Complex Dynamical Behaviour in an Epidemic Model with Control

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• 作者：Martin Vyska ; Christopher Gilligan
• 关键词：Disease dynamics modelling ; Control of epidemics ; Bifurcations in epidemic models
• 刊名：Bulletin of Mathematical Biology
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：78
• 期：11
• 页码：2212-2227
• 全文大小：1,857 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematical Biology
  
• 出版者：Springer New York
• ISSN：1522-9602
• 卷排序：78

文摘

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.