| 基于Kolmogorov前向方程评估甲型H1N1流感疫情的动态变化北大核心CSCD |
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| 引用本文： | 闫琴玲,唐三一. 基于Kolmogorov前向方程评估甲型H1N1流感疫情的动态变化北大核心CSCD[J]. 应用数学和力学, 2022, 43(4): 435-444. DOI: 10.21656/1000-0887.420243 |
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| 作者姓名： | 闫琴玲 唐三一 |
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| 作者单位： | 1.长安大学 理学院，西安 710064 |
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| 基金项目： | 国家自然科学基金(12001058;12031010)；;陕西省自然科学青年基金(2021JQ-215)；;中央高校基本科研业务费(300102121103)； |
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| 摘 要： | 基于个体水平的传染病模型可以揭示随机性在传染病疫情防控中的重要作用.研究此类模型的普遍方法是通过事件驱动的、大量重复的随机模拟来确定预测变量的范围.而基于Kolmogorov前向方程(KFE)研究个体水平的传染病模型,不仅不需要大量的重复模拟来确定预测变量的范围,而且可以同时考虑每种状态发生的概率.因此,基于2009年西安市第八医院甲型H1N1流感数据,建立了基于社交网络的个体决策心理模型,以确定行为改变率;进一步地,为得到传染病传播过程中各状态的概率分布,基于改进的个体SIR模型,通过Markov过程推导出KFE.结果表明:通过数值求解KFE可以得到整个爆发过程中每种状态发生的概率分布、最严重的时间段及相应的概率,从而能更快、更准确地了解甲型H1N1疫情的传播过程,因此有助于高效地进行甲型H1N1疫情防控.
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| 关 键 词： | 甲型H1N1 Markov过程 Kolmogorov前向方程(KFE) 隐式Euler(IE)法 最终规模 |
| 收稿时间： | 2021-08-13 |
Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation |
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| Yan Q.,Tang S.. Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation[J]. Applied Mathematics and Mechanics, 2022, 43(4): 435-444. DOI: 10.21656/1000-0887.420243 |
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| Authors: | Yan Q. Tang S. |
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| Affiliation: | 1.School of Sciences, Chang’an University, Xi’an 710064, P.R.China2.School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, P.R.China |
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| Abstract: | The individual-based infectious disease models show the important role of stochasticity in infectious disease prevention and control. To study these models and then determine the ranges of predictive variables, an increasingly common approach needs event-driven massive repetitive stochastic simulations. The study of the individual-based infectious disease models based on the Kolmogorov forward equation (KFE), not only could overcome the difficulty of repeated simulations, but could consider the probability of each state simultaneously. Therefore, according to the data of 2009 influenza A/H1N1 in the Xi’an 8th Hospital, to determine the rate of behavior change, an individual decision-making psychological model was established based on social network. Further, in order to obtain the probability distribution of each state in the process of infectious disease transmission, based on the modified individual SIR model, the KFE was derived through the Markov processes. The results show that, the numerical solution of the KFE gives the probability distribution of each state, the most serious period and the corresponding probability in the outbreak process of epidemic infectious diseases, so as to help understand the transmission process of A/H1N1 epidemic more quickly and accurately, which is valuable for the efficient prevention and control of A/H1N1 epidemic. |
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| Keywords: | A/H1N1 Final size Implicit Euler (IE) method Kolmogorov forward equation (KFE) Markov process |
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