Optimal control theory applied to the anti-viral treatment of AIDS

Souza, J. A. M. Felippe de; Caetano, Marco Antonio Leonel; Yoneyama, Takashi

doi:10.1109/cdc.2001.914696

Cited by 31 publications

(22 citation statements)

References 14 publications

(3 reference statements)

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“…Those that were not available were obtained from literature published by researchers in malaria endemic countries which have similar environmental conditions compare to Kenya. Table 5 provides a summary of the estimated values of all parameters as described by Otieno et al [23] in addition to some from the literature. Data was collected from the literature, Division of Malaria Control (DOMC), Kenya National Bureau of Statistics, Malaria Indicator Survey for Kenya, Demographic Health Survey (DHS) for Kenya, WHO websites and hospital records (from Kisumu, Kisii, Chuka (Tharake-Nithi) and Nyeri counties representing the four different transmission settings/epidemiological zones in Kenya).…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

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Cost Effectiveness Analysis of Optimal Malaria Control Strategies in Kenya

2016

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Malaria remains a leading cause of mortality and morbidity among the children under five and pregnant women in sub-Saharan Africa, but it is preventable and controllable provided current recommended interventions are properly implemented. Better utilization of malaria intervention strategies will ensure the gain for the value for money and producing health improvements in the most cost effective way. The purpose of the value for money drive is to develop a better understanding (and better articulation) of costs and results so that more informed, evidence-based choices could be made. Cost effectiveness analysis is carried out to inform decision makers on how to determine where to allocate resources for malaria interventions. This study carries out cost effective analysis of one or all possible combinations of the optimal malaria control strategies (Insecticide Treated Bednets-ITNs, Treatment, Indoor Residual Spray-IRS and Intermittent Preventive Treatment for Pregnant Women-IPTp) for the four different transmission settings in order to assess the extent to which the intervention strategies are beneficial and cost effective. For the four different transmission settings in Kenya the optimal solution for the 15 strategies and their associated effectiveness are computed. Cost-effective analysis using Incremental Cost Effectiveness Ratio (ICER) was done after ranking the strategies in order of the increasing effectiveness (total infections averted). The findings shows that for the endemic regions the combination of ITNs, IRS, and IPTp was the most cost-effective of all the combined strategies developed in this study for malaria disease control and prevention; for the epidemic prone areas is the combination of the treatment and IRS; for seasonal areas is the use of ITNs plus treatment; and for the low risk areas is the use of treatment only. Malaria transmission in Kenya can be minimized through tailor-made intervention strategies for malaria control which produces health improvements in the most cost effective way for different epidemiological zones. This offers the good value for money for the public health programs and can guide in the allocation of malaria control resources for the post-2015 malaria eradication strategies and the achievement of the Sustainable Development Goals.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

“…The restriction on the length of time interval r0, Ts is common in control problems [8,21,23], and it guarantees the uniqueness of the optimality system. By standard control arguments involving the bounds on the controls, we conclude that…”

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confidence: 99%

Cost Effectiveness Analysis of Optimal Malaria Control Strategies in Kenya

2016

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“…Zaman et al (2008) used optimal control to determine the optimal vaccination strategy to reduce the susceptible and infective individuals for a general SIR epidemic model. More studies on the applications of optimal control to infectious diseases, mainly HIV/AIDS and Tuberculosis can be found in Felippe de Souza et al (2000), Joshi (2002), Joshi et al (2006), Jung et al (2002), Kar andBatabyal (2011), Kirschner et al (1997), Lenhart and Yong (1997) and Rachik et al (2009), these studies focused more on cost minimization analysis of the examined control strategies.…”

Section: Introductionmentioning

confidence: 97%

Optimal control strategies and cost-effectiveness analysis of a malaria model

2013

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“…This smallness restriction of the length on the time is due to the opposite time orientations of (24 and (25)); the state problem has initial values and the adjoint problem has final values. This restriction is very common in control problems [16][17][18][19].…”

Section: Analysis Of Optimal Controlmentioning

confidence: 99%

“…where [15][16][17][18][19]. With the given objective function J(u 1 , u 2 , u 3 ), our goal is to minimize the number of carefree susceptible S 1 , while minimizing the cost of control u 1 (t), u 2 (t) and u 3 (t).…”

Section: Analysis Of Optimal Controlmentioning

confidence: 99%

On a drug-resistant malaria model with susceptible individuals without access to basic amenities

Okosun

Makinde

2012

J Biol Phys

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In this paper, a deterministic malaria transmission model in the presence of a drug-resistant strain is investigated. The model is studied using stability theory of differential equations, optimal control, and computer simulation. The threshold condition for disease-free equilibrium is found to be locally asymptotically stable and can only be achieved in the absence of a drug-resistant strain in the population. The existence of multiple endemic equilibria is also established. Both the Sensitivity Index (SI) of the model parameters and the Incremental Cost-Effectiveness Ratio (ICER) for all possible combinations of the disease-control measures are determined. Our results revealed among others that the most cost-effective strategy for drug-resistant malaria control is the combination of the provision of basic amenities (such as access to clean water, electricity, good roads, health care, and education) and treatment of infective individuals. Therefore, more efforts from policy-makers on the provisions of basic amenities and treatment of infectives would go a long way to combat the malaria epidemic.

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Optimal control theory applied to the anti-viral treatment of AIDS

Cited by 31 publications

References 14 publications

Cost Effectiveness Analysis of Optimal Malaria Control Strategies in Kenya

Cost Effectiveness Analysis of Optimal Malaria Control Strategies in Kenya

Optimal control strategies and cost-effectiveness analysis of a malaria model

On a drug-resistant malaria model with susceptible individuals without access to basic amenities

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