Bi-logistic model for disease dynamics caused by Mycobacterium tuberculosis in Russia

Anastasia I Lavrova; Eugene B Postnikov; Olga A Manicheva; Boris I Vishnevsky

doi:10.1098/rsos.171033

Bi-logistic model for disease dynamics caused by Mycobacterium tuberculosis in Russia

R Soc Open Sci. 2017 Sep 13;4(9):171033. doi: 10.1098/rsos.171033. eCollection 2017 Sep.

Authors

Anastasia I Lavrova^{1

2}, Eugene B Postnikov³, Olga A Manicheva², Boris I Vishnevsky²

Affiliations

¹ Saint-Petersburg State University, Medical Faculty, Universitetskaya emb., 7/9, Saint-Petersburg, Russia.
² Saint-Petersburg State Research Institute of Phthisiopulmonology, Lygovsky avenue 2-4, Saint-Petersburg, Russia.
³ Department of Theoretical Physics, Kursk State University, Radishcheva street 33, Kursk, Russia.

Abstract

In this work, we explore epidemiological dynamics by the example of tuberculosis in Russian Federation. It has been shown that the epidemiological dynamics correlates linearly with the virulence of Mycobacterium tuberculosis during the period 1987-2012. To construct an appropriate model, we have analysed (using LogLet decomposition method) epidemiological World Health Organization (WHO) data (period 1980-2014) and obtained, as result of their integration, a curve approximated by a bi-logistic function. This fact allows a subdivision of the whole population into parts, each of them satisfies the Verhulst-like models with different constant virulences introduced into each subsystem separately. Such a subdivision could be interconnected with the heterogeneous structure of mycobacterial population that has a high ability of adaptation to the host and strong mutability.

Keywords: Mycobacterium tuberculosis; compartmental model; mixed subpopulations; virulence.