报告题目【An epidemic model with age of vaccination and fluctuated transmission rate】
时间：2019年5月24日（星期五）8:30
地点：旗山校区理工北楼601报告厅
主讲：福州大学教授,魏凤英
主办：数学与信息学院、福建省分析数学及应用重点实验室、数学研究中心
参加对象：感兴趣的学生和老师
专家简介：魏凤英，福州大学数学与计算机科学学院教授，2006年7月博士毕业于东北师范大学应用数学专业。2007年获福州大学学术新人奖，2008年参加副校长范更华教授主持的离散数学及其应用“211工程”重点学科团队。曾主持国家自然科学基金两项、福建省自然科学基金三项；曾参与国家自然科学基金三项、教育部基金一项、福建省自然科学基金一项。目前累计发表及录用学术论文100余篇，其中SCI收录30余篇，国内一类及核心期刊收录60余篇。参加国内外学术会议及学术交流访问共计20余次，指导研究生共计26名，其中已毕业22名，4名在读。2014年破格评为教授，2015-2016年任芬兰赫尔辛基大学访问教授。现任福州大学数学系副主任，福建省生物数学学会第二届理事，主要研究随机微分方程及其在生物数学中的应用，包括流行病模型及阶段结构生态模型等。
报告摘要：In this talk, we formulate an epidemic model with age of vaccination and generalized nonlinear incidence rate, where the total population size consists of the susceptible, the vaccinated, the infected and the removed. Then a stochastic SVIR model is derived when we introduced fluctuation into transmission rate. According to Lyapunov methods and generalized Ito's formula, we firstly show that stochastic epidemic model admits a unique global positive solution with any positive initial values. Then, the threshold which determines the diseases spread or not is derived. Precisely, if intensity of white noise is small enough and threshold is less than one, then diseases eventually become extinct with negative exponential rate. And, if threshold is greater than one, then diseases are weakly permanent. Moreover, the persistence in the mean for infected individuals is obtained when another indicator is greater than one. As a consequence, several illustrative examples are separately carried out with numerical simulations to support main results of this article.