基于年龄及个体迁移行为的传染病重叠网络动力学模型研究

The transmission of group-level infectious diseases factually is the spread of viruses or bacteria at a specific social network structure, which can be mathematically seen as social network node dynamics evolution process. However, different infectious diseases involve different groups and have different ways of transmission. So the constructive network is infectious diseases dynamic overlapping network, which uses a particular group as node and is related with individual migration behavior, whose typological structure and node dynamics behavior becomes more complex when compared with present network infectious diseases model. So far, there have been very few dynamics researches of infectious diseases overlay network based on age and individual migration behavior. Therefore, this project will construct overlapped infectious diseases network according to age grouping, consider the effect of individual migration behavior on network infectious diseases, give the calculating formula of disease spread threshold, study the model stability, branch and other dynamical behavior, evaluate risk factors of migration, study optimal control strategies, apply research results into concrete disease network model, estimate and optimize model parameters using existing data, and then evaluate predictions, early warnings and intervention measures. The research results can enrich approaches to infectious disease dynamics and perfect basic theory of overlay network infectious disease node dynamics model.

群体水平的传染病的传播过程实际上是在特定社会网络结构上的病毒或细菌的传播，在数学上可看作是社会网络上的节点动力学演化过程。但不同的传染病，其涉及的群体与传播途径是完全不同的，因此，构成的网络是特定群体作为节点，并与个体迁移行为相关的传染病动态重叠网络，该网络的拓扑结构与节点动力学行为与现有的网络传染病模型相比会变的更加复杂。到目前为止，基于年龄及个体迁移行为的传染病重叠网络的动力学行为研究很少，为此，本项目将按照年龄分组建立重叠传染病网络，并考虑个体的迁移行为对网络传染病的影响，给出疾病传播阈值的计算公式，研究模型稳定性、分支等动力学性态，评估迁移的风险因素，研究最优控制策略，将所得成果应用到具体疾病网络模型中，利用已有的数据，对模型参数进行估计和优化，进而进行预测、预警及干预措施的评估，其研究成果可以丰富传染病动力学研究方法，完善重叠网络传染病节点动力学模型的基本理论。

本项目主要利用复杂网络的方法，研究了以性病、新产品等传播过程为背景的传播机理。建立了异性恋和同性恋均具有传染力的性病网络传染病模型，给出了基本再生数关于传染率参数的敏感性分析。建立了基于半有向网络的传染病模型，给出了疾病传播阈值的计算公式，研究了模型的稳定性等动力学性态，该模型具有一般性。建立了基于复杂网络的新产品扩散模型，为商家宣传新产品时采取不同的广告策略提供了相应的理论依据。该项目的研究结果为复杂网络上的传染病模型的研究提供了新的理论和方法，对传染病等的防治具有重要指导作用。