Nonlinear Dynamics of Infectious Diseases Transfer with Possible Applications for Tubercular Infection

Abstract

In this paper, we model a nonlinear dynamics of infectious diseases transfer. Particularly, we study possible applications to tubercular infection in models with different profiles (peak values) of the population density dependence on spatial coordinates. Our approach is based on the well known method of instantons which has been used by the authors to describe kinetics of adiabatic chemical reactions as a function of the heat-bath temperature and other system parameters. In our approach, we use "social temperature" T as one of the controlling parameters. Increase of T leads to acceleration of the infectious diseases transfer. The "blockage" effect for the infectious diseases transfer has been demonstrated in the case when peak values (in the population density) are equal to one and under condition that the "social temperature" is low. Existence of such effect essentially depends from environment "activity" (social and prophylactic). Results of our modeling qualitatively meet the tuberculosis dynamic spread data in Penza region of Russia.