Hanane Ferjouchia

We consider a class of linear discrete-time systems controlled by a continuous time input. Given a desired final state xd, we investigate the optimal control which steers the system, with a minimal cost, from an initial state x0 to xd. We consider both discrete distributed systems and finite dimensional ones. We use a method similar to the Hilbert Uniqueness Method (HUM) to determine the control and the Galerkin method to approximate it, we also give an example to illustrate our approach.

In this work, we consider a linear discrete system where a part of dynamics is affected by a disturbance. Being unable to cancel the effects of this disturbance, we propose a control law in closed loop to reduce the sensitivity of the system output to the disturbance. Finally, and to illustrate the results, we give examples in which it is based on the technique of pole placement. All simulations are done using Matlab/Simulink TM

Type 1 diabetes is a serious disease that affects many children and adolescents. The disease causes the pancreas to stop producing insulin, a hormone that regulates blood sugar level Insulin is a hormone that lowers the blood glucose concentration by catalyzing storage of glucose. In this work, the construction of a mathematical model describing the whole blood glucose-insulin system was tried. The model was derived both based upon the two minimal models of Bergman's minimal model, which is primarily used to interpret an IVGTT. Our objective is to propose a therapeutic scheme adapted to the needs of the diabetic patient and this through a mathematical model describing type 1.

This paper aims to predict the development of the COVID-19 pandemic in Morocco from a mathematical approach. Based on the reliability of the data and the nature of confirmed cases, the SEIRD model is employed to provide a theoretical framework to forecast COVID-19 ongoing epidemic. Findings suggest that the structure and parameters of the proposed model give insights into the dynamics of the virus. Hence, this study contributes to the conceptual areas of knowledge on COVID-19 in proposing an optimal control plan to help decrease the number of confirmed cases by applying preventive measures such as social distancing, wearing facial masks. Matlab/Simulink TM simulations are used to illustrate the findings.

In this paper, we aim to estimate and predict the situation of the new coronavirus pandemic (COVID-19) in countries under quarantine measures. First, we present a new discrete-time mathematical model describing the evolution of the COVID-19 in a population under quarantine. We are motivated by the growing numbers of infections and deaths in countries under quarantine to investigate potential causes. We consider two new classes of people, those who respect the quarantine and stay at home, and those who do not respect the quarantine and leave their homes for one or another reason. Second, we use real published data to estimate the parameters of the model, and then, we estimate these populations in Morocco. We investigate the impact of people who underestimate the quarantine by considering an optimal control strategy to reduce this category and then reducing the number of the population at risk in Morocco. We provide several simulations to support our findings.

In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that o...

We propose an optimal control strategy by conducting awareness campaigns for diabetics about the severity of complications of diabetes and the negative impact of an unbalanced lifestyle and the surrounding environment, as well as treatment and psychological follow-up. Pontryagin’s maximum principle is used to characterize the optimal controls, and the optimality system is solved by an iterative method. Finally, some numerical simulations are performed to verify the theoretical analysis using MATLAB.

Nowadays, Diabetes is one of the most common diseases, which has a huge and growing socio-economic burden affecting individuals, families, and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications and the effect of living environment. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment.

In this article, we propose a non-linear mathematical model with a variable size population to study the spread of HIV/AIDS in Morocco. We estimate the parameters that include this model based on real data. An estimation of the basic reproductive number R0 and some numerical simulations that provide insights into the future of HIV/AIDS in Morocco are also presented in this study