Approximated analytical solution to an Ebola optimal control problem

Hincapié-Palacio, Doracelly; Ospina, Juan; Torres, Delfim F. M.

doi:10.1080/15502287.2016.1231236

Cited by 9 publications

(9 citation statements)

References 8 publications

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“…Optimal control theory has been successfully applied to several epidemiological models, e.g., dengue [27,28], tuberculosis [12,29], Ebola [16,24], cholera [20], and HIV/AIDS [26,31]. However, we claim our work to be the first to apply optimal control to an HIV/AIDS model with PrEP.…”

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confidence: 99%

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Modeling and optimal control of HIV/AIDS prevention through PrEP

Silva¹,

Torres²

2018

Discrete &Amp; Continuous Dynamical Systems - S

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Pre-exposure prophylaxis (PrEP) consists in the use of an antiretroviral medication to prevent the acquisition of HIV infection by uninfected individuals and has recently demonstrated to be highly efficacious for HIV prevention. We propose a new epidemiological model for HIV/AIDS transmission including PrEP. Existence, uniqueness and global stability of the disease free and endemic equilibriums are proved. The model with no PrEP is calibrated with the cumulative cases of infection by HIV and AIDS reported in Cape Verde from 1987 to 2014, showing that it predicts well such reality. An optimal control problem with a mixed state control constraint is then proposed and analyzed, where the control function represents the PrEP strategy and the mixed constraint models the fact that, due to PrEP costs, epidemic context and program coverage, the number of individuals under PrEP is limited at each instant of time. The objective is to determine the PrEP strategy that satisfies the mixed state control constraint and minimizes the number of individuals with pre-AIDS HIV-infection as well as the costs associated with PrEP. The optimal control problem is studied analytically. Through numerical simulations, we demonstrate that PrEP reduces HIV transmission significantly.Comment: This is a preprint of a paper whose final and definite form is with 'Discrete and Continuous Dynamical Systems -- Series S' (DCDS-S), ISSN 1937-1632 (print), ISSN 1937-1179 (online), available at [https://www.aimsciences.org/journals/home.jsp?journalID=15]. In this version, typos detected while reading the proofs were correcte

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confidence: 99%

“…We solve the optimal control problem (17)- (20) numerically for concrete parameter values and initial conditions. The initial conditions are given by (16) and the HIV transmission parameters take the values β = 0.582, η C = 0.04, and η A = 1. 35.…”

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confidence: 99%

Modeling and optimal control of HIV/AIDS prevention through PrEP

Silva¹,

Torres²

2018

Discrete &Amp; Continuous Dynamical Systems - S

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“…Then the central issue is how to implement such interventions in an optimal way. This investigation program has been recently carried out for several infectious diseases, as diverse as dengue [5,23], tuberculosis [6,25], Ebola [11,21], HIV/AIDS [26,27], and cholera [12,15]. Here we investigate such approach to HRSV.…”

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confidence: 99%

“…ROSA AND D. F. Variation of the optimal control Ì (treatment). Efficacy function F (t) defined in(11).…”

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confidence: 99%

Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in Florida

Rosa

Torres

2018

Stat., optim. inf. comput.

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A state wide Human Respiratory Syncytial Virus (HRSV) surveillance system was implemented in Florida in 1999 to support clinical decision-making for prophylaxis of premature infants. The research presented in this paper addresses the problem of fitting real data collected by the Florida HRSV surveillance system by using a periodic SEIRS mathematical model. A sensitivity and cost-effectiveness analysis of the model is done and an optimal control problem is formulated and solved with treatment as the control variable.

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“…A detailed survey of such problems and relevant references are also given in [13]. Here we allocate only papers published at the end of 2016 ( [1,8,18,25]). Note that in all these papers, the considered functionals include the total costs of the control constraints on the given time interval that are defined by integrals of the squares of the controls.…”

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confidence: 99%

Determination of the optimal controls for an Ebola epidemic model

Grigorieva¹,

Хайлов²

2018

Discrete &Amp; Continuous Dynamical Systems - S

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A control SEIR type model describing the spread of an Ebola epidemic in a population of a constant size is considered on the given time interval. This model contains four bounded control functions, three of which are distancing controls in the community, at the hospital, and during burial; the fourth is burial control. We consider the optimal control problem of minimizing the fraction of infectious individuals in the population at the given terminal time and analyze the corresponding optimal controls with the Pontryagin maximum principle. We use values of the model parameters and control constraints for which the optimal controls are bang-bang. To estimate the number of zeros of the switching functions that determine the behavior of these controls, a linear non-autonomous homogenous system of differential equations for these switching functions and corresponding to them auxiliary functions are obtained. Subsequent study of the properties of solutions of this system allows us to find analytically the estimates of the number of switchings and the type of the optimal controls for the model parameters and control constraints related to all Ebola epidemics from 1995 until 2014. Corresponding numerical calculations confirming the results are presented.

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Approximated analytical solution to an Ebola optimal control problem

Cited by 9 publications

References 8 publications

Modeling and optimal control of HIV/AIDS prevention through PrEP

Modeling and optimal control of HIV/AIDS prevention through PrEP

Parameter Estimation, Sensitivity Analysis and Optimal Control of a Periodic Epidemic Model with Application to HRSV in Florida

Determination of the optimal controls for an Ebola epidemic model

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