Abdessamad Tridane

• Ph.D. Hassan II University
• Professor (Full) at United Arab Emirates University

This research gives a thorough examination of an HIV infection model that includes quiescent cells and immune response dynamics in the host. The model, represented by a system of ordinary differential equations, captures the complex interaction between the host's immune response and viral infection. The study focuses on the model's fundamental aspe...

In this paper, we examine a modified susceptible–infected–treatment–recovered (SITR) model. The SITR model is assumed to be a periodically switched system, where two parameters, i.e., transmission rate and treatment rate, are periodically switched. In the first part of the article, we analyze the stability of the switched model in the presence of p...

The spread of rumors within a crowd can lead to harmful consequences, ranging from misinfor- mation and social disturbances to public panic and injuries or fatalities. In this work, we propose a novel approach to an effective strategy for reducing the number of individuals affected by a rumor within a crowd. This strategy relies on developing contr...

This research investigates a novel approach to modeling an SIR epidemic in a heterogeneous environment by imposing certain restrictions on population mobility. Our study reveals the influence of partially restricting the mobility of the infected population, who are allowed to diffuse locally and can be modeled using random dispersion. In contrast,...

This paper investigates the maximal output set for a class of linear distributed systems with discrete output. This exploration is novel, as previous studies primarily focused on localized systems. We define an initial state as output admissible if its corresponding output satisfies specified constraints. This set of initial states termed the maxim...

As many countries are hit by the social economic impact of heroin addiction, there is an urgent need to have an effective awareness program that focuses on educating the population on the danger of heroin addiction and helping the heroin‐users quit. This paper aims to study the effect of the awareness program on the spread of heroin dependence usin...

We study a switched SIHR (Susceptible Infected Hospitalized Recovered) model for infectious diseases. The aim is to find the most effective switching signal to manage the disease's effects as effectively as maintaining a continuous vaccination program. A nonlinear, non-convex optimal control problem of the switched system is converted into a linear...

This paper explores a generalized nonlocal dispersion SIS epidemic model subject to the Neumann boundary conditions and spatial heterogeneity. We use a convolution operator to describe the nonlocal spatial movements of individuals. Our primary goal is to investigate this model, focusing on a generalized incidence function, which presents an additio...

Article HistoryDeveloping electronic platforms during education disruptions, particularly during the COVID-19 pandemic, had become crucial to addressing educational gaps. Research has shown technology's significant contribution to improving teaching and learning methods in labs, whether theoretical or experimental. This study creates an e-laborator...

There is an ongoing debate on the relative impact of the various nonpharmaceutical interventions employed to limit the spread of coronavirus disease 2019 (COVID-19). This study examined the com- bined e↵ect of vaccination and mobility using an agent-based model of an urban neighborhood with nine boroughs. The model was not designed to match a speci...

This study aims to create and examine a multimodal dataset to enhance crowd management during the Hajj seasons. Sixty-four participants were engaged in Hajj rituals such as Tawaf, Saai, prayer, and Doaa providing location and peripheral physiological data, collected and annotated using a custom-made smartphone application. The collected data was le...

In this paper, we discuss an epidemic switched system. A susceptible–infected–treated model is considered. The course of an epidemic is profoundly influenced by the allocation of resources. If these resources are limited, then we need to devise an optimal distribution strategy. One significant case to study is when the drug supply is insufficient....

This paper presents a comprehensive agent-based model for the spread of an infection in a network of cities. Directional mobility is defined between each two cities and can take different values. The work examines the role that such mobility levels play in containing the infection with various vaccination coverage and age distributions. The results...

In this article, we consider an epidemiological model in which we take into account the effects of direct and indirect transmissions. The first mode occurs through direct contact between infectious and susceptible individuals, and the second one will take place through the shedding of virus particles by infec- tious individuals and their acquisitio...

In this work, we study the possibility of using a new non-homogeneous stochastic diffusion process based on the Rayleigh density function to model the evolution of the active cases of COVID-19 in Morocco. First, the main probabilistic characteristics and analytic expression of the proposed process are obtained. Next, the parameters of the model are...

The evolution of digital tools in education has created a disparity between the tools teachers use and those available to students, leading to an unequal relationship. This disparity has hindered the shift from traditional teaching to student-centered learning, a crucial aspect of novel approaches in cognitive psychology. The primary objective of t...

In this paper, we discuss a discrete mathematical model of Islamic polygamy and thesocial position of Muslims. In eleven compartments we explain the social situation andgive an explanation of the marital status of each Males and females in Islamic societiesthat allow polygamy. In order to controlling and reducing the number of virgins menand women,...

