A combined numerical algorithm for reconstructing the mathematical model for tuberculosis transmission with control programs

作者：Kabanikhin Sergey; Krivorotko Olga; Kashtanova Victoriya^*

来源：Journal of Inverse and Ill-Posed Problems, 2018, 26(1): 121-131.

DOI：10.1515/jiip-2017-0019

• Model of tuberculosis transmission
• reconstruction of model parameters
• system of ordinary differential equations
• parameter identification
• numerical method
• simulated annealing method
• gradient descent method

A new combined numerical algorithm for solving inverse problems of epidemiology is described in this paper. The combined algorithm consists of optimization and iterative methods, and determines the parameters specific to a particular population by using the statistical information for a few previous years. The coefficients of the epidemiology model describe particular qualities of the population and the development of the disease. The inverse problem of parameter identification in a mathematical model is reduced to the problem of minimizing an objective function characterizing the square deviation of the statistical data from the experimental data. The combination of statistical and optimization algorithms demonstrates the identification of parameters with an appropriate relative accuracy of 30%. The results can be used by public health organizations to predict the infectious disease epidemic in a given region by comparing the data of simulation with historical data.

• 出版日期2018-2