Optimal control methods applied to disease models

Joshi, Hem Raj; Lenhart, Suzanne; Li, Michael Y.; Wang, Liancheng

doi:10.1090/conm/410/07728

Cited by 70 publications

(70 citation statements)

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“…The existence of optimal control can be proved by using the result from [19] Maximum Principle such that…”

Section: Characterization Of the Optimal Controlmentioning

confidence: 99%

Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

Lhous¹,

Rachik²,

Larrache³

2017

IJCA

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In the present paper, we consider a mathematical model of a SEIR with immigration of infectives. The optimal control theory is applied to reduce the latent and infectious groups, increase the number of recovered individuals and this with an optimal cost. We use two controls representing the effort that reduces the contact between the infectious and susceptible individuals and a therapeutic treatment. We presents an approach that investigates a free terminal optimal time control witch give a minimum duration of a vaccination campaign. The Pontryagin's maximum principle is used to characterize the optimal controls and the optimal final time. We obtained an optimality system that we sought to solve numerically by an iterative discrete scheme that converges following an appropriate test similar the one related to the forward-backward sweep method.

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“…The existence of optimal control can be proved by using the result from [19] Maximum Principle such that…”

Section: Characterization Of the Optimal Controlmentioning

confidence: 99%

Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

Lhous¹,

Rachik²,

Larrache³

2017

IJCA

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“…This is due to the opposite time orientations of the optimality system; the state problem has initial values and the adjoint problem has final values. This restriction is very common in control problems (see [6,28,32,33]). Next we discuss the numerical solutions of the optimality system and the corresponding optimal control pair, the parameter choices, and the interpretations from various cases.…”

Section: Optimal Control Analysis Of the Leptospirosis Modelmentioning

confidence: 99%

Global stability analysis and control of leptospirosis

2016

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Abstract:The aim of this paper is to investigate the effectiveness and cost-effectiveness of leptospirosis control measures, preventive vaccination and treatment of infective humans that may curtail the disease transmission. For this, a mathematical model for the transmission dynamics of the disease that includes preventive, vaccination, treatment of infective vectors and humans control measures are considered. Firstly, the constant control parameters' case is analyzed, also calculate the basic reproduction number and investigate the existence and stability of equilibria. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved when the basic reproduction number is less than unity. The model is found to exhibit the existence of multiple endemic equilibria. Furthermore, to assess the relative impact of each of the constant control parameters measures the sensitivity index of the basic reproductive number to the model's parameters are calculated. In the time-dependent constant control case, Pontryagin's Maximum Principle is used to derive necessary conditions for the optimal control of the disease. The cost-effectiveness analysis is carried out by first of all using ANOVA to check on the mean costs. Then followed by Incremental Cost-Effectiveness Ratio (ICER) for all the possible combinations of the disease control measures. Our results revealed that the most cost-effective strategy for the control of leptospirosis is the combination of the vaccination and treatment of infective livestocks. Though the combinations of all control measures is also effective, however, this strategy is not cost-effective and so too costly. Therefore, more efforts from policy makers on vaccination and treatment of infectives livestocks regime would go a long way to combat the disease epidemic.

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“…For instance, it was used in deriving control strategies for mitigating the spread of different infectious diseases [8,18,6,2]. Also, the theory was used to evolve effective treatment strategies for the treatment of some deadly or terminal ailments/infections [9,11,4].…”

Section: Tunde T Yusuf / Journal Of Modeling Simulation Identi Icamentioning

confidence: 99%

Modelling Marijuana Smoking Epidemics among Adults: An Optimal Control Panacea

Yusuf¹

2014

JMSIC

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Reducing the number of individuals involved in substance abuse in any community is usually a challenging problem. We consider the control of the spread of Marijuana smoking, one substance that is majorly abused, among adults. We propose a deterministic model for controlling the spread of Marijuana smoking incorporating education and awareness campaign as well as rehabilitation as control measures. We formulate a ixed time optimal control problem subject to the model dynamics with the goal of inding the optimal combination of the control measures that will minimize the cost of the control efforts as well as the prevalence of marijuana smoking in a community. We use Pontryagin's maximum principle to derive the optimality system and solve the system numerically. Results from our simulations are discussed.

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Optimal control methods applied to disease models

Cited by 70 publications

References 0 publications

Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

Free Optimal Time Control Problem for a SEIR-Epidemic Model with Immigration of Infective

Global stability analysis and control of leptospirosis

Modelling Marijuana Smoking Epidemics among Adults: An Optimal Control Panacea

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