空间约束对个体行为影响的网络传染病动力学建模与分析

Network transmission model, as one of the most successful topics in the realm of disease dynamics, has attracted great research interest. In essence, it is such a framework: network nodes represent agents, while the edges connecting them represent contacts that enable the disease to be transmitted. Its aim is to study how the disease spreads upon the specific network topology. Despite good progress, such a hypothesis neglects the potential influence of spatial distance among agents. In realistic social networks, however, agents’ activity and contact behavior are subject to spatial distance. To this aim, this project will mainly research the impact of spatial constraints on individual behavior and disease transmission at the basis of mean-field theory, moment closure approximation and probability generating function approaches. In detail, we consider three following models: disease model on static embedded networks with distance constraints, disease model on 2D lattice networks where link rewiring is subject to spatial distance, and disease model (and then with vaccination) on adaptive networks where link rewiring is restricted by the shortest path length. For different spatial constraints, we will focus on the basic reproduction number and the final epidemic size; analyze the dynamical behavior such as stability, bifurcation and periodic solutions of the models as well as the network topology properties including degree distribution, clustering coefficient and degree correlations, and therefore unveil the impact of spatially constrained individual behavior on disease transmission and network topology. These possible research outcomes can provide theoretical instruction to prevention and control of realistic infectious diseases.

复杂网络上的传染病传播模型研究是目前传染病动力学模型的研究热点，其本质是将个体看作网络的节点，个体之间的接触看成网络的边，研究传染性疾病在特定拓扑结构网络上的传播过程。这一过程忽略了个体之间的物理空间距离。事实上，在真实社会接触网络中，每个人的活动范围往往受到空间距离的限制，其接触行为也会受到空间约束的影响。为此，本项目将考虑空间约束对个体行为及疾病传播的影响，利用平均场、矩封闭和概率生成函数等方法，建立具有空间距离约束的空间嵌入静态网络传染病模型、二维晶格上自适应重连受空间距离约束的传染病模型、具有路径长度限制的自适应网络传染病传播（及其接种）模型。在不同空间约束下，计算疾病的基本再生数和最终规模，研究模型的稳定性、分支、周期解等动力学性态及网络的度分布、聚类系数、度相关性等拓扑性质，揭示在空间约束下个体行为对疾病传播及网络结构的影响。该研究成果可对真实传染病的预防和控制提供理论指导。

本项目针对空间约束、个体移动、个体自适应行为、风险感知、意识扩散、免疫接种以及人口变化等因素对网络传染病传播动力学的影响进行研究，取得的主要成果如下：（i）建立了个体移动受空间约束影响的动态接触网络传染病传播及其免疫接种模型，研究了疾病传播阈值、最终染病规模，给出了平衡点的稳定性分析，揭示了空间约束及个体行为对传染病传播的影响机制，并提出了最优的免疫接种控制策略；（ii）研究了具有个体自适应行为影响的网络传染病模型，对模型的传播阈值、稳定性以及极限环、后向分支、Hopf分支、BT分支等动力学性态进行了严格的数学分析与证明，解决了这类自适应网络传染病动力学模型动力学性态分析及证明的关键理论问题；（iii）基于个体的风险感知行为，建立了网络传染病传播与信息扩散动力学模型，研究了个体意识行为与传染病传播动力学的相互影响；（iv）建立了人口变化的动态网络传染病传播模型，研究了个体自适应行为与人口动力学因素对疾病传播阈值、流行规模及动力学性态的影响。项目实施以来，在国内外学术期刊发表论文14篇，其中SCI论文11篇，还有相关论文未发表。本项目研究结果可以丰富和完善空间接触网络、动态网络传染病传播动力学建模方法及基本理论，为制定实用有效的传染病防控策略提供科学的理论依据。