Department of Applied Mathematics, University of Waterloo, 200 University Avenue West, Ontario, Waterloo N2L 3G1, Canada; School of Environmental Sciences, University of Guelph, 50 Stone Road East, Ontario, Guelph N1G 2W1, Canada.
School of Environmental Sciences, University of Guelph, 50 Stone Road East, Ontario, Guelph N1G 2W1, Canada.
J Theor Biol. 2018 Jul 7;448:17-25. doi: 10.1016/j.jtbi.2018.03.032. Epub 2018 Mar 31.
Early warning signals of sudden regime shifts are a widely studied phenomenon for their ability to quantify a system's proximity to a tipping point to a new and contrasting dynamical regime. However, this effect has been little studied in the context of the complex interactions between disease dynamics and vaccinating behaviour. Our objective was to determine whether critical slowing down (CSD) occurs in a multiplex network that captures opinion propagation on one network layer and disease spread on a second network layer. We parameterized a network simulation model to represent a hypothetical self-limiting, acute, vaccine-preventable infection with short-lived natural immunity. We tested five different network types: random, lattice, small-world, scale-free, and an empirically derived network. For the first four network types, the model exhibits a regime shift as perceived vaccine risk moves beyond a tipping point from full vaccine acceptance and disease elimination to full vaccine refusal and disease endemicity. This regime shift is preceded by an increase in the spatial correlation in non-vaccinator opinions beginning well before the bifurcation point, indicating CSD. The early warning signals occur across a wide range of parameter values. However, the more gradual transition exhibited in the empirically-derived network underscores the need for further research before it can be determined whether trends in spatial correlation in real-world social networks represent critical slowing down. The potential upside of having this monitoring ability suggests that this is a worthwhile area for further research.
早期的突跳转变预警信号是一个被广泛研究的现象，因为它们能够量化系统接近突跳点的程度，从而进入一个新的、对比鲜明的动态状态。然而，在疾病动态和接种行为之间复杂的相互作用的背景下，这一效应的研究还很少。我们的目的是确定在一个捕捉到意见在一个网络层上传播，疾病在另一个网络层上传播的复杂相互作用的多重网络中，是否存在关键减速（CSD）。我们对一个网络模拟模型进行了参数化，以代表一种假设的自我限制、急性、疫苗可预防的感染，具有短暂的自然免疫力。我们测试了五种不同的网络类型：随机、晶格、小世界、无标度和经验衍生的网络。对于前四种网络类型，随着感知到的疫苗风险超过一个转折点，从完全接受疫苗和消除疾病转变为完全拒绝疫苗和疾病流行，模型会出现一个状态转变。在分叉点之前，非接种者意见的空间相关性就开始增加，这表明存在关键减速。早期预警信号出现在广泛的参数值范围内。然而，经验衍生网络中表现出的更渐进的转变，突出了在确定现实世界社交网络中空间相关性的趋势是否代表关键减速之前，还需要进一步的研究。拥有这种监测能力的潜在好处表明，这是一个值得进一步研究的领域。
