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讲座题目:Disease Dynamics on Growing Contact Networks

讲座时间:20171120日(星期一)

讲座地点:9号楼924学术报告厅

主讲人:原三领教授

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.\

主讲人简介:原三领,博士,上海理工大学教授,博士生导师,应用数学硕士点学科带头人,中国数学会生物数学学会常务理事,美国《Mathematical Reviews》评论员。研究方向为:微分方程与动力系统、生物数学。曾先后主持和参与完成了多项国家和省部级项目的研究工作;目前正在主持一项国家自然科学基金(面上项目)和一项上海市教委科研创新重点项目的研究工作。研究内容涉及常微分方程(泛函微分方程、随机微分方程)定性与稳定性理论、分支理论、动力系统、种群动力学、流行病动力学、海洋生态学以及生物化学工程等诸多领域,具有多学科交叉的特点。曾多次到国内和国际多所高校进行访问进修和做访问学者,已在国内外重要学术刊物上发表论文70余篇,其中SCI收录40余篇。


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