A METHOD FOR PREDICTING THE SPREAD OF EPIDEMIOLOGICAL THREATS BASED ON THE TELEGRAPH EQUATION

Mathematical modeling of epidemic dynamics plays a crucial role in understanding, predicting, and controlling the spread of infectious diseases.Traditional approaches are often based on diffusion-type equations, which assume instantaneous propagation of changes in infection density.However, such models may oversimplify real transmission processes, as the spread of infection among the population usually occurs at a finite rate and exhibits wave-like behavior.To overcome these limitations, this article presents a method for predicting epidemiological threats based on the telegraph equation.The telegraph equation, being a second-order hyperbolic differential equation, allows the terminal velocity of propagation and inertial effects to be included in the model.This makes it possible to reflect both diffusion and wave-like modes of epidemic propagation, depending on the balance between diffusion and transport mechanisms.The proposed model describes the spatial-temporal distribution of infection cases and provides insight into the dynamics of epidemic fronts.Analytical methods make it possible to obtain solutions and analyze them under complex initial and boundary conditions.The results confirm that the approach based on the telegraph equation provides a more realistic description of the spread of the epidemic wave compared to classical diffusion models.Moreover, this method allows identifying critical thresholds, predicting infection peaks, and estimating the time required for the epidemic to spread in specific regions.The proposed approach can be applied both in theoretical research and as a practical forecasting tool for healthcare systems.It provides a flexible and physically consistent mathematical framework for predicting the spread of epidemiological Vda a perspektivy 9(52) 2025