We will investigate the optimal control strategy of an SIR epidemic model with time delay in state and control variables. We use a vaccination program to minimize the number of susceptible and infected individuals and to maximize the number of recovered individuals. Existence for the optimal control is established; Pontryagin’s maximum principle is used to characterize this optimal control, and the optimality system is solved by a discretization method based on the forward and backward difference approximations. The numerical simulation is carried out using data regarding the course of influenza A (H1N1) in Morocco. The obtained results confirm the performance of the optimization strategy.

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In the present paper, we address to construct a structured user profile in a Small Private Online Course (SPOC) based on user’s video clickstream analysis. We adopt an implicit approach to infer user’s preferences and experience difficulty based on user’s video sequence viewing analysis at the click-level as Play, Pause, Move forward… the Bayesian method is used in order to infer implicitly user’s interests. Learners with similar clickstream behavior are then segmented into clusters by using the unsupervised K-Means clustering algorithm. Videos that could meet the individual learner interests and offer a best and personalized experienced learning can therefore be recommended for a learner while enrolling in a SPOC based on his videos interactions and exploiting similar learners’ profiles.

Abstract-E-learning takes advantage of the use of information and communication technology. Its objectives can be defined as self-learning, distance learning, individualizing learning paths and the development of online teaching relationships.Keeping interoperability between e-learning content in a universities cloud is not always easy, diffusion of training modules on the cloud by various institutions causes heterogeneous e-learning systems which affect the educational quality offered by university to teachers and learners, from this reason, comes the idea of modeling and synchronizing content between the different parts included in the learning task.Our contribution result a model aims to ensure the interoperability in distributed architectures of large sizes using the IMS-LD specification to facilitate the task of identification, reuse, sharing, adapting teaching and learning resources in the Cloud.