Stochastic optimal control of pre-exposure prophylaxis for HIV infection.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2020-09-08 DOI:10.1093/imammb/dqac003
Jasmina Ðorđević, Kristina Rognlien Dahl
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引用次数: 0

Abstract

The aim of the paper is to apply the stochastic optimal control problem in order to optimize the number of individual which will have the pre-exposure prophylaxis (PReP) treatment in the stochastic model for HIV/AIDS with PReP. By using the stochastic maximum principle, we derive the stochastic optimal control of PReP for the unconstrained control problem. Furthermore, by combining the stochastic maximum principle with a version of the Lagrange multiplier method, we solve the PReP problem for two different types of budget constrains with a given constrain for the costs (possible of different kind, transportation, price of the treatment, etc.). Obtained results for the different percentage of the individuals who got the vaccine, as well as results for unconstrained and constrained problems, are illustrated by a numerical example.
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HIV感染暴露前预防的随机最优控制。
针对HIV/AIDS暴露前预防(PReP)随机模型,应用随机最优控制问题来优化接受暴露前预防(PReP)治疗的个体数量。利用随机极大值原理,导出了无约束控制问题的暴露前预防随机最优控制。进一步,将随机极大值原理与拉格朗日乘数法相结合,在给定成本约束(不同种类的可能性、运输、治疗价格等)的情况下,求解了两种不同类型预算约束的PReP问题。通过一个数值例子说明了接种疫苗的不同个体百分比的结果,以及无约束和有约束问题的结果。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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