Ilnytskyi H. Mathematical modelling of the epidemiologic, clinical and laboratory aspects of tuberculosis

The work covers both the aspects related to general methodology and these of practical applications. The former is ensured by the analysis of three types of epidemiology models, two of them, SIS and SEIS, are relatively general, whereas the third, SICS, is developed in this work to take into account typical features for the TB spread. For each model, the analysis is performed both for its compartmental realization, using the differential equations, and when defined on a graph in a form of a square lattice, with the local disease spread dynamics given by the cellular automaton algorithm. All models, and their analysis, may be used for the description of other diseases with similar characteristics. Practical application aspect is ensured by development of the TB diagnostics algorithm, based on a wide set of known primary and secondary indications. It is tested on a set of patients and is used in clinical practice in Lviv Lung Health Centre.