甲型H1N1流感的微分流行病模型与分析

The Modeling and Analysis of H1N1 Influenza

从经典的SIR模型入手,在考虑隔离、治愈后的免疫能力、迁移及防控因子等因素后,建立了适合于甲型H1N1流感的微分方程模型,对其平衡态进行了稳定性分析.另外,考虑到"贫"数据信息的特点,在简化模型后,结合国内H1N1流感数据进行模型的求解和预测,结果表明拟合效果非常好.可以看到,起初确诊人数急剧上升,在11月左右达到最大值,随后有减缓趋势,大约在80天后灭亡.

Based on the statistics of H1N1 flu in China, a suitable differential equation of H1N1 model is established, which extended from the classical SIR model. The mortality rate of infection, the immunity rate after cure, prevention and control factors are all integrated in the model. Then we have conducted a stability analysis of the model. In addition, by simplifying the model the values of parameters are estimated and the equation is solved. The error map of residues is also given. We can see that the number of initial diagnosed patients has risen sharply, which reached the maximum in November and followed by a slow trend. The influenza is eliminated about 80 days later. Finally, we compared the predicted data with the new reported data, showing that the fitting result is very good.