An optimal strategy for HIV multitherapy

Zhou, Yinggao; Liang, Yiting; Wu, Jianhong

doi:10.1016/j.cam.2013.12.007

Cited by 21 publications

(16 citation statements)

References 8 publications

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“…Since economic resources are limited, epidemiological models have started taking into consideration the economic constraints imposed by limited resources when analyzing control strategies. Optimal control theory has been applied to the mathematical models of HIV models Zarei et al (2010), Kwon et al (2012), Karrakchou et al (2006), Kwon (2007), Roshanfekr et al (2014), , Zhou et al (2014), Adams et al (2005), Costanza et al (2013), Orellana (2011), Malaria Okosun et al (2013, Okosun et al (2011), Okosun and Makinde (2014), Okosun (2011), Kim (2012), Prosper et al (2014), Tuberculosis Moualeu et al (2015), Silva and Torres (2013), Agusto and Adekunle (2014), Bowong and Aziz Alaoui (2013), Whang et al (2011), Vector borne diseases Lashari (2012), Graesboll et al (2014), Sung Lee and Ali Lashari (2014) and other diseases Yan and Zou (2008), Agusto (2013), Brown andJane White (2011), Zaman et al (2008), Okosun and Makinde (2014), Su and Sun (2015), Buonomo et al (2014), Lowden et al (2014), Roshanfekr et al (2014), Apreutesei et al (2014), Imran et al (2014).…”

Section: Introductionmentioning

confidence: 99%

Optimal control in epidemiology

2015

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Mathematical modelling of infectious diseases has shown that combinations of isolation, quarantine, vaccine and treatment are often necessary in order to eliminate most infectious diseases. However, if they are not administered at the right time and in the right amount, the disease elimination will remain a difficult task. Optimal control theory has proven to be a successful tool in understanding ways to curtail the spread of infectious diseases by devising the optimal diseases intervention strategies. The method consists of minimizing the cost of infection or the cost of implementing the control, or both. This paper reviews the available literature on mathematical models that use optimal control theory to deduce the optimal strategies aimed at curtailing the spread of an infectious disease.

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Section: Introductionmentioning

confidence: 99%

Optimal control in epidemiology

2015

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“…It is well known that the mathematical models play vital roles in the dynamics and control of many epidemics including malaria, severe acute respiratory syndromes (SARS) and TB (see, for example, [9][10][11][12][13][14][15][16][17] and references therein). Many mathematical dynamic models for TB have been studied extensively in the literature; for instance we refer the reader to [18][19][20][21][22][23] .…”

Section: Introductionmentioning

confidence: 99%

Optimal control analysis of a tuberculosis model

Da-peng

Huang

2018

Applied Mathematical Modelling

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a b s t r a c tIn this paper, we extend the model of Liu and Zhang (Math Comput Model 54:836-845, 2011) by incorporating three control terms and apply optimal control theory to the resulting model. Optimal control strategies are proposed to minimize both the disease burden and the intervention cost. We prove the existence and uniqueness of optimal control paths and obtain these optimal paths analytically using Pontryagin's Maximum Principle. We analyse our results numerically to compare various strategies of proposed controls. It is observed that implementation of three controls is most effective and less expensive among all the strategies. Thus, we conclude that in order to reduce tuberculosis threat all the three controls must be taken into consideration concurrently.

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“…e majority of above-mentioned papers on the optimal anti-HIV therapy consider models with a single control, which correspond to the therapies where a single drug (a single action) is used. Very few of existing publications consider a possibility of simultaneous use of two drugs [15,20,[37][38][39][40], whereas works exploring interaction of three or more controls are rather exceptional [41,42]. On the other hand, the current anti-HIV therapy guidelines necessitate the use of the highly active antiretroviral therapy (HAART) that implies administering a combination of several (typically, three or four) antiretrovirals.…”

Section: Interaction Of Several Simultaneously Acting Controlsmentioning

confidence: 99%

Optimal Controls of the Highly Active Antiretroviral Therapy

Grigorieva

Хайлов

Korobeinikov

2020

Abstract and Applied Analysis

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In this paper, we study generic properties of the optimal, in a certain sense, highly active antiretroviral therapy (or HAART). To address this problem, we consider a control model based on the 3-dimensional Nowak–May within-host HIV dynamics model. Taking into consideration that precise forms of functional responses are usually unknown, we introduce into this model a nonlinear incidence rate of a rather general form given by an unspecified function of the susceptible cells and free virus particles. We also add a term responsible to the loss of free virions due to infection of the target cells. To mirror the idea of highly active anti-HIV therapy, in this model we assume six controls that can act simultaneously. These six controls affecting different stage of virus life cycle comprise all controls possible for this model and account for all feasible actions of the existing anti-HIV drugs. With this control model, we consider an optimal control problem of minimizing the infection level at the end of a given time interval. Using an analytical mathematical technique, we prove that the optimal controls are bang-bang, find accurate estimates for the maximal possible number of switchings of these controls and establish qualitative types of the optimal controls as well as mutual relationships between them. Having the estimate for the number of switchings found, we can reduce the two-point boundary value problem for Pontryagin Maximum Principle to a considerably simpler problem of the finite-dimensional optimization, which can be solved numerically. Despite this possibility, the obtained theoretical results are illustrated by numerical calculations using BOCOP–2.0.5 software package, and the corresponding conclusions are made.

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An optimal strategy for HIV multitherapy

Cited by 21 publications

References 8 publications

Optimal control in epidemiology

Optimal control in epidemiology

Optimal control analysis of a tuberculosis model

Optimal Controls of the Highly Active Antiretroviral Therapy

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