Abstract
In order to have realistic model. In this paper, we propose to study an optimal control approach with delay in state and control variables in our discrete mathematical model of kouidere et al [5] talking about the dynamics of a population of diabetics with highlighting the impact of living environment, that time with delay represent the measuring the extent of interaction with the means of treatment or awareness campaigns.The existence for the optimal control with delay is also provided by Pontryagin’s maximum principle is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the forward and backward difference approximation.
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