The monitoring, analysis and prediction of epidemic spread in the region require the construction of mathematical model, big data processing and visualization because the amount of population and the size of the region could be huge. One of the important steps is refinement of mathematical model, i.e. determination of initial data and coefficients of system of differential equations of epidemiologic processes using additional information. We analyze numerical method for solving inverse problem of epidemiology based on genetic algorithm and traditional optimization approach. Our algorithms are applied to analysis and prediction of epidemic situation in regions of Russian Federation, Republic of Kazakhstan and People's Republic of China. Due to a great amount of data we use a special software "Digital Earth"for visualization of epidemic.