Comparison Of Modeling Schemes for Natural Course Of Pulmonary Tuberculosis

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.

Mathematical modelling of the progression of active tuberculosis: Insights from fluorography data

“…It is possible to construct an agent-based model in calendar time, as we did in our previous work ( Avilov et al., 2019 ), but it proved to be not effective. The new approach is to simplify the assumptions so that an analytical model is feasible.…”

“…Not so many published TB epidemiological models explicitly include case-detection processes. In this work, we followed a simple per capita rate-based detection model that we had used in our previous works ( Avilov et al., 2015 , 2019 ). This model assumes that all individuals in the population have equal access to health care, which appears to be a reasonable first approximation for the resident population of a big city like Moscow.…”

“…Just like in ( Avilov et al., 2019 ), passive case-detection was modelled by time-independent per capita rates which were different for T - and T + cases. This corresponds to the plausible assumption that the longer the patient is ill, the higher is their cumulative chance to seek medical care because of the symptoms.…”