Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation

YAN Qinling; TANG Sanyi

doi:10.21656/1000-0887.420243

Volume 43 Issue 4

Apr. 2022

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YAN Qinling, TANG Sanyi. 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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Dynamic Changes of Influenza A/H1N1 Epidemic Evaluated Based on the Kolmogorov Forward Equation

doi: 10.21656/1000-0887.420243

YAN Qinling^1
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TANG Sanyi^{2
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1.
School of Sciences, Chang’an University, Xi’an 710064, P.R.China
2.
School of Mathematics and Statistics, Shaanxi Normal University, Xi’an 710119, P.R.China

Received Date: 2021-08-13
Accepted Date: 2021-09-13
Rev Recd Date: 2021-09-13

Available Online: 2022-03-25

Publish Date: 2022-04-01

Abstract

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.
- A/H1N1,
- Markov process,
- Kolmogorov forward equation (KFE),
- implicit Euler (IE) method,
- final size

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References(31)

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