Analysis of the dynamics of the viral infection spread model

Abstract

This paper analyzes the dynamics of a mathematical model based on a proposed three-dimensional quadratic
stochastic operator developed to simulate the spread of viral infections. The model employs Lotka–Volterratype
operators defined on a simplex, and the behavior of the resulting dynamical systems under various
signatures is thoroughly investigated. The model variables represent the proportions of population groups—
susceptible, infected, recovered, and hidden carriers—while the coefficients denote the interaction
parameters among these groups. Within the study, the Jacobian matrix is constructed to identify stationary
points and classify their stability properties as attractors, repellers, or neutral points. Additionally, the basic
reproduction number is calculated analytically to determine the conditions under which the infection may
spread. Using this model, the stages of infectious disease progression, the role of hidden carriers in
transmission, and the probability of reinfection are analyzed from a mathematical perspective. The results
provide valuable insights into real-world epidemiological dynamics and can support the development of
effective disease control strategies