Colloque International de Management de la Qualite dans l'Enseignement Superieur et la Formation. Regards Croises des Acteurs et de la Recherche, CIMQESF2023, July 13-14, Ecole Normale Superieur (ENS), Casablanca, Morocco

Vaccination programs are crucial for reducing the prevalence of infectious diseases and ultimately eradicating them. A new age-structured SEIRV (S-Susceptible, E-Exposed, I-Infected, R-Recovered, V-Vaccinated) model with imperfect vaccination is proposed. After formulating our model, we show the existence and uniqueness of the solution using semigr...

We study the problem of optimal switching on a treatment-vaccination model with four switches. These switches provide a more realistic approach when dealing with the control of an epidemic. We have used a relatively new approach to investigate optimal switching. The main idea behind this approach is to convert the switched system, a nonlinear, nonc...

In this article we study the existence and stability of bounded solutions for semilinear abstract dynamic equations on time scales in Banach spaces. In order to do so, we use the defnition of the Riemann delta-integral to prove a result about closed operator in Banach spaces and then we just use the representation of bounded solutions as an imprope...

Developing new approaches that help control the spread of infectious diseases is a critical issue for public health. Such approaches must consider the available resources and capacity of the healthcare system. In this paper, we present a new mathematical approach to controlling an epidemic model by investigating the optimal control that aims to bri...

One of the phenomena that characterize any political process in any democratic country is the switch of political orientation for the politicians. This paper aims to study the dynamic of the change in political afiliation via a difference-equations model. The model deals with three types of population: The susceptible to switch their political part...

In this paper, we discuss a new size- structured population model with a delay in birth pro- cess. The focus is to discuss the existence and the uniqueness results along with basic reproduction ratio ( R0 ). The birth function h is not necessarily a Ricker type of function but expression of R0 obtained in this paper works for a more general functio...

The world has faced the COVID-19 pandemic for over two years now, and it is time to revisit the lessons learned from lockdown measures for theoretical and practical epidemiological improvements. The interlink between these measures and the resulting change in mobility (a predictor of the disease transmission contact rate) is uncertain. We thus prop...

In this paper, we propose another extension of the basic prey-predators model. We incorporate the spatial behavior of the fish population and a term of regional control to provide a realistic description of the prey effects of two predators. We present a study of regional optimal control strategies of a spatiotemporal prey-predator model. Based on...

The aim of this work is to investigate the controllability of a class of switched Hilfer neutral fractional systems with non-instantaneous impulses in the finite-dimensional spaces. We construct a new class of control function that controls the system at the final time of the time-interval and controls the system at each of the impulsive points i.e...

This work is devoted to the prove of the existence of solutions for a semilinear retarded differential equation with infinite delay and impulses on timescales , which is done by using a version of the Arzela-Ascoli theorem on timescales , and applying the Leray-Schauder alternative. After that, the uniqueness of solutions is proved by applying a ve...

Since the beginning of the COVID-19 pandemic, vaccination has been the main strategy to contain the spread of the coronavirus. However, with the administration of many types of vaccines and the constant mutation of viruses, the issue of how effective these vaccines are in protecting the population is raised. This work aimed to present a mathematica...

With the increasing global adoption of COVID-19 vaccines, limitations on mass gathering events have started to gradually loosen. However, the large vaccine inequality recorded among different countries is an important aspect that policymakers must address when implementing control measures for such events. In this paper, we propose a model for the...

In this paper, we revisit the classical SIR epidemic model by replacing the simple bilinear transmission rate by a nonlinear one. Our results show that in the presence of environmental fluctuations represented by Brownian motion and that mainly act on the transmission rate, the generalized non-concave force of infection adopted here, greatly affect...

This paper aims to study the relative equivalence of the solutions of the following dynamic equations y (t) = A(t)y(t) and x (t) = A(t)x(t) + f (t, x(t)) in the sense that if y(t) is a given solution of the unperturbed system, we provide sufficient conditions to prove that there exists a family of solutions x(t) for the perturbed system such that y...

In this paper, we discuss a size-structured population model with a delay in birth process. The focus is to discuss the existence and uniqueness results along with basic reproduction ratio ( R 0 ). The birth function h is not necessarily a Ricker type of function but expression of R 0 obtained in this paper works for a more general function h . Thi...

Annually, a huge number of pilgrims visit Mecca to perform Al Hajj ritual. Crowd management is critical in this occasion in order to avoid crowd disasters (e.g., stampede and suffocation). Recent studies stated that various factors, such as the environment, fatigue level, health condition and emotional status have a significant effect on crowded ev...

