optimal control

A discrete mathematical model SIRS with the evolution of regions to attack infectious diseases

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 employed to characterize the optimal controls, and the optimality system is solved using an iterative approach.  Finally, numerical simulations are conducted to validate the theoretical analysis using MATLAB.

Mathematical modeling and optimal control strategy for the monkeypox epidemic

In this study, we propose a discrete time mathematical model (SEIQR) that describes the dynamics of monkeypox within a human population.  The studied population is divided into five compartments: susceptible ($S$), exposed ($E$), infected ($I$), quarantined ($Q$), and recovered ($R$).  Also, we propose an optimal strategy to fight against the spread of this epidemic.  In this sense we use three controls which represent: 1) the awarness of vulnerable people through the media, civil society and education; 2) the quarantine of infected persons at home or, if required, in h

Modeling and mathematical analysis of drug addiction with the study of the effect of psychological and biological treatment

In this article, we propose a discrete mathematical model which describes the propagation of the drug phenomenon in a human population.  The population is unscrewed in five compartments: "$S$" People likely to become drug addicts, "$M$" Moderate drug addicts, "$H$" Heavy drug addicts, "$T$" People receiving drug addiction treatment, "$R$" The recovered people who have completely abstained from drug addiction.  Our goal is to find a better strategy to reduce the number of heavy addicts and to maximize the number of people receiving full treatment.  The tools of optimal c

Optimal control strategy for the administration of the third vaccine dose in the treatment of pandemic COVID-19

In this paper, we propose a mathematical model of COVID-19 infection, taking into account the division of the population according to vaccination criteria.  Our goal is to demonstrate the positive effect of receiving the third dose of the Corona vaccine.  We proposed two strategies to limit the spread of the COVID-19 pandemic respectively awareness programs on the importance of the third dose of the vaccine and the delivery of treatment to infected individuals who have health problems.  Pontryagin's maximum principle is applied in order to characterize the optimal contr

Discrete mathematical modeling and optimal control of the marital status: Islamic polygamous marriage model case

In this paper, we discuss a discrete mathematical model of Islamic polygamy and the social position of Muslims.  In eleven compartments we explain the social situation and give an explanation of the marital status of each Males and females in Islamic societies that allow polygamy.  In order to controlling and reducing the number of virgins men and women, divorced men and women we implement two control variables.  The first control characterizes the benefits of an awareness campaign to educate virgin men and women about the benefits marriage to the individual and society

Mathematical modeling of the gaming disorder model with media coverage: optimal control approach

In this article, we propose a PEARM mathematical model to depict the dynamic of a population that reacts in the spread of the gaming disorder with media coverage.  The basic reproduction number and existence of free equilibrium point and endimec equilibrium point are obtained with same fundamental properties of the model including existence and positivity as well as boundedness of equilibria are investigated.  By using Routh–Hurwitz criteria, the local stability of free equilibrium point and endimec equilibrium point are obtained.  Also, we propose an optimal strategy to implement the optim

Dynamics of a fractional optimal control HBV infection model with capsids and CTL immune response

This paper deals with a fractional optimal control problem model that describes the interactions between hepatitis B virus (HBV) with HBV DNA-containing capsids, liver cells (hepatocytes), and the cytotoxic T-cell immune response.  Optimal controls represent the effectiveness of drug therapy in inhibiting viral production and preventing new infections.  The optimality system is derived and solved numerically.  Our results also show that optimal treatment strategies reduce viral load and increase the number of uninfected cells, which improves the patient's quality of lif

A spatiotemporal spread of COVID-19 pandemic with vaccination optimal control strategy: A case study in Morocco

On March 2, 2020, the Moroccan Ministry of Health announced the first case of COVID-19 in the city of Casablanca for a Moroccan tourist who came from Italy.  The SARS-COV-2 virus has spread throughout the Kingdom of Morocco.  In this paper, we study the spatiotemporal transmission of the COVID-19 virus in the Kingdom of Morocco.  By supporting a SI$_{\rm W}$IHR partial differential equation for the spread of the COVID-19 pandemic in Morocco as a case study.  Our main goal is to characterize the optimum order of controlling the spread of the COVID-19 pandemic by adopting

On stability analysis study and strategies for optimal control of a mathematical model of hepatitis HCV with the latent state

In this work, we analyze a viral hepatitis C model.  This epidemic remains a major problem for global public health, in all communities, despite the efforts made.  The model is analyzed using the stability theory of systems of nonlinear differential equations.  Based on the results of the analysis, the proposed model has two equilibrium points: a disease-free equilibrium point $E_0$ and an endemic equilibrium point $E^{*}$.  We investigate the existence of equilibrium point of the model.  Furthermore, based on the indirect Lyapunov method, we study the local stability o