MATHEMATICAL MODELING OF THE SPREAD OF EPIDEMICS ACROSS THE TERRITORY

Abstract

The process of epidemic spread across a territory is considered. Among the many mathematical models of epidemiology, compartmental models are most commonly used. They identify groups of people in a given epidemiological state, describe the transitions of people from one group to another over time, and represent systems of ordinary differential equations. Studies devoted to the mathematical modeling of epidemic spread across a territory typically employ the concept of reaction-diffusion systems, which involves adding appropriate diffusion terms to the standard equations of compartmental models. This paper demonstrates that such an approach is ineffective in the situation under consideration. As an alternative, an equation for the change in the infection rate of the territory is derived based on known information about the course of the epidemic. This equation is a first-order partial differential equation with variable coefficients, belonging to the class of transport equations. The resulting equation, with appropriate boundary conditions and a particular method for choosing the law of change in the area of infection, can be used as a mathematical model of the system under consideration to predict the spread of the epidemic across a territory.