Dinamika nekih stohastičkih modela širenja bolesti

Abstract

The topic of this doctoral dissertation is the application of stochastic differential equations in epidemiology in the modeling of the spread of some diseases (addiction, infectious and hematological diseases). Based on the existing deterministic models, by using appropriate stochastic perturbation, the system of stochastic differential equations is obtained. The dynamics of such stochastic models are studied throughout this dissertation. In that sense, bearing in mind the nature of the problem under consideration, for each of the obtained models the existence and uniqueness of a global positive solution is shown. The central part of the paper deals with the dynamical properties of the considered models: extinction or persistence of the disease in the population. To illustrate the obtained theoretical results, numerical illustrations with real life data are carried out. The obtained simulations show that the theoretical results coincide with real data.