异质群组中疾病传播的若干动力学问题研究

Heterogenous epidemic models reflecting the variance of disease transmission among different groups as well as their cross-infection, they are of great significance for one to understand the transmission mechanism and control of many emerging infectious diseases. However, heterogeneity among groups also brings challenges in the analytic studies of disease transmission and control. This project focuses on the investigations on some dynamical topics of heterogeneous epidemic models in different time scales as well as variant environments, revealing the spreading dynamics of infectious diseases as well as the corresponding control strategies, it has the following contents: (1)For long-term time scale systems, considering the effects of heterogeneity of the infectious disease on disease transmission dynamics and control strategy, and applying these theoretical to the analysis of measles, influenza, AIDS and other infectious diseases; (2)Modeling and analyzing the short-scale heterogeneous epidemic models and study the dynamics, explore the optimal control problem under limited resources and applying these results to the prevention and control of new and emerging infectious disease; (3)Modeling and analyzing the transmission dynamics of infectious disease model under the stochastic environments, and investigating the complicated effects of stochastic environments to the dynamics of disease and its control.

异质性传染病模型体现了疾病在不同人群群组中传播风险的差异性及群组间的交叉感染现象，对于认识我国突发、新发传染病的传播机制及防治策略有着重要的意义；同时，群组间的异质性也给疾病传播与控制的研究带来了动力学方面的挑战。本项目研究异质性传染病模型在不同传播时间尺度、诸类环境下的若干疾病传播动力学问题，揭示这些情形下的传染病传播规律与防控策略，包含如下研究内容：(1)针对长时间尺度的异质性传染病模型，研究群组的异质性对疾病传播动力学及控制策略的影响，并应用于麻疹、流感、性病等传染病的分析；(2)建立并研究短时间尺度传播的异质性传染病模型动力行为，探索防治资源有限前提下的疾病最优控制策略，并应用于突发、新发传染病的防控分析；(3)建立并研究环境随机干扰下的异质性传染病模型的传播动力学，分析环境随机干扰对疾病传播动力学行为与控制的影响。

群组间的异质性给疾病传播与控制的研究带来了很多动力学方面的挑战，这是本项目研究的出发点。项目主要研究了异质性传染病模型在不同传播时间尺度、诸类环境下的若干疾病传播动力学问题，揭示这些情形下的传染病传播规律与防控策略，包含如下研究内容：(1)针对长时间尺度的异质性传染病模型，研究群组的异质性对疾病传播动力学及控制策略的影响，并应用于麻疹、流感、性病等传染病的分析；(2)建立并研究短时间尺度传播的异质性传染病模型动力行为，探索防治资源有限前提下的疾病最优控制策略，并应用于突发、新发传染病的防控分析；(3)建立并研究环境随机干扰下的异质性传染病模型的传播动力学，分析环境随机干扰对疾病传播动力学行为与控制的影响。