Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, United Kingdom.
BMC Public Health. 2012 Aug 20;12:679. doi: 10.1186/1471-2458-12-679.
Existing epidemiological models have largely tended to neglect the impact of individual behaviour on the dynamics of diseases. However, awareness of the presence of illness can cause people to change their behaviour by, for example, staying at home and avoiding social contacts. Such changes can be used to control epidemics but they exact an economic cost. Our aim is to study the costs and benefits of using individual-based social distancing undertaken by healthy individuals as a form of control.
Our model is a standard SIR model superimposed on a spatial network, without and with addition of small-world interactions. Disease spread is controlled by allowing susceptible individuals to temporarily reduce their social contacts in response to the presence of infection within their local neighbourhood. We ascribe an economic cost to the loss of social contacts, and weigh this against the economic benefit gained by reducing the impact of the epidemic. We study the sensitivity of the results to two key parameters, the individuals' attitude to risk and the size of the awareness neighbourhood.
Depending on the characteristics of the epidemic and on the relative economic importance of making contacts versus avoiding infection, the optimal control is one of two extremes: either to adopt a highly cautious control, thereby suppressing the epidemic quickly by drastically reducing contacts as soon as disease is detected; or else to forego control and allow the epidemic to run its course. The worst outcome arises when control is attempted, but not cautiously enough to cause the epidemic to be suppressed. The next main result comes from comparing the size of the neighbourhood of which individuals are aware to that of the neighbourhood within which transmission can occur. The control works best when these sizes match and is particularly ineffective when the awareness neighbourhood is smaller than the infection neighbourhood. The results are robust with respect to inclusion of long-range, small-world links which destroy the spatial structure, regardless of whether individuals can or cannot control them. However, addition of many non-local links eventually makes control ineffective.
These results have implications for the design of control strategies using social distancing: a control that is too weak or based upon inaccurate knowledge, may give a worse outcome than doing nothing.
现有的流行病学模型在很大程度上忽略了个体行为对疾病动态的影响。然而，对疾病存在的认识会促使人们改变行为，例如待在家里并避免社交接触。这种变化可以用来控制传染病，但会带来经济成本。我们的目的是研究健康个体采取基于个体的社交距离措施作为控制手段的成本和收益。
我们的模型是在没有和加入小世界相互作用的空间网络上叠加的标准 SIR 模型。通过允许易感个体在其当地社区内出现感染时暂时减少社交接触来控制疾病传播。我们将社交接触的损失归因于经济成本，并将其与通过减少传染病影响获得的经济收益进行权衡。我们研究了两个关键参数的敏感性，即个体的风险态度和意识社区的大小。
根据传染病的特征以及接触与避免感染的相对经济重要性，最佳控制是两种极端情况之一：要么采取高度谨慎的控制，即在疾病检测到后立即通过大幅减少接触迅速抑制疫情；要么放弃控制，让疫情自行发展。当尝试控制但不够谨慎以至于不能抑制疫情时，会出现最坏的结果。接下来的主要结果来自于比较个体意识到的社区的大小和可以发生传播的社区的大小。当这些大小匹配时，控制效果最佳，而当意识社区小于感染社区时，控制效果特别差。结果对于包括破坏空间结构的远程小世界链接是稳健的，无论个体是否可以控制这些链接。然而，添加许多非本地链接最终会使控制无效。
这些结果对使用社交距离的控制策略的设计具有启示意义：过于薄弱或基于不准确知识的控制可能会导致比不采取任何措施更差的结果。
