报告题目：The effect of cumulatively released environmental pathogens on spread dynamics of epidemic models

报告人：张龙教授

时间：2026年9月4日（周五）10：30-11：30

地点：文理楼290报告厅

报告摘要：In this talk, two kinds epidemic models are proposed, wherein the pathogens derive from environmental breeding and accumulative excretion by the infected individuals or corpses. The former is characterized by Logistic growth, while the latter is in the form of infinite integral. First, the positivity and ultimate boundedness of solutions are obtained. Second, the basic reproduction number R₀ is obtained, by which the model is analyzed if either the intrinsic growth rate of environmental pathogens is lower or higher than its clearance rate. For the first case, the disease-free equilibrium is globally asymptotically stable when R₀ < 1, while the endemic equilibrium is globally asymptotically stable when R₀ > 1. Conversely, if the growth rate exceeds the removal rate, the disease-free equilibrium is always unstable, meanwhile, the uniform persistence of the model indicates that there could exist one or multi-endemic equilibria, and it is globally asymptotically stable if the endemic equilibrium is unique. Finally, the theoretical results are illustrated by numerical simulations. We find that the accumulative release of pathogens by the infected individuals in the form of infinite integral is more realistic and consistent with the disease spread than that of linear form by real data.

专家简介：张龙，新疆大学教授，博士生导师。1997-2007年间在新疆大学分别取得理学学士、硕士、博士学位，导师滕志东教授。2010年国家留学基金委公派赴美国迈阿密大学博士后，合作导师阮士贵教授。中国数学会生物数学专业员会委员。主要从事微分方程理论及其应用、生物数学模型研究。主持国家自然科学基金项目5项；新疆维吾尔自治区杰出青年基金、应用数学重点实验室开放课题等10余项。获新疆维吾尔自治区自然科学奖一等奖1项；科技进步奖二等奖1项；自然科学优秀论文奖一等奖1次，二等奖2次。获国务院政府特殊津贴，新疆维吾尔自治区天山英才科技创新领军人才等称号。在J. Math. Biol., Math. Biosci., J. Theoret. Biol., Stud. Appl. Math., Appl. Math. Model., Int. J. Bifur. Chaos.等国内外核心期刊发表论文多篇。