In this research, we investigate the global properties of the heroin epidemic model with time distributed delay and nonlinear incidence function. We show that the system has threshold dynamics in terms of R0, and we prove, a Lyapunov function, that for R0<1 the drug-free equilibrium is globally asymptotically stable. For R0>1, we give the persisten...

This paper deals with non-fragile fault-tolerant control for discrete-time networked control systems (NCS) with data packet dropout and transmission delays induced by communication channels. We model the discrete-time NCSs with data packet dropout and transmission delays which are assumed to be randomly time-varying in Bernoulli distributed sequenc...

Given a discrete-time controlled bilinear systems with initial state x 0 and output function y i , we investigate the maximal output set Q(W) = {x 0 2 R n , y i 2 W, 8 i 0} where W is a given constraint set and is a subset of R p. Using some stability hypothesis, we show that Q(W) can be determined via a finite number of inequations. Also, we give...

This paper aim to investigate the global dynamics of an alcoholism epidemic model with distributed delays. The main feature of this model is that it includes the effect of the social pressure as a factor of drinking. As a result, our global stability is obtained without a "basic reproduction number" nor threshold condition. Hence, we prove that the...

With the coronavirus (COVID-19) pandemic continuing to spread around the globe, there is an unprecedented need to develop different approaches to containing the pandemic from spreading further. One particular case of importance is mass-gathering events. Mass-gathering events have been shown to exhibit the possibility to be superspreader events; as...

The novel coronavirus disease (COVID-19) may be introduced into a population through arrival passengers outside the host population. The development of mathematical models is used to forecast, evaluate, and attempt to control the spread of diseases. In this paper, a new epidemiological model with seven compartments that include passengers is constr...

This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold Rs(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when Rs(g) = 1. Numeri...

Simple Summary One of the challenges facing the countries to contain the COVID-19 is to trace people that were in contact with an infected person. Failing to identify the possible infected people leads to unreported cases of the COVID-19, which results in massive infection among the population and even superinfection events. In this work, we study...

This work investigates the optimal control of the second phase of the COVID-19 lockdown in Morocco. The model consists of susceptible, exposed, infected, recovered, and quarantine compartments (SEIRQD model), where we take into account contact tracing, social distancing, quarantine, and treatment measures during the nationwide lockdown in Morocco....

As the COVID-19 is still spreading in more than 180 countries, according to WHO. There is a need to understand the dynamics of this infection and predict its the impact on the public health capacity. This work aims to forecast the progress of the disease in three countries from different continents: The United States of America, the United Arab Emi...

As the COVID-19 is still spreading in more than 180 countries, according to WHO. There is a need to understand the dynamics of this infection and predict its the impact on the public health capacity. This work aims to forecast the progress of the disease in three countries from different continents: The United States of America, the United Arab Emi...

In this paper, we consider a SEIS model type compartmental model to explore the evolution of the Influenza epidemic in Morocco. To consider a more realistic model we consider the seasonality of parameters, by considering time-dependent infection rate, time-dependent recovery rate, and time-dependent intervention rate. The next-generation matrix met...

In this paper, we aim to analyze the classical SIS epidemic model with a generalized force of infection (including nonmonotonic cases), where the transmission rate is perturbed by white noise. Using Feller's test for explosions, we prove that the disease dies out with probability one without any restriction on the model parameters.

In this paper, we consider an infinite dimensional linear systems. It is assumed that the initial state of system is not known throughout all the domain Ω ⊂ Rn, the initial state x0 ∈ L2(Ω) is supposed known on one part of the domain Ω and uncertain on the rest. That means Ω = ω1 ∪ω2 ∪. . .∪ωt with ωi ∩ ωj = ∅, ∀i, j ∈ {1, . . . , t}, i ̸= j where...

In this paper, we present a mathematical model governing the dynamics of tumour-immune cells interaction under HIV infection. The interactions between tumour cells, helper T-cells, infected helper T-cells and virus cells are explained by using delay differential equations including two different discrete time delays. In the model, these time lags d...

In this work, we investigate the stability of an SIR epidemic model with a generalized nonlinear incidence rate and distributed delay. The model also includes vaccination term and general treatment function, which are the two principal control measurements to reduce the disease burden. Using the Lyapunov functions, we show that the disease-free equ...

This paper takes the reaction–diffusion approach to deal with the quiescent females phase, so as to describe the dynamics of invasion of aedes aegypti mosquitoes, which are divided into three subpopulations: eggs, pupae and female. We mainly investigate whether the time of quiescence (delay) in the females phase can induce Hopf bifurcation. By mean...

