Optimal control of treatments in a two-strain tuberculosis model

Jung, Eunok; Lenhart, Suzanne; Feng, Zhilan

doi:10.3934/dcdsb.2002.2.473

Cited by 215 publications

(169 citation statements)

References 12 publications

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“…It is also assumed that cost of treatment is nonlinear and takes a quadratic nature, which is found to be consistent with previous works in the literature (see, e.g. [8] ). In other words, the cost incurred in improving successfully treatment rate (the effort s such as regularity of drug intake) is taken as…”

Section: The Control Problemsupporting

confidence: 74%

“…Neglecting the compliance with drug treatments might result in a relapse and antibiotic resistant TB, i.e. multidrug-resistant TB (MDR-TB) [8] . MDR-TB is one of the most serious health problems and the progress in curing that is slow.…”

Section: Introductionmentioning

confidence: 99%

“…The dynamics of transmission of the disease has been analyzed in terms of the reduction of the basic reproductive number. Since the first paper published by Jung et al [8] in 2002, the time dependent optimal control strategies have been employed in the study of dynamics of TB mathematical models by many authors (see, for example, [8,[26][27][28][29][30][31][32][33][34] ). Valuable theoretical results generated by both approaches of studying control strategies can be used to guide epidemic control programs.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: The Control Problemsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Optimal control analysis of a tuberculosis model

Da-peng

Huang

2018

Applied Mathematical Modelling

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“…In this paper, in the framework of multiple optimal controls [15][16][17], the controls both in the susceptible and in the infected class are introduced and the existence of the optimal solution is assessed in the SIRC epidemic model. Note that a similar approach was presented in [18] with reference to vector-borne diseases and not considering the cross-immune class.…”

Section: Introductionmentioning

confidence: 99%

Optimal control for SIRC epidemic outbreak

Iacoviello

Stasio

2013

Computer Methods and Programs in Biomedicine

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In this paper the mathematical SIRC epidemic model is considered. It efficiently describes diseases in which a cross immune class (C) is present, along with the susceptible (S), the infected (I) and the removed (R) ones. Controlling epidemic diseases corresponds to the introduction of vaccination, quarantine and treatment strategies; generally only one of these actions is considered. In this paper the possibility of optimal controls both over the susceptible and the infected subjects is assumed, taking into account also limitations of resources. A suitable cost index is introduced and via the Pontryagin's Minimum Principle the optimal control strategy is determined and the existence of the optimal solution is assessed. Numerical results are developed analyzing the effects of different control strategies.

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“…Our analytical tool is based primarily on the concept of optimal control theory which has been successfully used to make decisions involving biological models. Important applications include optimal treatment strategies in HIV models [30,31], tuberculosis [32,33] and design of optimal cardiopulmonary resuscitation techniques [34,35]. We formulate the control problem of maintaining sufficiently high levels of miR-451 to keep glioma cells in their proliferative mode restraining them from invading the brain tissue.…”

Section: Introductionmentioning

confidence: 99%

Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery

Reyes

Jung

Kim

2015

J. R. Soc. Interface.

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Glioblastoma, the most aggressive type of brain cancer, has median survival time of 1 year after diagnosis. It is characterized by alternating modes of rapid proliferation and aggressive invasion in response to metabolic stress in the microenvironment. A particular microRNA, miR-451, and its downstream signalling molecules, AMPK complex, are known to be key determinants in switching cell fate. These components form a core control system determining a balance between cell growth and migration which is regulated by fluctuating glucose levels in the microenvironment. An important factor from the treatment point of view is that low levels of glucose affect metabolism and activate cell migration through the miR-451-AMPK control system, creating 'invisible' migratory cells and making them inaccessible by conventional surgery. In this work, we apply optimal control theory to deal with the problem of maintaining upregulated miR-451 levels that prevent cell infiltration to surrounding brain tissue and thus induce localization of these cancer cells at the surgical site. The model also considers the effect of a drug that blocks inhibitive pathways of miR-451 from AMPK complex. Glucose infusion control and drug infusion control are chosen to represent dose rates of glucose and drug intravenous administrations, respectively. The characteristics of optimal control lead us to investigate the structure of optimal intravenous infusion regimen under various circumstances and predict best clinical outcomes with minimum expense possible.

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Optimal control of treatments in a two-strain tuberculosis model

Cited by 215 publications

References 12 publications

Optimal control analysis of a tuberculosis model

Optimal control analysis of a tuberculosis model

Optimal control for SIRC epidemic outbreak

Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery

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