Vyska Martin, Gilligan Christopher
University of Cambridge, Cambridge, United Kingdom.
Bull Math Biol. 2016 Nov;78(11):2212-2227. doi: 10.1007/s11538-016-0217-6. Epub 2016 Oct 18.
We analyse the dynamical behaviour of a simple, widely used model that integrates epidemiological dynamics with disease control and economic constraint on the control resources. We consider both the deterministic model and its stochastic counterpart. Despite its simplicity, the model exhibits mathematically rich dynamics, including multiple stable fixed points and stable limit cycles arising from global bifurcations. We show that the existence of the limit cycles in the deterministic model has important consequences in modelling the range of potential effects the control can have. The stochastic effects further interact with the deterministic dynamical structure by facilitating transitions between different attractors of the system. The interaction is important for the predictive power of the model and in using the model to optimize allocation when resources for control are limited. We conclude that when studying models with constrained control, special care should be given to the dynamical behaviour of the system and its interplay with stochastic effects.
我们分析了一个简单且广泛使用的模型的动力学行为，该模型将流行病学动力学与疾病控制以及控制资源的经济约束整合在一起。我们考虑了确定性模型及其对应的随机模型。尽管该模型很简单，但它展现出数学上丰富的动力学特性，包括多个稳定不动点以及由全局分岔产生的稳定极限环。我们表明，确定性模型中极限环的存在对于模拟控制可能产生的潜在影响范围具有重要意义。随机效应通过促进系统不同吸引子之间的转变，进一步与确定性动力学结构相互作用。这种相互作用对于模型的预测能力以及在控制资源有限时利用模型优化资源分配都很重要。我们得出结论，在研究具有受限控制的模型时，应特别关注系统的动力学行为及其与随机效应的相互作用。