With the increase of ICT infrastructure investments in educational institutions, blended learning is becoming one of the most innovative approaches in teaching in many universities around the world. The efficacy of blended learning in achieving the learning outcomes varies from discipline to others. For Mathematics courses, there are many attempts...

The aim of this work is to study a new stochastic SIR epidemic model that includes two types of white noises. These noises perturb two important parameters in the disease dynamic: the disease transmission rate and the recovery rate. By means of the Lyapunov functions, we prove the global existence and positivity of the solution. We also investigate...

As Malaria represents one of the major health burdens in Africa,there is a risk of reappear- ance of this vector-borne disease in malaria-free or low risk countries such as those in North Africa. One of the factors that can lead to this situation is the flow of sub-Saharan immigrants trying to reach Europe through North Africa. In this work, we inv...

The aim of this work is to investigate incubation period, via delay differential equation, of the Zika virus disease (ZIKV). This incubation period could be extrinsic, which means the interval between the vector getting the agent and the vector’s ability to transmit the virus to a new hosts, or intrinsic, define as the time taken by the virus to co...

This paper aims to study the global stability of an Ebola virus epidemic model. Although this epidemic ended in September 2015, it devastated several West African countries and mobilized the international community. With the recent cases of Ebola in the Democratic Republic of the Congo (DRC), the threat of the reappearance of this fatal disease rem...

Given a desired signal yd=(yid)i∈{0,…,N}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ y^d= (y^{d}_{i})_{i \in \{0,\ldots ,N \}}$$\end{document}, we investigate the o...

The aim of this paper is to study the early stage of HBV infection and impact delay in the infection process on the adaptive immune response, which includes cytotoxic T-lymphocytes and antibodies. In this stage, the growth of the healthy hepatocyte cells is logistic while the growth of the infected ones is linear. To investigate the role of the tre...

Aedes aegypti (Ae. aegypti: mosquito) is a known vector of several viruses including yellow fever, dengue, chikungunya and zika. In the current paper, we present a delayed mathematical model describing the dynamics of Ae. aegypti. Our model is governed by a system of three delay differential equations modeling the interactions between three compart...

The Middle Eastern Respiratory Syndrome Coronavirus (MERS-CoV) has exhibited super-spreading events in recent years. In this work, we investigate the effects a possible super-spreading event in one of the largest annual mass gatherings: the Hajj season in the Kingdome Saudi Arabia (KSA). Since the KSA has the most significant confirmed number of ME...

Thalassemia is a genetic blood disorder that causes abnormal hemoglobin. Hemoglobin is a protein in red blood cells that carries oxygen and is made of two proteins from four α-globin genes and two β-globin genes. A defect in one or more of these genes causes thalassemia. The treatment of thalassemia mostly depends on life-long blood transfusions an...

Supplementary material for mathematical model. (PDF)

The aim of this work is to investigate the optimal control of the treatment in a simple pandemic model as a switched nonlinear system. We used a newly developed approach based on the theory of moments. This approach allows to transform a nonlinear, non-convex optimal control problem to an equivalent linear and convex one. To illustrate our finding,...

In this paper, we provide a differential mathematical model with non-integer order derivative (fractional-order) to investigate the dynamics of Hepatitis-C Virus (HCV) replication, in presence of interferon-(IFN) treatment. The fractional-order is considered to represent the intermediate cellular interactions and intracellular delay of the viral li...

In HIV infection, the latent cells represent a reservoir that contributes to the failure of the Highly Active Anti-Retroviral Therapy (HAART). This fact requires investigating the possible strategy to improve the administration of the HAART therapy, in order to guarantee the control of the virus load to the lost level as long as possible. In this w...

In this paper, we study the dynamical behaviour of HBV infection model with antiviral therapy and CTL immune response. The model is given by a system of four ordinary differential equations with discrete time delay which describes the time between infection and the immune response. The existence and stability/unstability of the equilibrium points w...

The efficacy of border screening as a prophylactic measure against mosquito-borne diseases in Africa depends on the value of the lower bound of the basic reproduction number. If this lower bound is greater than one, then border screening may be ineffective. In this case, the best prophylaxis is to isolate and treat patients in their region of resid...

The efficacy of border screening as a prophylactic measure against mosquito-borne diseases in Africa depends on the value of the lower bound of the basic reproduction number. If this lower bound is greater than one, then border screening may be ineffective. In this case, the best prophylaxis is to isolate and treat patients in their region of resid...

In this chapter, we consider a more general model describing the dynamics of a hematopoietic stem cell (HSC) model with Wazewska–Lasota functional production type describing the cycle of proliferating and quiescent phases. The model is governed by a system of two ordinary differential equations with discrete delay. Its dynamics are studied in terms...

