Optimal intervention strategy for prevention tuberculosis using a smoking-tuberculosis model

Choi, Sunhwa; Jung, Eunok; Lee, Seok-Min

doi:10.1016/j.jtbi.2015.05.022

Cited by 25 publications

(10 citation statements)

References 39 publications

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“…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%

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: Introductionmentioning

confidence: 99%

Optimal control analysis of a tuberculosis model

Da-peng

Huang

2018

Applied Mathematical Modelling

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“…In many works of literature of tuberculosis models, it is usually considered drug administration or vaccination, as in (Baba et al, 2020;Blaser et al, 2016;Brooks-Pollock et al, 2014;Byrne et al, 2015;Kim et al, 2018;Kuddus et al, 2020;Kyu et al, 2018). Many of the TB models use optimal control theory regarding their treatment strategies (Agusto & Adekunle, 2014;Baba et al, 2020;Bowong, 2010;Choi et al, 2015;Emvudu et al, 2011;Fatmawati et al, 2020;Gao & Huang, 2018;Moualeu et al, 2015). In a within-host tuberculosis model, the immune response to bacteria is generally assumed, as in (Adi & Thobirin, 2020;Zhang, 2020;Zhang et al, 2020).…”

Section: A Introductionmentioning

confidence: 99%

A Within-host Tuberculosis Model Using Optimal Control

Adi

2021

JTAM

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In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis. We considered an in-host tuberculosis model that described the interaction between Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal control is applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula is obtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results. The results suggest that control or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large. In this paper, we studied a mathematical model of tuberculosis with vaccination for the treatment of tuberculosis.We considered an in-host tuberculosis model that described the interaction between macrophages Macrophages and Mycobacterium tuberculosis and investigated the effect of vaccination treatments on uninfected macrophages. Optimal controlis applied to show the optimal vaccination and effective strategies to control the disease. The optimal control formula isobtained using the Hamiltonian function and Pontryagin's maximum principle. Finally, we perform numerical simulations to support the analytical results.The results suggest thatcontrol or vaccination is required if the maximal transmission of infection rate at which macrophages became infected is large.

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“…In the last few years, several transmission models based on different approaches have been suggested to analyze the dynamics of TB disease in various regions. Most of the researchers who have studied mathematical models of tuberculosis have focused on the continuous-time models described by ordinary differential equations (see [8][9][10][11][12][13][14][15]). We observe that most of those researchers focused on the continuous-time models described by the differential equations.…”

Section: Introductionmentioning

confidence: 99%

A Multiregion Discrete-Time Epidemic Model of Mycobacterium tuberculosis Infections: An Optimal Control Approach

Bouajaji

Laarabi

Rachik

et al. 2021

Discrete Dynamics in Nature and Society

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The main goal of this article is to devise the spatial-temporal spread of TB, in multiple neighboring domains, taking into account the epidemiological diversity of their populations. However, since both the environment and any population are spatially heterogeneous, it is obviously desirable to include spatial structure into an epidemic model. Individuals with tuberculosis can spread the disease by moving from one area to another. In addition, people travel by air between cities, so diseases can be spread quickly between very distant places (as was the case with the COVID-19). In our model, each region’s studied population is divided into five compartments S, L1, I, L2, and R. Further, we introduce in our discrete systems three control variables which represent the effectiveness rates of vaccination, travel-blocking operation, and treatment. We focus in our study to control the outbreaks of an epidemic that affects a hypothetical population belonging to a specific region. Firstly, we analyze the epidemic model when the control strategy is based on the vaccination control only, and secondly, when the travel-blocking control is added, we finish with the introduction of the treatment control. The optimal control theory, based on Pontryagin’s maximum principle, is applied thrice in this paper, for the characterizations of the vaccination, travel-blocking, and treatment controls. The numerical results associated with the multipoint boundary value problems are obtained based on the forward-backward sweep method combined with progressive-regressive Runge–Kutta fourth-order schemes.

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Optimal intervention strategy for prevention tuberculosis using a smoking-tuberculosis model

Cited by 25 publications

References 39 publications

Optimal control analysis of a tuberculosis model

Optimal control analysis of a tuberculosis model

A Within-host Tuberculosis Model Using Optimal Control

A Multiregion Discrete-Time Epidemic Model of Mycobacterium tuberculosis Infections: An Optimal Control Approach

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