Hassan Laarabi

Université Hassan II de Casablanca · Department of Mathematics and Computer Sciences

This research article presents a mathematical model that tracks and monitors the spread of COVID-19 strains in a discrete time frame. The study incorporates two control strategies to reduce the transmission of these strains: vaccination and providing appropriate treatment and medication for each strain separately. Optimal controls were established...

In this paper, we developed a new discrete-time mathematical model as a promising approach to understand and analyze the progression of disease complications related to excessive alcohol consumption, namely potential drinkers (P i), moderate drinkers (M i), heavy drinkers (H i), and heavy drinkers (C i, j) with different disease complications and q...

In this study, we propose an advanced stochastic mathematical model that delves into the intricate dynamics of multi-strain COVID-19 transmission. By accounting for environmental fluctuations, we introduce white noise into each compartment of the multi-strain system, enriching our understanding of its behavior. Rigorous proofs establish the system'...

This paper presents a new SIRS mathematical model describing the evolution of an infectious disease, assuming that the spatial supports of this infection are also evolutionary and obey a compartmental model. We propose four control strategies to manage the spread of the disease among individuals and regions. The Pontryagin maximum principle is empl...

In this article, we extended the concept of controllability, traditionally used to control the final state of a system, to the exact control of its final speed. Inspired by Kalman's theory, we have established some conditions to characterize the control that allows the system to reach a desired final speed exactly. When the assumptions ensuring spe...

In this paper, we propose a mathematical model that describes the correlation between the spread of smoking and tuberculosis, and three control strategies that are characterised by the Pontryagin maximum principle. Simulations in Matlab show the effectiveness of the model and the control strategies we propose. Finally, in order to control both tube...

In this paper, our aim is to study the optimal control strategy of a mathematical model of the tuberculosis transmission in the discrete case, and to investigate, in discrete time, optimal control strategy in which the controls are: vaccination and treatment and sensibilisation. The studied population is divided into five compartments SL 1 IL 2 R....

This study proposes a corona pandemic model that incorporates both reported and unreported cases of virus to be more realistic. In addition, it is advised to employ both preventive measures: vaccination and treatment and applied them at the simultaneously. The optimal controls were characterized with the maximum Pontryagin principle. Finally, the r...

Scale insects are parasitic insects that attack many indoor and outdoor plants, including cacti and succulents. These insects are among the frequent causes of diseases in cacti: for the reason that they are tough, multiply in record time and could be destructive to these plants, although they are considered resistant. Mealybugs feed on the sap of p...

A mathematical model of infectious disease contagion that accounts for population stratification based on immunity criteria is proposed. Our goal is to demonstrate the effectiveness of this idea in preventing different epidemics and to lessen the significant financial and human costs these diseases cause. We determined the fundamental reproduction...

In this paper, we consider a scenario to attack the infectious disease monkeypox taking advantage of the experience we have with the Corona epidemic to reduce its negative effects on humanity and the world economies. This by proposing three control strategies. Pontryagin’s maximum principle is applied in order to characterize the optimal controls,...

In this paper, we propose a mathematical model of infection by infectious diseases, taking into account the division of the population according to the criteria of immunity. Our objective is to demonstrate the positive effect of this idea against the different epidemics. We have proposed two strategies to reduce the great human and material losses...

In this study, we analyze the transmission dynamics of several variants of Covid-19 that have appeared around the world. Our aim is to propose a discrete mathematical model that describes the dynamics of different infectious compartments, namely, Susceptible (S), Exposed (E), Individuals infected with the Alpha variant (I 1), Individuals infected w...

The main goal of this article is to devise the spatial-temporal spread of TB, in multiple neighboring domains, taking into account the epidemiological diversity of their populations. However, since both the environment and any population are spatially heterogeneous, it is obviously desirable to include spatial structure into an epidemic model. Indi...

In the present work, we have proposed a new mathematical model of alcohol abuse with delay, saturated incidence function and logistic recruitment. The model is made up of the following four population classes: occasional drinkers, heavy drinkers, drinkers during treatment and drinkers who are temporarily recovered. In particular, we incorporate tim...

Rumor is an important form of social interaction, and its spreading has a significant impact on human lives. The optimal control theory is an important tool to better manage the spread of rumors. Most of the literature on rumor propagation models deals with quadratic cost functions relative to the control variable. In this paper, we have considered...

In this paper, we investigate the effect of spatial diffusion and delay on the dynamical behavior of the SIR epidemic model. The introduction of the delay in this model makes it more realistic and modelizes the latency period. In addition, the consideration of an SIR model with diffusion aims to better understand the impact of the spatial heterogen...

In this paper, we consider a discrete model of the marital status of the family dynamics. It is assumed that individuals in the society can be classed in one of the eight compartments: virgin men, virgin women, married men, married women, divorced men, divorced women, widowed men and widowed women. The objective of this work is to treat the modelin...

In this paper, we investigated a novel rumor spreading model with latent and constant recruitment. The delay is introduced into the model in order to modeled the latent period. The local dynamics of the model is completely determined by using concepts from the Dynamical Systems Theory. The stability of equilibrium points is established, according t...

This article deals with optimal control applied to vaccination and treatment strategies for an SIRS epidemic model with logistic growth and delay. The delay is incorporated into the model in order to modeled the latent period or incubation period. The existence for the optimal control pair is also proved. Pontryagin's maximum principle with delay i...

We propose a delayed SIR model with saturated incidence rate. The delay is incorporated into the model in order to model the latent period. The basic reproductive number is obtained. Furthermore, using time delay as a bifurcation parameter, it is proven that there exists a critical value of delay for the stability of diseases prevalence. When the...

We propose an SEIR epidemic model with latent period and a modified saturated incidence rate. This work investigates the fundamental role of the vaccination strategies to reduce the number of susceptible, exposed, and infected individuals and increase the number of recovered individuals. The existence of the optimal control of the nonlinear model i...

This study considers an optimal therapy strategy for HBV infection by incorporating two controls laws into a previous hepatitis B viral infection model with logistic hepatocyte growth. Our goal is to maximize the number of healthy cells and to minimize the cost of the therapy. In this context, the existence of an optimal control is proved. The opti...

In this study we consider a mathematical model of an SIR epidemic model with a saturated incidence rate. We used the optimal vaccination strategies to minimize the susceptible and infected individuals and to maximize the number of recovered individuals. We work in the nonlinear optimal control framework. The existence result was discussed. A charac...

This work studies the construction of observers for a class of finite dimensional systems in which the dynamics are partially unknown. In this work we consider the class of the dynamics with a single unknown element in the first one and in the second one the case of several unknown elements. We give sufficient conditions in which the existence of a...

The focus of this paper is on the conception of observers for a class of finite dimensional systems in which the dynamics are partially unknown. Here, we start by considering the class of the dynamics with a single unknown element. Then we move to studying the case of several unknown elements. We give sufficient conditions in which the existence of...