Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.
Optimal control of HIV/AIDS in the workplace in the presence of careless individuals.
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DOI：
10.1155/2014/831506
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发表时间：
2014
影响因子：
--
通讯作者：
Makinde OD
中科院分区：
文献类型：
--
作者：
Seidu B;Makinde OD
提出了一种非线性动力系统，并对其进行了定性分析。当基本繁殖数小于1时，该模型的无病平衡点是局部渐近稳定的；当基本繁殖数大于1时，该模型表现出唯一的地方性平衡。结果表明，在没有招募感染者的情况下，当指数指数< 1时，疾病被根除，而在有招募感染者的情况下，疾病仍然存在。基本模型被扩展到包括旨在减少工作场所感染、不负责任和非生产力的控制努力。这导致了一个最优控制问题，并利用庞特里亚金极大值原理（PMP）进行了定性分析。对所得到的最优控制问题进行了数值模拟，以获得对模型含义的定量见解。模拟结果表明，与单一的控制策略相比，采用多方面的方法与疾病作斗争更为有效。
A nonlinear dynamical system is proposed and qualitatively analyzed to study the dynamics of HIV/AIDS in the workplace. The disease-free equilibrium point of the model is shown to be locally asymptotically stable if the basic reproductive number, ℛ 0, is less than unity and the model is shown to exhibit a unique endemic equilibrium when the basic reproductive number is greater than unity. It is shown that, in the absence of recruitment of infectives, the disease is eradicated when ℛ 0 < 1, whiles the disease is shown to persist in the presence of recruitment of infected persons. The basic model is extended to include control efforts aimed at reducing infection, irresponsibility, and nonproductivity at the workplace. This leads to an optimal control problem which is qualitatively analyzed using Pontryagin's Maximum Principle (PMP). Numerical simulation of the resulting optimal control problem is carried out to gain quantitative insights into the implications of the model. The simulation reveals that a multifaceted approach to the fight against the disease is more effective than single control strategies.