An optimal control problem for a spatiotemporal SIR model

Laaroussi, Adil El-Alami; Rachik, Mostafa; Elhia, Mohamed

doi:10.1007/s40435-016-0283-5

Cited by 29 publications

(18 citation statements)

References 21 publications

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“…Simply apply (SP. 7), observing that (f ), (g), (m) and (b) were proved above exhibiting bounds that hold uniformly on X n , once the norm of the initial datum u o and the constants in (IBVP.1)-(IBVP.5) are fixed.…”

Section: Proofs Related To Section 3 -About the Ibvp (31)mentioning

confidence: 88%

Well Posedness and Control in a NonLocal SIR Model

Colombo

Garavello

2020

Appl Math Optim

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SIR models, also with age structure, can be used to describe the evolution of an infective disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolutions of the S and R populations. It is then natural to seek the "best" vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the SIR model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies.+∞ 0 λ(a, a ′ ) I(t, a ′ ) da ′ S(t, a) in the former two right hand sides represents the total number of susceptible individuals of age a

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Section: Proofs Related To Section 3 -About the Ibvp (31)mentioning

confidence: 88%

Well Posedness and Control in a NonLocal SIR Model

Colombo

Garavello

2020

Appl Math Optim

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“…e approach used is based on the work of El Alami Laaroussi et al [17,18], which was applied on a SIR model. So, our goal is to characterize optimal control in the form of a vaccination program, maximizing the number of people reestablished and minimizing the number of susceptible, infected people and the cost associated with vaccination over an infinite space and in a time domain.…”

Section: Introductionmentioning

confidence: 99%

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

Adnaoui

Laaroussi

2020

International Journal of Differential Equations

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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.

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“…Optimal control strategies. In this section, we put forward some control strategies to suppress the diffusion of rumors in online social networks [35,3,10,32]. We consider intervention measures, such as network supervision like forced silence, that is, prohibiting rumor-infected users from speaking online.…”

Section: 3mentioning

confidence: 99%

“…We suggest readers refer to Ref. [35] as some other related literatures [3,10,32] on the optimal control of epidemic and eco-epidemiological models. It is remarked that optimal control has vital practical significance for rumor propagation models.…”

mentioning

confidence: 99%

Spatial dynamics and optimization method for a network propagation model in a shifting environment

Zhu¹,

Liu²

2021

Discrete &Amp; Continuous Dynamical Systems - A

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In this paper, a reaction-diffusion ISCT rumor propagation model with general incidence rate is proposed in a spatially heterogeneous environment. We first summarize the well-posedness of global solutions. Then the basic reproduction number R 0 is introduced for the model which contains the spatial homogeneity as a special case. The threshold-type dynamics are also established in terms of R 0 , including the global asymptotic stability of the rumor-free steady state and the uniform persistence of all positive solutions. Furthermore, by applying a controller to this model, we investigate the optimal control problem. Employing the operator semigroup theory, we prove the existence, uniqueness and some estimates of the positive strong solution to the controlled system. Subsequently, the existence of the optimal control strategy is established with the aid of minimal sequence techniques and the first order necessary optimality conditions for the optimal control is deduced. Finally, some numerical simulations are performed to validate the main analysis. The results of our study can theoretically promote the regulation of rumor propagation on the Internet.

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An optimal control problem for a spatiotemporal SIR model

Cited by 29 publications

References 21 publications

Well Posedness and Control in a NonLocal SIR Model

Well Posedness and Control in a NonLocal SIR Model

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

Spatial dynamics and optimization method for a network propagation model in a shifting environment

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