复杂网络上基于演化博弈理论的疾病动力学建模研究

In recent years, humans have been more and more frequently suffered from large-scale outbreaks of infectious epidemics that are increasingly threatening the entire human society, like severe acute respiratory syndrome (SARS) in 2003, avian influenza (bird flu) and pandemic influenza (H1N1) in 2009. On one hand, much attention of researchers has been focused on the related study on outbreak control measures for infectious epidemics. If not being involuntary, anti-epidemic strategies (such as the vaccination policy) typically allow individuals of a population to self-decide whether to take up vaccine or not, in which case individual decisions are heavily affected not only by their varied beliefs or experiences about the risk from infection and the implementation cost of vaccination, but also, more importantly, by others' decisions. Evolutionary game theory provides a universal framework to model such individual interactions. In particular, game-theoretical models (e.g., the vaccine game) have been proposed and investigated to mimic the reality of individual behavioral response to the spread of infectious diseases on complex networks, which successfully guides the collective behavior of a population of individuals to achieve a lowered risk of infection. On the other hand, our interest is also on to evolutionary-game-based models of viral evolutionary dynamics. For this part, note that mutation/adaption of virus may give birth to new strains of pathogens that are even more virulent, and as a direct result, some original vaccines could lose their effects after a passage of time. Evolutionary game theory also provides good descriptions of multi-faceted interactions between many-strain pathogens, including competition, cooperation, and cross-immunity, to name a few. Similarly, such interaction between virus and its host (e.g., the host immune response) can be also well reflected and modeled by evolutionary game theory, which not only promises to deepen our understanding of underlying mechanisms responsible for both viral evolutionary dynamics and epidemic spreading processes on complex networks, but also, for the practical purpose, potentially leads to more effective means of prevention measures for controlling infectious diseases.

近年来，人类社会不断受到日益严重的大规模爆发传染病的威胁，针对性的疾病防控策略成为复杂网络疾病传播动力学研究中的重要课题。一方面，相关的反疾病措施（例如疫苗接种等）,通常在非强制性的实施原则下,群集中的每个个体需要进行决策，其过程不仅取决于病情的危害、策略的代价，更受其他人决策行为的影响。而演化博弈论提供了复杂网络环境下个体策略交互学习的理论框架，通过建立和研究博弈模型，模拟真实个体对疾病传播的行为反应，从而更好的达到降低传染病危害的目的。另一方面，我们关注病毒层面的演化建模，例如最常见的，病毒变异所产生的新株系会直接导致原有疫苗在一段时间后失效的可能性。演化博弈论同样为病毒演化动力学中涉及到的多株系病原体间竞争、互惠、交叉免疫等相互作用提供了良好的刻画。借助演化博弈论来理解和揭示疾病传播、病毒演化等现象的内在机制，不仅对疾病防控策略研究具有重要的现实意义，同时也为我们开拓了新的研究视野。

复杂网络为研究人类交互行为和现代流行病学提供了蓝本。而随着二者的联系日趋紧密，建立网络扩散过程中的人类应激反应模型便成为亟待解决的问题。我们这里从演化博弈理论借鉴了（在自私的博弈者中的）合作激励机制（例如间接互惠中基于记忆的形象分值，基于搭档选择的类聚效应等），并应用到疾病觉察，疫苗接种，信息扩散等于网络流行病学相关的若干问题中。具体地，1. 我们首次利用微分积分方程对邻域接触史指导下的基于疾病察觉的疾控策略进行建模，并给出了传播阈值与最终爆发规模的解析解，同时发现在绝大部分模型参数范围内分布式疾病觉察机制优于集中式疾病觉察机制；2. 研究了个体感染史相关的疫苗接种博弈及其在网络疾病传播过程中的调控作用，计算表明疾病传播阈值于疫苗接种阈值不仅取决于疫苗-治疗费用比，也取决于在重复博弈设定下个体的历史感染次数；3. 讨论了碎片化（即连续化）的信息融合策略与网络结构与状态相关的同伴选择效应在网络传播中的作用，从理论和数值两方面对多种不同的策略进行了检验，并将原有的同伴选择推广到了多人情况；4. 研究了一类树状层次网络骨干以外的捷径对网络扩散的影响，进一步利用特征值扰动分析研究了树状层次网络上信息捷径效应，为改善树型社会网络的沟通度提出了一种新的捷径重要性指标。我们得到的主要结果反映了演化博弈中的记忆效应和搭档选择效应在网络扩散动力学中的作用，前者通过个体记忆的累积起到了强化了感染风险进而降低接触率，后者通过选择性接触在接触率不变的前提也降低了感染风险。我们得到的结果还表明，在某些场合需要加速有利信息（例如疾病察觉信号）的传播时可采用相应的搭档选择策略，从而最终达到调控网络扩散动力学过程的目的。