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عنوان انگلیسی مقاله:

Optimal control application to an Ebola model

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4. Numerical simulation and discussion

In this section, we investigate the effect of optimal strategy on Ebola transmission applying some numerical techniques. The optimal strategy is achieved by obtaining a solution for the state system (1) and co-state system (4). An iterative scheme is explored and used to determine the solution for the optimality system

The state equations are initially solved by guessing for the controls over the simulated time applying a forward fourth order Runge-Kutta scheme.

In addition, the co-state equations are at the same time computed by employing a backward fourth order Runge-Kutta scheme with the transversality conditions. This is then followed by the controls being updated by employing a convex combination of the preceding controls and the value obtained from the characterizations of u1 * , u2 * , u3 * . This process is allowed to go on and iteration is ended if the values of unknowns at the previous iteration are almost the same as the value obtained at present iteration [30]. For numerical simulation, the state system solution is determined based on forward in time with initial conditions x(0) = (10 000, 300, 100, 40, 60, 70), whereas the co-state system is also dealt with backward in time. In the light of numerical simulation, we employed the following parameters: d1 = 0.6/days; a = 8/days; b1 = 0.9/days; d2 = 0.7/ days; gF = 1.2/days; m = 0.000 054 79/days; g1 = 5.7/days; g2 = 1.4/days; b2 = 0.67/days and the weighting control B1 = 20, B2 = 40, B3 = 50. The weight factor B1 associated with control u1 is less or equal to weight factor B2 associated with control, however, weight factor B3 associated with control u3 could be higher than all due to cost associated with it because of the cost implications.