甲型流感与艾滋病协同感染的数学模型的动力学研究

项目名称： 甲型流感与艾滋病协同感染的数学模型的动力学研究

项目编号： No.11201002

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 闫萍

作者单位： 安徽农业大学

项目金额： 22万元

中文摘要： 人们通过大量研究发现，肺结核与艾滋病之间存在协同感染，这一发现在艾滋病的防控中发挥了重要作用. 当今甲型流感与艾滋病不断流行蔓延，我们发现艾滋病死亡人数会定期受到甲型流感的影响，但甲型流感与艾滋病的协同感染问题却尚未引起学者们的关注. 由于艾滋病具有年龄相关性、甲型流感具有突发性和周期性，现有模型不再适用于研究二者的协同感染.为了揭示甲型流感与艾滋病之间尚不为人知的相互影响，项目首先建立具脉冲与年龄结构的偏微分模型；然后通过建立双边脉冲偏微分不等式，对模型周期解的动力学性态进行分析；最后结合模型的数值模拟，预测在甲型流感影响下艾滋病病人的发病与死亡趋势，讨论艾滋病对甲型流感发病时间的影响。 项目利用双边脉冲偏微分不等式处理脉冲项的尝试，为消去脉冲偏微分方程中的脉冲影响提供了新思路；而探讨甲型流感与艾滋病的相互影响，为甲型流感及艾滋病等传染病的防控提供了新策略.

中文关键词： 传染病模型；偏微分方程；稳定性；数据分析；

英文摘要： The co-infection between TB(Tuberculosis) and AIDS (Acquired Immune Deficiency Syndrome) is known through the studies of many researchers, which plays an important role in the prevention and control of AIDS. We have discovered a new phenomenon that the death number of AIDS is affected periodically by Influenza A during the prevalence of Influenza A and AIDS. But the co-infection between Influenza A and AIDS has not been noticed by researchers so far. The existing models are not suitable to study the co-infection between Influenza A and AIDS any more because of the high age-dependence of AIDS and the sudden outbreak and periodicity of Influenza A. In order to show the correlation between Influenza A and AIDS that has not been noticed before, this project establishes a partial differential equation model with impulse and age structure firstly. Secondly, the analyses on dynamics of periodic solution to our model are discussed by giving a two-side impulsive partial differential inequality in this project. Finally, according to the numerical simulation of the established model, the outbreak trend and the mortality trend under the influence of influenza A will be predicted, and the influence on the disease time of influenza A from AIDS will be discussed. This project provides a new idea to eliminate the impulsive ter

英文关键词： epidemic model；partial differential equation；stability；data analysis；