Miller Joel C
Department of Mathematics and Department of Biology, Penn State University, University Park, Pennsylvania 16802, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Jun;87(6):060801. doi: 10.1103/PhysRevE.87.060801. Epub 2013 Jun 20.
We consider multiple diseases spreading in a static configuration model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a disease-specific rate. Infection by one disease confers immediate and permanent immunity to infection by any disease. Under these assumptions, we find a simple, low-dimensional ordinary differential equations model which captures the global dynamics of the infection. The dynamics depend strongly on initial conditions. Although we motivate this Rapid Communication with infectious disease, the model may be adapted to the spread of other infectious agents such as competing political beliefs, or adoption of new technologies if these are influenced by contacts. As an example, we demonstrate how to model an infectious disease which can be prevented by a behavior change.
我们考虑多种疾病在静态配置模型网络中的传播情况。我们做出标准假设，即感染以特定疾病的速率在邻居之间传播，且感染个体以特定疾病的速率康复。感染一种疾病会使人立即获得对任何疾病感染的永久免疫力。在这些假设下，我们找到了一个简单的低维常微分方程模型，该模型捕捉了感染的全局动态。动态情况强烈依赖于初始条件。尽管我们以传染病来推动这篇快速通讯，但如果其他传染因素（如相互竞争的政治信仰或新技术的采用）受到接触的影响，该模型也可适用于它们的传播。作为一个例子，我们展示了如何对一种可通过行为改变预防的传染病进行建模。
