On the control of a reaction–diffusion system: a class of SIR distributed parameter systems

International Journal of Differential Equations

2020

In this paper, we present an application of optimal control theory on a two-dimensional spatial-temporal SEIR (susceptible, exposed, infected, and restored) epidemic model, in the form of a partial differential equation. Our goal is to minimize the number of susceptible and infected individuals and to maximize recovered individuals by reducing the cost of vaccination. In addition, the existence of the optimal control and solution of the state system is proven. The characterization of the control is given in terms of state function and adjoint. Numerical results are provided to illustrate the effectiveness of our adopted approach.

Section: Introductionmentioning

confidence: 99%

An Optimal Control for a Two-Dimensional Spatiotemporal SEIR Epidemic Model

Adnaoui

International Journal of Differential Equations

2020

“…In this paper and based on the previous hypothesis, we will exploit the mathematical model that has been formulated to represent the cholera epidemics [26] and combine it with the previous work model by adding a new compartment F which represents page's rumor. Other models from population dynamics and optimal controls can be found in [3,27].…”

Section: Related Workmentioning

confidence: 99%

“…is increase contributes significantly to huge consequences on the other hand. e development of the phenomenon of rumors and the strength of their influence and impact within societies gave this phenomenon another dimension [3], as it became used by the media and intelligence in competition between countries and what is known as propaganda and polemic or buzz by publishing some false news in whole or in part to influence the opinions of voters by raising or decreasing the popularity of politicians [4] as happened in the elections between Trump and Hillary where Hillary was the most popular and was the favorite to win until the last weeks before the presidential election [5], where some of the specialized communication agencies published many news about Hillary contributed significantly to influence public opinion tendency to Trump, who eventually won. Jennifer et al in their article [6] did a study in order to understand the dynamics of this exceptional campaign in which social media played a major role.…”

Section: Introductionmentioning

confidence: 99%

Modeling a Rumor Propagation in Online Social Network: An Optimal Control Approach

Ghazzali

Bhih

Discrete Dynamics in Nature and Society

et al. 2020

Self Cite

We propose to model the phenomenon of the spread of a rumor in social networks in this paper. From an existing SIR model, we manipulate a new one that is based on the model of cholera in order to take into account professional pages that specialize in spreading rumors. In the second part, we introduce a control strategy to fight against the diffusion of the rumor. Our main objective is to characterize the three optimal controls that minimize the number of spreader users, fake pages, and the corresponding costs. For that matter, using the maximum principle of Pontryagin, we prove the existence and we give characterization of our controls. Numerical simulations are given to concretize our approach.

“…In the literature, there are a great deal of mathematical studies of diseases that give an interesting insight into the use of mathematical models in epidemiology. For example, Baily et al [2], Anderson et al [3], Hethcote [4], Brauer and Castillo-Chavez [5], Keeling and Rohani [6] , Huppert and Katriel [7] and [8,9,10,11,12,13,25,26]. In this contribution, we consider an epidemic SIR model, spatiotemporal in two dimensions in the work of Lotfi.…”

Section: Introductionmentioning

confidence: 99%

A spatiotemporal SIR epidemic model two-dimensional with problem of optimal control

Adnaoui¹,

Elberrai²,

et al. 2022

bspm

In this work, we are interested in studying a spatiotemporal two-dimensional SIR epidemic model, in the form of a system of partial differential equations (PDE). A distribution of a vaccine in the form of a control variable is considered to force immunity. The purpose is to characterize a control that minimizes the number of susceptible, infected individuals and the costs associated with vaccination over a nite space and time domain. In addition, the existence of the solution of the state system and the optimal control is proved. The characterization of the control is given in terms of state function and adjoint function. The numerical resolution of the state system shows the effectiveness of our control strategy.