¹G.I. Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences (INM RAS)
²Moscow Scientific and Clinical Center for TB Control
³M.V. Lomonosov Moscow State University

Abstract.In construction of mathematical models of propagation and control of pulmonary tuberculosis, presence or absence of bacterioexcretion is often used as the marker of disease severity. There are two major schemes of modeling for natural corse of tuberculosis. The first  one is so called  parallel scheme, the more frequently used, which assumes that a fraction of incident cases develops bacterioexcretion rapidly and retains it till the end of the disease. The second one is  serial scheme, the less often used one, which assumes that tuberculosis always starts without bactrioexcretion, and then a fraction of cases progresses to the bacterioexcretion stage. In this article, we compare these two modeling schemes on the basis of their fit to the real data from Moscow city, 2013-2018, which contain information on time and results of the last fluorography examination of the detected tuberculosis cases and their health condition at the moment of detection. Such data limit the possible duration of the disease, and, thus, permit an estimation of the dynamics of progression to bacterioexcretion for untreated tuberculosis. We have developed an agent-based model with realistic profiles of mortality and undergoing fluorography examinations and with an analog of the traditional compartmental model of natural history of tuberculosis on the basis of ordinary differential equations. On the basis of computational experiments with the model, the serial modelling scheme turned out to be closer to reality. On the other hand, due to the bad fit to the real data, we concluded that both the detection submodel and the submodel of natural course of pulmonary tuberculosis should be redesigned.

Key words: mathematical model, tuberculosis, pathogenesis scheme, bacterioexcretion, real data, fluorography, agent-based modeling.