极大似然在随机区域型传染病中的应用研究
|
摘要
探讨区域型传染病在人群中的传播规律,可为传染病的预防和控制提供理论依据.采用SIR模型模拟传染病中的三类人群的转化过程.由于区域型传染病具有随机传播的特点,每个时间区间内新增的感染者人数和移除者人数都是服从二项分布的随机变量,从而分别构造关于感染率β和移除率γ的似然函数.由于待估计参数并无显式解,用等价无穷小得到近似似然函数,进而得到感染率和移除率的似然函数估计值.进一步以校园急性出血性结膜炎传染扩散为例,估计出感染率β为0.6493和移除率γ为0.125.最后用以上估计值作为随机传播的参数去模拟而得到整个疫情周期内每个时间区间内三类人群的人数.
To explore the propagation pattern of regional infectious diseases in the population can provide a theoretical basis for the prevention and control of infectious diseases. This paper uses the SIR model to simulate the transformation process of three types of infectious diseases. Because of the random propagation of regional infectious diseases, the number of newly infected and removed persons in each time interval is a random variable that obeys the binomial distribution, thus constructing a likelihood function for the infection rate β and the removal rate y. Since there is no explicit solution for the parameter to be estimated, the approximate likelihood function is obtained using the equivalent infinitesimal small, and then the likelihood function estimates of infection rate and removal rate are obtained. Taking the infection spread of acute hemorrhagic conjunctivitis on campus as an example, the infection rate β is estimated to be 0.6493 and the removal rate γ is 0.125. Finally, the above estimates are used as parameters for random propagation to simulate the number of three types of population in each time interval within the entire epidemic cycle.
To explore the propagation pattern of regional infectious diseases in the population can provide a theoretical basis for the prevention and control of infectious diseases. This paper uses the SIR model to simulate the transformation process of three types of infectious diseases. Because of the random propagation of regional infectious diseases, the number of newly infected and removed persons in each time interval is a random variable that obeys the binomial distribution, thus constructing a likelihood function for the infection rate β and the removal rate y. Since there is no explicit solution for the parameter to be estimated, the approximate likelihood function is obtained using the equivalent infinitesimal small, and then the likelihood function estimates of infection rate and removal rate are obtained. Taking the infection spread of acute hemorrhagic conjunctivitis on campus as an example, the infection rate β is estimated to be 0.6493 and the removal rate γ is 0.125. Finally, the above estimates are used as parameters for random propagation to simulate the number of three types of population in each time interval within the entire epidemic cycle.
引文
[1] Alonso D, Mckane A J, Pascual M. Stochastic amplification in epidemics[J]. Journal of the Royal Society Interface, 2007, 4(14):575.
[2]陈田木,刘如春,王琦琦,等.SIR模型在一起校园急性出血性结膜炎暴发疫情处理中的应用[J].中华流行病学杂志,2011,32(8):830-833.
[3]朱仲邃.基于非线性回归模型参数估计[J].内蒙古科技与经济,2014(2):99-99.
[4]李琼,叶鹰,魏晟,等.一类SIR流行病模型及参数的贝叶斯估计[J].湖北民族学院学报(自科版),2005,23(4):326-329.
[5] Fierro R, Leiva V, Balakrishnan N. Statistical inference on a stochastic epidemic model[J]. Communications in Statistics-Simulation and Computation, 2015, 44(9):2297-2314.
[2]陈田木,刘如春,王琦琦,等.SIR模型在一起校园急性出血性结膜炎暴发疫情处理中的应用[J].中华流行病学杂志,2011,32(8):830-833.
[3]朱仲邃.基于非线性回归模型参数估计[J].内蒙古科技与经济,2014(2):99-99.
[4]李琼,叶鹰,魏晟,等.一类SIR流行病模型及参数的贝叶斯估计[J].湖北民族学院学报(自科版),2005,23(4):326-329.
[5] Fierro R, Leiva V, Balakrishnan N. Statistical inference on a stochastic epidemic model[J]. Communications in Statistics-Simulation and Computation, 2015, 44(9):2297-2314.