Study of a singularly perturbed tuberculosis model

Abstract

A detailed analysis of the dynamic model of the tuberculosis epidemic was conducted. It is shown that the dynamic model contains several time scales and can be represented in a singularly perturbed form. With help of the integral manifolds theory and the reduction principle, the reduction of the modeling system was justified and carried out. This approach allow us to replace the original system by another system of a lower order on an integral manifold whose dimension is equal to that of the slow subsystem and which, at the same time, preserves the essential properties of the original system. The conditions for the stabilization of the epidemiology based on the selection of necessary treatment and preventive measures are determined.