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

Adnaoui, Khalid; Elberrai, Imane; Laaroussi, Adil El Alami; Hattaf, Khalid

doi:10.5269/bspm.51110

Cited by 4 publications

(3 citation statements)

References 22 publications

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“…The functions 1 2 B 1 u 2 1 , 1 2 B 2 u 2 2 and 1 2 B 3 u 2 3 are the costs of the controls u 1 , u 2 and u 3 , respectively. The cost terms are assumed to be nonlinear quadratic functions (as in [17][18][19]).…”

Section: Tb Model With Controlsmentioning

confidence: 99%

Tuberculosis in Ethiopia: Optimal Intervention Strategies and Cost-Effectiveness Analysis

Mengistu

Witbooi

2022

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This paper searches for optimal strategies for the minimization of the number of high-risk latent and active tuberculosis (TB) infectious individuals using real data from Ethiopia. Optimal control theory is harnessed for investigation and analysis of the optimal combination of interventions for controlling the transmission of TB using distancing, case finding, and case holding as controls. We calculate and compare the incremental cost-effectiveness ratio (ICER) for each of the strategies to determine the most effective combination of interventions for curbing the spread of the disease. Our findings suggest that, for optimal cost-effective management of the TB disease, the government of Ethiopia must focus more on prevention strategies such as isolation of infectious people, early TB patient detection, treatment, and educational programs. The optimal strategy is quantified through simulation.

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Section: Tb Model With Controlsmentioning

confidence: 99%

Tuberculosis in Ethiopia: Optimal Intervention Strategies and Cost-Effectiveness Analysis

Mengistu

Witbooi

2022

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“…Recently, several works related with the control problem and parameter identification problems in epidemiological compartmental models (SIS and SIR) were developed [8,[22][23][24][25][26]. In [8], the authors obtained results for the one-dimensional case, which were extended to the multidimensional case in [22,23].…”

Section: Introductionmentioning

confidence: 99%

“…In [24], a generalized SIR model for indirectly transmitted diseases was considered, and the authors proved results for the existence of optimal solutions, a first-order optimal condition, and the local uniqueness of the coefficient identification problem. In [25,26], the authors study the optimal control problems in SIR models related with vaccination such that the control variable force immunity. In a broad sense, we should emphasize that the results in [8,[22][23][24] are deduced by assuming that the coefficients and the initial condition belong to appropriate holder spaces.…”

Section: Introductionmentioning

confidence: 99%

Results for a Control Problem for a SIS Epidemic Reaction–Diffusion Model

et al. 2023

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This article is focused on investigating the mathematical model calibration of a reaction–diffusion system arising in the mathematical model of the spread of an epidemic in a society. We consider that the total population is divided into two classes of individuals, called susceptible and infectious, where a susceptible individual can become infectious, and that upon recovery, an infected individual can become susceptible again. We consider that the population lives in a spatially heterogeneous environment, and that the spread of the dynamics is governed by a reaction–diffusion system consisting of two equations, where the variables of the model are the densities of susceptible and infected individuals. In the reaction term, the coefficients are the rates of disease transmission and the rate of infective recovery. The main contribution of this study is the identification of the reaction coefficients by assuming that the infective and susceptible densities at the end time of the process and on overall spatial domain are observed. We apply the optimal control methodology to prove the main findings: the existence of positive solutions for the state system, the existence of at least one solution for the identification problem, the introduction of first-order necessary conditions, and the local uniqueness of optimal solutions.

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The diffusion identification in a SIS reaction-diffusion system

Coronel,

Huancas,

Hess

et al. 2023

MBE

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<abstract><p>This article is concerned with the determination of the diffusion matrix in the reaction-diffusion mathematical model arising from the spread of an epidemic. The mathematical model that we consider is a susceptible-infected-susceptible model with diffusion, which was deduced by assuming the following hypotheses: The total population can be partitioned into susceptible and infected individuals; a healthy susceptible individual becomes infected through contact with an infected individual; there is no immunity, and infected individuals can become susceptible again; the spread of epidemics arises in a spatially heterogeneous environment; the susceptible and infected individuals implement strategies to avoid each other by staying away. The spread of the dynamics is governed by an initial boundary value problem for a reaction-diffusion system, where the model unknowns are the densities of susceptible and infected individuals and the boundary condition models the fact that there is neither emigration nor immigration through their boundary. The reaction consists of two terms modeling disease transmission and infection recovery, and the diffusion is a space-dependent full diffusion matrix. The determination of the diffusion matrix was conducted by considering that we have experimental data on the infective and susceptible densities at some fixed time and in the overall domain where the population lives. We reformulated the identification problem as an optimal control problem where the cost function is a regularized least squares function. The fundamental contributions of this article are the following: The existence of at least one solution to the optimization problem or, equivalently, the diffusion identification problem; the introduction of first-order necessary optimality conditions; and the necessary conditions that imply a local uniqueness result of the inverse problem. In addition, we considered two numerical examples for the case of parameter identification.</p></abstract>

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

Cited by 4 publications

References 22 publications

Tuberculosis in Ethiopia: Optimal Intervention Strategies and Cost-Effectiveness Analysis

Tuberculosis in Ethiopia: Optimal Intervention Strategies and Cost-Effectiveness Analysis

Results for a Control Problem for a SIS Epidemic Reaction–Diffusion Model

The diffusion identification in a SIS reaction-diffusion system

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