susceptible and hospitalized, and, lastly, between susceptible and buried individuals. The fourth control represents the burial efforts. We state the optimal control problem of minimizing the number of the infectious individuals at the given terminal time. The corresponding optimal solutions are obtained with the use of the Pontryagin maximum principle. Such values of the model parameters and control constraints are used, for which the optimal controls are bang-bang. Their types are found and investigated analytically. An approach for estimating the number of zeros of the corresponding switching functions, different from the one that was used in our previous papers, is applied. The resulting estimates enable us to reduce the optimal control problem to a considerably simpler problem of the finite-dimensional constrained minimization.