Kenkre V M, Sugaya S
Consortium of the Americas for Interdisciplinary Science, Department of Physics and Astronomy, University of New Mexico, Albuquerque, NM, 87131, USA,
Bull Math Biol. 2014 Dec;76(12):3016-27. doi: 10.1007/s11538-014-0042-8. Epub 2014 Nov 18.
A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in [Formula: see text] dimensions. The motion of an animal pair is taken to obey a Smoluchowski equation in [Formula: see text]-dimensional space that combines diffusion with confinement of each animal to its particular home range. An additional (reaction) term that comes into play when the animals are in close proximity describes the process of infection. Analytic solutions are obtained, confirmed by numerical procedures, and shown to predict a surprising effect of confinement. The effect is that infection spread has a non-monotonic dependence on the diffusion constant and/or the extent of the attachment of the animals to the home ranges. Optimum values of these parameters exist for any given distance between the attractive centers. Any change from those values, involving faster/slower diffusion or shallower/steeper confinement, hinders the transmission of infection. A physical explanation is provided by the theory. Reduction to the simpler case of no home ranges is demonstrated. Effective infection rates are calculated, and it is shown how to use them in complex systems consisting of dense populations.
基于在[公式：见原文]维中移动的随机漫步者（受感染和易感动物）的稀疏系统中的成对相互作用，构建了一种流行病传播理论。动物对的运动被认为遵循[公式：见原文]维空间中的斯莫卢霍夫斯基方程，该方程将扩散与每个动物限制在其特定的栖息地范围内相结合。当动物彼此靠近时起作用的一个额外（反应）项描述了感染过程。获得了解析解，并通过数值程序进行了验证，结果表明这些解析解预测了一种令人惊讶的限制效应。这种效应是感染传播对扩散常数和/或动物对栖息地范围的附着程度具有非单调依赖性。对于吸引力中心之间的任何给定距离，这些参数都存在最佳值。与这些值的任何偏差，包括更快/更慢的扩散或更浅/更深的限制，都会阻碍感染的传播。该理论提供了一种物理解释。证明了该理论可简化为无栖息地范围的更简单情况。计算了有效感染率，并展示了如何在由密集种群组成的复杂系统中使用这些感染率。
