Keeping Options Open: an Optimal Control Model with Trajectories That Reach a DNSS Point in Positive Time

Zeiler, Irmgard; Caulkins, Jonathan P.; Grass, Dieter; Tragler, Gernot

doi:10.1137/080719741

Cited by 19 publications

(12 citation statements)

References 18 publications

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“…Therefore, the cost for covering larger proportion of population involved in vaccination process will be not only increasing but also growth of cost will be faster and steeper. Hence, we consider the biquadratic form in the vaccination control to represent high expensiveness of vaccination process [16] . That is, the cost involved in vaccination process is taken as…”

Section: The Control Problemmentioning

confidence: 99%

“…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%

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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 Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal control analysis of a tuberculosis model

Da-peng

Huang

2018

Applied Mathematical Modelling

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“…The limitations of this method are more of practical nature, e.g., computational capacity, than theoretical nature. In fact the MATLAB package OCMat has already been successfully applied to a number of different models, e.g., Caulkins et al (2005a, 2005b, 2007, 2008, 2011, 2009) , Zeiler et al (2010) , and Levy et al (2006) . The presented bifurcations have analogous counterparts in higher dimensions and can numerically be computed using the same procedures.…”

Section: Introductionmentioning

confidence: 99%

Numerical computation of the optimal vector field: Exemplified by a fishery model

Grass

2012

Journal of Economic Dynamics and Control

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Numerous optimal control models analyzed in economics are formulated as discounted infinite time horizon problems, where the defining functions are nonlinear as well in the states as in the controls. As a consequence solutions can often only be found numerically. Moreover, the long run optimal solutions are mostly limit sets like equilibria or limit cycles. Using these specific solutions a BVP approach together with a continuation technique is used to calculate the parameter dependent dynamic structure of the optimal vector field. We use a one dimensional optimal control model of a fishery to exemplify the numerical techniques. But these methods are applicable to a much wider class of optimal control problems with a moderate number of state and control variables.

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“…Mathematical models have been used extensively to predict, control and also to formulate policies to eradicate or contain diseases including the interventions mentioned in the previous paragraph [5,8,19,25,27,28,30,38,43,44,50]. For example, screening or identification on active infectious population has been used by many researchers as an intervention [5,23,30].…”

Section: Introductionmentioning

confidence: 99%

Role of Optimal Screening and Treatment on Infectious Diseases Dynamics in Presence of Self-protection of Susceptible

Kumar

Srivastava

2019

Differ Equ Dyn Syst

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In this study, a nonlinear S E I R model has been proposed and analysed that accounts for the screening of exposed population, limited treatment of infective and self-protection in susceptible population. We observe that for the basic reproduction number (R 0) below one, a backward bifurcation exists due to saturation in treatment. Also, R 0 depends on selfprotection parameter and hence self-protection can help in reducing it. Further to understand the impact of screening and treatment on disease dynamics, we extend this model to an optimal control problem. Using Pontryagin's Maximum Principle, optimal control paths are obtained analytically corresponding to the proposed cost functional. Our numerical experimentations suggest that between only screening and only treatment control policies, screening is more effective and economically viable than the only treatment policy. The combined usage of both screening and treatment is found highly effective and least expensive. Hence, we conclude that implementation of screening along with treatment not only reduces the infection level but also minimizes the associated economic burden. Also, when optimal controls are applied, the cumulative count of infective reduces with the increase in self-protection, therefore, selfprotection helps in reducing the disease burden. The epidemic peak as well as cost is also shown to be reduced when self-protection is high for various values of basic reproduction number.

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Keeping Options Open: an Optimal Control Model with Trajectories That Reach a DNSS Point in Positive Time

Cited by 19 publications

References 18 publications

Optimal control analysis of a tuberculosis model

Optimal control analysis of a tuberculosis model

Numerical computation of the optimal vector field: Exemplified by a fishery model

Role of Optimal Screening and Treatment on Infectious Diseases Dynamics in Presence of Self-protection of Susceptible

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