Title | Mathematical model of medical insurance |
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Authors | S. I. Spivak^{1}, G. K. Khisametdinova^{1}^{1}Bashkir State University, Ufa |

Annotation | Based on the theory of Markov processes, a mathematical model of health insurance, issued the corresponding model system of the differential Kolmogorov equations and the corresponding graphical interpretation. Formulated direct and inverse problem for mathematical models of medical insurance. The result of solving the inverse problem are the intensity of transitions between different States of the process, preserving constant insurance rates. The solution to the dual problems allows to assess the sensitivity of the boundaries of the intervals to the variation of initial statistical data. Conducted actuarial analysis of mathematical model for medical insurance prevention and treatment of diabetes. The mathematical model and computer program used in the analysis of real data on the disease diabetes. The study was held over real data, to provide Medical Information and Analytical Centre under the Ministry of Health of the Republic of Bashkortostan. The conducted studies give the specialists in health insurance the actual mechanism of calculation of insurance rates. |

Keywords | Markov processes, the intensity of the transition, probability, Kolmogorov equation |

Citation | Spivak S. I., Khisametdinova G. K. ''Mathematical model of medical insurance'' [Electronic resource]. Proceedings of the XIII International scientific conference ''Differential equations and their applications in mathematical modeling''. (Saransk, July 12-16, 2017). Saransk: SVMO Publ, 2017. - pp. 41-44. Available at: http://conf.svmo.ru/files/deamm2017/papers/paper06.pdf. - Date of access: 22.10.2020. |

**© SVMO, National Research Mordovia State University, 2020**

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