Analysis of the dynamics of the viral infection spread model (Международный научный журнал «Инженер», 2026)
This paper analyzes the dynamics of a mathematical model based on a proposed three-dimensional quadraticstochastic operator developed to simulate the spread of viral infections. The model employs Lotka–Volterratypeoperators defined on a simplex, and the behavior of the resulting dynamical systems under varioussignatures is thoroughly investigated. The model variables represent the proportions of population groups—susceptible, infected, recovered, and hidden carriers—while the coefficients denote the interactionparameters among these groups. Within the study, the Jacobian matrix is constructed to identify stationarypoints and classify their stability properties as attractors, repellers, or neutral points. Additionally, the basicreproduction number is calculated analytically to determine the conditions under which the infection mayspread. Using this model, the stages of infectious disease progression, the role of hidden carriers intransmission, and the probability of reinfection are analyzed from a mathematical perspective. The resultsprovide valuable insights into real-world epidemiological dynamics and can support the development ofeffective disease control strategies