﻿ 北京市甲型H1N1流感建模与仿真研究 Modeling and Simulation of Influenza A (H1N1) in Beijing

Vol.04 No.03(2015), Article ID:15941,7 pages
10.12677/AAM.2015.43036

Modeling and Simulation of Influenza A (H1N1) in Beijing

Xin Wen, Yakui Xue*, Zhiqiang Xia

Department of Mathematics, North University of China, Taiyuan Shanxi

Email: *wenxindd@aliyun.com

Received: Aug. 3rd, 2015; accepted: Aug. 19th, 2015; published: Aug. 24th, 2015

ABSTRACT

According to the mechanism and characteristics of influenza A (HIN1), this essay constructed a mathematical model. Then, the article got a threshold R0 indicating whether the disease had been controlled or not. At the same time, this essay used the prevention data of Beijing in 2009 when the epidemic broke out simulating the model. The parameters of the model, which got sensitivity analysis, are clear, and data source is reliable. The model reflects the process of the epidemic spread, and intuitively describes the development of influenza A (HIN1). Thus, this article is useful in providing decisions for the prevention and control of the epidemic.

Keywords:Influenza A (HIN1), The Basic Reproductive Rate, Simulation

Email: *wenxindd@aliyun.com

1. 引言

2. 甲型H1N1流感模型

(1)

Figure 1. The number of influenza A (H1N1) in Beijing from 30 June to 11 June 2009

3. 数值拟合

Table 1. Statistics of the influenza A (H1N1) in Beijing in 2009

Table 2. The parameter estimation of model (1)

(a) 实际数据和模拟趋势箱图 (b) 实际数据和模拟趋势图

Figure 2. Star represents the actual cases of the influenza A (H1N1) in Beijing, and blue box figure represents the dispersion of statistical for predict data, and green line represents the model and results

Figure 3. Do not take control measures, under this condition, the change of E, H, I and R

Figure 4. When R0 < 1, the disease-free equilibrium is locally asymptotically stable

Figure 5. When R0 > 1, the positive equilibrium point is locally asymptotically stable

4. 参数敏感性分析

(a) 疾病爆发阈值R0随β1变化图 (b) 疾病爆发阈值R0随β2变化图(c) 疾病爆发阈值R0随β3变化图

Figure 6. Disease outbreak threshold R0 with the change of β1, β2, β3

Figure 7. Disease outbreak threshold R0 with the change of β2, β3

5. 总结

Modeling and Simulation of Influenza A (H1N1) in Beijing[J]. 应用数学进展, 2015, 04(03): 292-298. http://dx.doi.org/10.12677/AAM.2015.43036

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