Communication is one of the main pillars of successful m-learning. This work aims to highlight the possibility of improving communication between instructors and students via WhatsApp. The preliminary data analysis of this pilot study shows that students are already using WhatsApp to communicate among themselves in the college context, and they are...

In this work, we develop a mathematical model to study the effect of drug on the development of cancer including the quiescent compartment. The model is governed by a system of delay differential equations where the delay represents the time that the cancer cell take to proliferate. Our analytical study of the stability shows that by considering th...

Communication is one of the main pillars of successful m-learning. This work aims to highlight the possibility of improving communication between instructors and students via WhatsApp. The preliminary data analysis of this pilot study shows that students are already using WhatsApp to communicate among themselves in the college context, and they are...

The aim of this work is to study, via mathematical models, the impact of imported communicable diseases on the population of the United Arab Emirates (UAE). The nature of the health policies in the UAE imposes on us to consider models that categorize the living population in the UAE based on epidemic and immigration status. For example, there are n...

In this study, we propose a mathematical model of HIV infection with tumor cells. We model the interaction between tumor cells, helper T cells, infected helper T cells and virus cells by using a nonlinear dynamical system approach which gives rates of change of the four cell populations in the body. First, we prove the positivity of the solution, a...

Structured data has an inherently great automation value. It renders itself readily for software tools to help store, organize and search effectively. With the growing dependence of data, we face many new problems. While software applications replace each other, and older software has rapidly diminishing value, data has the extreme opposite nature,...

In this paper, we consider a model describing the dynamics of Hematopoietic Stem Cells (HSC) disease with chemotherapy. The model is given by a system of three ordinary differential equations with discrete delay. Its dynamics are studied in term of local stability of the possible steady states for the case without drug intervention term. We prove t...

Periodic collection of field data, analysis and interpretation of data are key to a good healthcare service. This data is used by the subsequent decision makers to recognize preventive measures, provide timely support to the affected and to help measure the effects of their interventions. While the resources required for good disease surveillance a...

Structured data is easy to parse and process using simple software tools with effective results. However, most valuable information is typically found in unstructured data. The problem is that unstructured data is significantly harder to process, especially at large scale. Adding some structure can greatly improve data reuse. To demonstrate our app...

The aim of this work is to study the dynamical behavior of a virus dynamics model with general incidence rate and two delays. The first delay represents the time from the virus entry to the production of new viruses and the second delay corresponds to the time necessary for a newly produced virus to become infectious. Lyapunov functionals are const...

The main goal of this work is to propose a mathematical model, based on two-dimensional cellular automata (CA), to simulate an infectious disease outbreak. Specifically, we revisit the general deterministic SEIR (Susceptible Exposed Infectious Recovered) model by adding terms describing the spatial spreading of disease. The state of each cell is a...

This special issue of Discrete and Continuous Dynamical Systems Series B in Cancer Modeling, Analysis and Control originated as a result of the Casablanca International Workshop on Mathematical Biology, held in Casablanca, Morocco from June 20-24, 2011. This five-day workshop was aimed at: (1) bringing together US, international, and African expert...

In this paper, the dynamical behavior of a virus dynamics model with general incidence rate and intracellular delay is studied. Lyapunov functionals are constructed and LaSalle invariance principle for delay differential equation is used to establish the global asymptotic stability of the disease-free equilibrium and the chronic infection equilibri...

The aim of this work is to study the global stability of a generalized model of a viral dynamic that includes the adaptive immune response, represented by Cytotoxic Lymphocyte T-cell (CTL-cell ). The incidence function introduced in this model is the generalization of a variety of viral models including HIV, influenza, HBV, and HCV. We show that th...

A deterministic model is constructed and an-alyzed to study the dynamics of West Nile Virus (WNV) trans-mission between two bird populations—domestic and wild— through vectors (mosquitoes). Different effective contact rates are assumed between vectors and each of the two bird popu-lations. The analysis of the model, which is based on a sys-tem of o...

The rate of infection in many virus dynamics models is assumed to be bilinear in the virus and uninfected target cells. In this paper, the dynamical behavior of a virus dynamics model with general incidence rate and cure rate is studied. Global dynamics of the model is established. We prove that the virus is cleared and the disease dies out if the...

The aim of this work is to investigate a new mathematical model that describes the interactions between Hepatitis B virus (HBV), liver cells (hepatocytes), and the adaptive immune response. The qualitative analysis of this as cytotoxic T lymphocytes (CTL) cells and the antibodies. These outcomes are (1) a disease free steady state, which its local...