| 摘要: |
| 针对印度新型冠状病毒肺炎(COVID-19)疫情的传播,建立通过设定目标函数求最优解来确定模型未知参数的 SIR 传染病动力学模型。 首先通过线性回归拟合参数范围,设定目标函数作为约束条件,结合龙格-库塔法,借助 Matlab 软件确定参数值最优解,进行 SIR 模型拟合和预测,发现印度疫情拐点将出现在 2021 年 5 月 8 日左右,结合预测数据推导未来每日新增及累计新增病例数,虽未来 100 d 内将持续出现新增病例,但疫情现期已经有消退趋势;其次考虑印度变种病毒 B. 1. 617 以及当下疫苗接种情况的影响,建立加入疫苗影响因素的 SIR 预测模型,通过进行疫苗接种灵敏度分析模拟出印度疫苗接种率大约需要达到
75%,考虑有效保护率则接种率需要高达 95%,才可以建立起群体免疫屏障;最后通过基本传染数验证了疫苗接种率,并对新冠波及影响做出了相应对策分析。 |
| 关键词: COVID-19 SIR 传染病动力模型 预测 群体免疫屏障 |
| DOI： |
| 分类号: |
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| Influence Analysis of COVID-19 in India Based on SIR Infectious Disease Model |
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DING Huang-yan, TIE Xi-yue
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School of Mathematics and Statistics, Chongqing Technology and
Business University, Chongqing 400067, China
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| Abstract: |
| In response to the spread of the novel coronavirus pneumonia (COVID-19) in India, this paper
proposes to establish a SIR infectious disease dynamic model that determines the unknown parameters of the model
by setting the objective function and seeking the optimal solution. First, the parameter range is fitted by linear
regression, the objective function is set as the constraint condition, and the Runge-Kutta method is combined with
the Matlab software to determine the optimal solution of the parameter value, and the SIR model is fitted and
predicted. It is found that the inflection point of the epidemic in India will appear around May 8, 2021, and the
number of new daily and cumulative new cases in the future is derived based on the forecast data. Although new
cases will continue to appear in the next 100 days, the current epidemic situation has already subsided. Secondly,
considering the influence of the Indian variant virus B. 1. 617 and the current vaccination situation, a SIR
prediction model with vaccine influencing factors was established. Based on the vaccination sensitivity analysis, it
is simulated that the vaccination rate in India needs to reach about 75%, and considering the effective protection
rate, the vaccination rate needs to be as high as 95%, so that the herd immunity barrier can be established.
Finally, the vaccination rate was verified by the basic infection number, and the corresponding countermeasures
were analyzed for the impact of COVID-19. |
| Key words: COVID-19 SIR infectious disease dynamic model prediction herd immune barrier |
