Epidemiological analysis of morbidity natural-focal infections showed, that at Tula state territory registers high level of morbidity leptospirosis, hemolytic fever with renal syndrome, that exceeds morbidity at Central Federal State and average Russian indexes. For prediction of morbidity used analysis of time series, regression analysis, method group analysis arguments, algebraic model constructive logic. By using method artificial neural networks made mathematical model of prediction morbidity hemolytic fever with renal syndrome (hemolytic fever with renal syndrome), leptospirosis, tick-borne infectious borelliosis. Found that number of main infection carriers and climatic factors effect on morbidity level. By modeling of prediction morbidity prediction morbidity found that main role playing number of bank vole (Myodes glareolus) and average temperatures at April and July.