Epidemiological Modeling (EMOD) Group, Intellectual Ventures Laboratory, 1555 132nd Ave. NE, Bellevue, WA 98005, USA.
Math Biosci. 2013 Aug;244(2):125-34. doi: 10.1016/j.mbs.2013.04.013. Epub 2013 May 9.
Contact rates and patterns among individuals in a geographic area drive transmission of directly-transmitted pathogens, making it essential to understand and estimate contacts for simulation of disease dynamics. Under the uniform mixing assumption, one of two mechanisms is typically used to describe the relation between contact rate and population density: density-dependent or frequency-dependent. Based on existing evidence of population threshold and human mobility patterns, we formulated a spatial contact model to describe the appropriate form of transmission with initial growth at low density and saturation at higher density. We show that the two mechanisms are extreme cases that do not capture real population movement across all scales. Empirical data of human and wildlife diseases indicate that a nonlinear function may work better when looking at the full spectrum of densities. This estimation can be applied to large areas with population mixing in general activities. For crowds with unusually large densities (e.g., transportation terminals, stadiums, or mass gatherings), the lack of organized social contact structure deviates the physical contacts towards a special case of the spatial contact model - the dynamics of kinetic gas molecule collision. In this case, an ideal gas model with van der Waals correction fits well; existing movement observation data and the contact rate between individuals is estimated using kinetic theory. A complete picture of contact rate scaling with population density may help clarify the definition of transmission rates in heterogeneous, large-scale spatial systems.
在地理区域内，个体之间的接触率和模式驱动着直接传播病原体的传播，因此了解和估计接触对于模拟疾病动态至关重要。在均匀混合假设下，通常使用两种机制之一来描述接触率与人口密度之间的关系：密度依赖性或频率依赖性。基于人口阈值和人类流动模式的现有证据，我们制定了一个空间接触模型来描述适当的传播形式，即在低密度时初始增长，在高密度时饱和。我们表明，这两种机制是极端情况，无法在所有尺度上捕捉到真实的人口流动。人类和野生动物疾病的实证数据表明，当观察整个密度范围时，非线性函数可能效果更好。这种估计可以应用于一般活动中人口混合的大面积区域。对于密度异常大的人群（例如，交通枢纽、体育场或大规模集会），缺乏有组织的社会接触结构会使物理接触偏向于空间接触模型的特殊情况——动力学气体分子碰撞的动态。在这种情况下，带有范德华修正的理想气体模型拟合得很好；现有的运动观测数据和个体之间的接触率是使用动力学理论来估计的。接触率与人口密度的关系的完整图景可能有助于澄清在异质的、大规模的空间系统中传播率的定义。
