Department of Industrial Engineering and Management Sciences, Northwestern University, USA.
Math Biosci. 2010 Mar;224(1):35-42. doi: 10.1016/j.mbs.2009.12.006. Epub 2010 Jan 4.
Chronic viral diseases such as human immunodeficiency virus (HIV) and hepatitis B virus (HBV) afflict millions of people worldwide. A key public health challenge in managing such diseases is identifying infected, asymptomatic individuals so that they can receive antiviral treatment. Such treatment can benefit both the treated individual (by improving quality and length of life) and the population as a whole (through reduced transmission). We develop a compartmental model of a chronic, treatable infectious disease and use it to evaluate the cost and effectiveness of different levels of screening and contact tracing. We show that: (1) the optimal strategy is to get infected individuals into treatment at the maximal rate until the incremental health benefits balance the incremental cost of controlling the disease; (2) as one reduces the disease prevalence by moving people into treatment (which decreases the chance that they will infect others), one should increase the level of contact tracing to compensate for the decreased effectiveness of screening; (3) as the disease becomes less prevalent, it is optimal to spend more per case identified; and (4) the relative mix of screening and contact tracing at any level of disease prevalence is such that the marginal efficiency of contact tracing (cost per infected person found) equals that of screening if possible (e.g., when capacity limitations are not binding). We also show how to determine the cost-effective equilibrium level of disease prevalence (among untreated individuals), and we develop an approximation of the path of the optimal prevalence over time. Using this, one can obtain a close approximation of the optimal solution without having to solve an optimal control problem. We apply our methods to an example of hepatitis B virus.
慢性病毒疾病，如人类免疫缺陷病毒（HIV）和乙型肝炎病毒（HBV），影响着全球数百万人。管理此类疾病的一个主要公共卫生挑战是识别感染但无症状的个体，以便他们能够接受抗病毒治疗。这种治疗对治疗个体（通过改善生活质量和延长寿命）和整个人群（通过减少传播）都有益处。我们建立了一个慢性可治疗传染病的房室模型，并利用它来评估不同水平的筛查和接触者追踪的成本和效果。我们表明：（1）最优策略是以最大速度让感染个体接受治疗，直到增加的健康效益与控制疾病的增量成本相平衡；（2）随着将更多的人转移到治疗中（减少他们感染他人的机会）来降低疾病流行率，应增加接触者追踪的水平以补偿筛查效果的降低；（3）随着疾病流行率降低，发现每个病例的成本最佳化；（4）在任何疾病流行率水平下，筛查和接触者追踪的相对混合方式是，接触者追踪的边际效率（发现的每个感染者的成本）尽可能等于筛查的效率（例如，当能力限制不是约束条件时）。我们还展示了如何确定具有成本效益的疾病流行率的均衡水平（在未治疗的个体中），并开发了一种最优流行率随时间变化的近似路径。利用这一点，无需解决最优控制问题，就可以获得最优解的近似值。我们将我们的方法应用于乙型肝炎病毒的例子。
