基于数值积分的传染病SIRS模型参数估计  

Parameter estimation of the SIRS infectious disease model based on numerical integration

作　　者：宋丹丹[1] 王晶囡[1] 杨光旭[1] 李佳思[1] 杨嘉欣[1] 

机构地区：[1]哈尔滨理工大学应用科学学院,黑龙江哈尔滨150080

出　　处：《高师理科学刊》2016年第5期10-14,共5页Journal of Science of Teachers＇College and University

基　　金：哈尔滨理工大学大学生创新项目(201512);哈尔滨理工大学教学改革项目(320150023)

摘　　要：针对具有免疫的传染病SIRS模型,利用三次Hermite插值函数及数值积分公式,基于患病的各个种群人数估计值的误差最小原则,将参数估计问题转化为非约束优化问题.将数据带入后可得关于模型参数的多项式,为求得该式最小值,将其分别对各个参数进行微分,得到关于模型参数的非线性方程组.使用最速下降法获得较为合理与精确的初值,在该初值的基础上利用牛顿法对非线性方程组进行求解,得到了该模型的高精度参数估计值.并对计算结果进行数值仿真,数值仿真实验表明,所给出的参数估计方法能够较为精确地估计出相应参数值.The third-order Hermite interpolation function and numerical integral formula are applied to an SIRS infectious disease model.Based on the principle of minimum error, the parameter estimation problem in the model is transformed to the unconstrained optimization problem and a polynomial can be obtained after the data is substituted into the formula.In order to get the minimum value of the polynomial, the partial derivatives of the polynomial with respect to each parameter are obtained after which a system of nonlinear equations related to the model is obtained. The steepest descent method is used to get a set of accurate and reasonable initial values,based on which Newton method is used to solve the nonlinear equations and then the specific parameter values are obtained.Finally,the equilibriums of SIRS model and the effectiveness of general parameter estimation are validated by numerical simulations.

关 键 词：SIRS模型 数值积分 牛顿法 数值仿真 参数估计 

分 类 号：O29[理学—应用数学]