Stochastic SIRS+V model of infections spread

Background and Objectives: The aim of the paper is to construct a model of the spread of infection in the form of a system of stochastic differential equations that takes into account fluctuations in the parameters characterizing the processes of infection, restoration and loss of immunity. Methods: Numerical simulation of oscillations of a system of stochastic differential equations with Langevin sources. Results: A stochastic SIRS+V model of epidemic spread has been constructed in the form of a system of three differential equations with multiplicative sources of quasi-Gaussian noise. The model does not take into account the effect of the disease on the population size, while the population density is considered as a parameter affecting the course of the epidemic. The model demonstrates the long-term oscillatory dynamics observed in many viral diseases. Conclusion: Studies have shown that to model the course of infectious diseases, it is not enough to know the average values of the rates of infection, recovery and loss of immunity, but it is also necessary to know the intensity of fluctuations of these values. The different levels of such fluctuations lead to qualitatively different observed dynamics of the epidemic. The root-mean-square values of parameter fluctuations can be estimated during the analysis of empirical data obtained from observations of the spread of specific diseases, and then used in modeling. For example, when statistically analyzing a disease in the course of medical practice, it is not difficult to obtain a distribution of recovery times and loss of immunity. These observations will also make it possible to clarify the type of distribution functions for the Langevin sources used, which in practice may differ from Gaussian ones.