# optimal control

## Optimal control problem of a discrete spatiotemporal prey–predator three-species fishery model

In this work, we discuss a spatiotemporal discrete prey–predator model.  It consists of three compartments: prey, predator, and super-predator.  The proposed model describes the interaction between prey, predator, and super-predator in a region with a discrete displacement.  We also provide research on appropriate regional control strategies.  The controls are applied to the predator and the super-predator, respectively; they represent catching these in measured quantities in a space and a time chosen.  The aim is to increase the number of prey and reduce the number of

## Analysis and optimal control problem for a fractional mathematical model of tuberculosis with smoking consideration

This article studies a mathematical model of the fractional order of tuberculosis (TB).  It describes the dynamics of the spread of tuberculosis among smokers.  The purpose of this research is to protect vulnerable people against the virus.  According to the survey results, the required model has an equilibrium point: the disease-free equilibrium point $E_f$.  We also analyze the local stability of this equilibrium point of the model, using the basic reproduction number $\mathcal{R}_{0}$ calculated according to the new generation method.  In our model, we include three

## The impact of rumors on the success of Covid-19 vaccination programs in a Coronavirus-infected environment: optimal control approach

In this paper, we propose a mathematical model that describes the effect of rumors on the success of vaccination programs against Covid-19 in an environment infected by the coronavirus.  The aim of this study is to highlight the role of addressing the spread of rumors regarding vaccination risks and booster doses in the success of vaccination programs and in achieving herd immunity.  Additionally, we formulate an optimal control problem by proposing several strategies, including awareness and anti-rumor programs, to assist country officials in achieving successful vacci

## Development of Models and Methods for Automated Control of Heat Supply System with Optimization of Technical Means Structure

Analysis of the controlled object, as well as methods and models applied for controlling the heat supply process in a city and urban districts has been carried out. Simulation models of the controlled object functioning in the presence of alternative energy flows with different costs have been developed. The criteria and objective function for optimizing the city’s heat supply process have been synthesized and substantiated.

## 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

## Tikhonov regularization for a spatiotemporal model of the human monkeypox outbreak

Monkeypox is a contagious disease caused by the monkeypox virus.  There is currently an outbreak of monkeypox in the U.S.

## 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