登革热数学模型及疫情防控策略分析

Model of Dengue Fever and Disease Prevention Strategies

对于前期登革热模型d N(t)/dt=K(t)(N(t)-N(t-L))(N(t)表示t时刻的累计病例数,L为已被传染的人患病天数,K为某种社会条件下平均每天传染源数),考虑相关部门和群众等影响因素,对每日传染源率K进行函数化,从而更好地描述了K值的变化,利用差分方程建立更为贴近际的登革热模型。采用线性回归、最小二乘法等数学方法对传染源数进行讨论,进而求得模型的解并利用Matlab软件对模型结果进行数值模拟,分析传染源数及疾病防控情况,从而制定了一系列疾病防控策略,对媒介传播疾病的研究工作有一定实用价值。

For the early dengue model dN(t)/dt=K(N(t)- N(t-L))(N(t)denotes the cumulativenumber of cases at time t,L denotes the number of persons infected with the number of days,K denotes the average number of infections per day under certain social conditions),in consideration of the factors such as the relevant departments and the masses,it makes the daily infection source rate Kas a function,the change of the value of Kis better described,and difference equations are used to establish a model more close to the actual situation of dengue fever.By using mathematical methods of linear regression and least squares,its source number is discussed,then the solution of the model is obtained.And the Matlab software is used to numerically simulate the result of the model,analyze the source of infection for the disease control and prevention,so as to formulate a series of disease prevention and control strategy,the study of vector-borne diseases provide certain practical value for disease control.