Optimal control of non-autonomous SEIRS models with vaccination and treatment

Mateus, Joaquim P.; Rebelo, Paulo; Rosa, Silvério; Silva, César M.; Torres, Delfim F. M.

doi:10.3934/dcdss.2018067

Cited by 18 publications

(25 citation statements)

References 32 publications

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“…Remark 1. When α = 1, the fractional compartmental model (1) represent the classical SIRS model investigated in [28].…”

Section: Sirs-α Modelmentioning

confidence: 99%

“…The paper is organized as follows. In Section 2, we introduce the SIRS-α and SEIRS-α fractional epidemic models, which generalize corresponding integer-order (α = 1) models of [28]. The main results are then given in Section 3: estimation of the fractional order α with real data of Florida, for the two proposed fractional models (Section 3.1); fractional optimal control, costeffectiveness and numerical simulations for the more realistic SEIRS-α model (Sections 3.2 and 3.3).…”

Section: Introductionmentioning

confidence: 99%

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Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

Rosa

Torres

2018

Chaos, Solitons & Fractals

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A human respiratory syncytial virus surveillance system was implemented in Florida in 1999, to support clinical decision-making for prophylaxis of premature newborns. Recently, a local periodic SEIRS mathematical model was proposed in [Stat. Optim. Inf. Comput. 6 (2018), no. 1, 139-149] to describe real data collected by Florida's system. In contrast, here we propose a non-local fractional (non-integer) order model. A fractional optimal control problem is then formulated and solved, having treatment as the control. Finally, a cost-effectiveness analysis is carried out to evaluate the cost and the effectiveness of proposed control measures during the intervention period, showing the superiority of obtained results with respect to previous ones.

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“…Remark 1. When α = 1, the fractional compartmental model (1) represent the classical SIRS model investigated in [28].…”

Section: Sirs-α Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

Rosa

Torres

2018

Chaos, Solitons & Fractals

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“…that are widely used for modelling infectious diseases [1,14]. These epidemiological models are based on dividing the population into compartments, with the assumption that every individual in the same compartment has the same characteristics [5,15,17]. In this paper, we use the classic Kermack and McKendrick SIR model [11] to describe the epidemic spreading.…”

Section: Epidemiological Modelmentioning

confidence: 99%

The Risk of Contagion Spreading and its Optimal Control in the Economy

Kostylenko

Rodrigues

Torres

2019

Stat., optim. inf. comput.

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The global crisis of 2008 provoked a heightened interest among scientists to study the phenomenon, its propagation and negative consequences. The process of modelling the spread of a virus is commonly used in epidemiology. Conceptually, the spread of a disease among a population is similar to the contagion process in economy. This similarity allows considering the contagion in the world financial system using the same mathematical model of infection spread that is often used in epidemiology. Our research focuses on the dynamic behaviour of contagion spreading in the global financial network. The effect of infection by a systemic spread of risks in the network of national banking systems of countries is tested. An optimal control problem is then formulated to simulate a control that may avoid significant financial losses. The results show that the proposed approach describes well the reality of the world economy, and emphasizes the importance of international relations between countries on the financial stability.

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“…The susceptible population is increased by recruitment of susceptible individuals at a rate Λ, while µ is the natural death rate of all individuals. The transmission process is governed by a general incidence function f (S, I) [24]. Individuals in the class I progress to the class C at a rate φ and to the class A at a rate ρ.…”

Section: Introductionmentioning

confidence: 99%

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

Lotfi

Mahrouf

Maziane

et al. 2019

Stat., optim. inf. comput.

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We study the global dynamics of a SICA infection model with general incidence rate. The proposed model is calibrated with cumulative cases of infection by HIV-AIDS in Morocco from 1986 to 2015. We first prove that our model is biologically and mathematically well-posed. Stability analysis of different steady states is performed and threshold parameters are identified where the model exhibits clearance of infection or maintenance of a chronic infection. Furthermore, we examine the robustness of the model to some parameter values by examining the sensitivity of the basic reproduction number. Finally, using numerical simulations with real data from Morocco, we show that the model predicts well such reality.

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Optimal control of non-autonomous SEIRS models with vaccination and treatment

Cited by 18 publications

References 32 publications

Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

Optimal control of a fractional order epidemic model with application to human respiratory syncytial virus infection

The Risk of Contagion Spreading and its Optimal Control in the Economy

A Minimal HIV-AIDS Infection Model with General Incidence Rate and Application to Morocco Data

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