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数统学院学术沙龙活动公告

2022-05-30来源:数统学院作者:戴佳华审核人:齐玉辉编辑:袁好雨阅读:10

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专职教师

61

1600-1640

数统院办301

 腾讯会议:805-910-486

教师:胡智

个人简介:南京理工大学数学与统计学院副教授,研究方向为数学物理与代数几何。

twistor theory and hodge theory

Twistor theory was proposed by Sir. Penrose. Since thenPenrose correspondence becomes an important tool in differential geometry and algebraic geometryIn this talkwe will introduce various applications of twistor theory and recent progresses related to Hodge theory.

邱志鹏

61

1650-1730

 数统院办301

 腾讯会议:805-910-486

赵昕博士

Dynamic behavior of stochastic epidemic models with Markov switching

 Epidemic diseases, including plague, cholera, AIDS and bird flu, have always been a major problem affecting the life and survival of all human beings. By using deterministic differential equations to establish a mathematical model, epidemiology describes and studies the internal transmission laws of diseases, predicts disease trends and gives the optimal control strategy. However, there always exists noise in the environment. Whether it is the change of light intensity in a day or the change of temperature and humidity caused by the alternation of seasons, it will affect the transmission rate of diseases. Random noise is generally divided into two types: one is the sum of many independent tiny random noises, which are usually described in mathematics by white noise; the other is random noise with a small number but a large intensity, such color noise will cause the system to switch between different states and is usually described by continuous-time Markov chains. Based on deterministic epidemic models, scholars established the stochastic epidemic model driven by a mixture of white noise and color noise. They achieved many important results by using the theories of stochastic differential equation and properties of hybrid diffusion system. By mathematical modeling, stochastic analysis and other methods, the SIRS stochastic epidemic models under different noises with nonlinear transmission rate and vaccination are studied in this paper. We further study the SIS epidemic model in complex network under the influence of color noise, and give an improved numerical method. This dissertation is a preliminary study on the dynamic modeling of epidemic with Markov switching.

邱志鹏



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