报告题目：Disease invasion risk in a growing population （在增长网络上的疾病传播风险）
报告时间：2016.11.13上午10:30-11:30
报告地点：理学院二楼会议室
报告人：马君领。加拿大维多利亚大学教授，博士生导师。研究方向为数学生态学，在种群生态、网络上流行病传播的动力学建模与演化方面做了系列富有影响的研究工作。
报告摘要：The spread of an infectious disease may depend on the population size. For simplicity, classic epidemic models assume homogeneous mixing, usually standard incidence or mass action. For standard incidence, the contact rate between any pair of individuals is inversely proportional to the population size, and so the basic reproduction number (and thus the initial exponential growth rate of the disease) is independent of the population size. For mass action, this contact rate remains constant, predicting that the basic reproduction number increases linearly with the population size, meaning that disease invasion is easiest when the population is largest. In this paper, we show that neither of these may be true on a slowly evolving contact network: the basic reproduction number of a short epidemic can reach its maximum while the population is still growing. The basic reproduction number is proportional to the spectral radius of a contact matrix, which is shown numerically to be well approximated by the average excess degree of the contact network. We base our analysis on modeling the dynamics of the average excess degree of a random contact network with constant population input, proportional deaths, and preferential attachment for contacts brought in by incoming individuals (i.e., individuals with more contacts attract more incoming contacts). In addition, we show that our result also holds for uniform attachment of incoming contacts (i.e., every individual has the same chance of attracting incoming contacts), and much more general population dynamics. Our results show that a disease spreading in a growing population may evade control if disease control planning is based on the basic reproduction number at maximum population size.