Catastrophe on Epidemic and Endemic Transitions in SEIQRV Dynamics

Methodology: In this paper, we aim to investigate endemic and epidemic transitions in the SEIQRV model using catastrophe theory. By incorporating nonlinear interactions among susceptible, exposed, infected, quarantined, recovered, and vaccinated populations, the model reveals that disease dynamics may undergo abrupt qualitative changes under small variations in epidemiological or control parameters. Using catastrophe-theoretic analysis, we show that epidemic onset, persistence, and elimination correspond to structural changes in the equilibrium landscape, giving rise to fold and cusp catastrophes. Results: These structures explain the coexistence of disease-free and endemic equilibria, hysteresis effects, and delayed epidemic collapse under gradual parameter adjustment. The results demonstrate that traditional threshold-based analysis may be insufficient to capture critical transitions in SEIQRV systems. Discussion: Catastrophe geometry provides a unified analytical and visual framework for identifying epidemic tipping points and for designing robust intervention strategies. This approach highlights the nonlinear nature of epidemic dynamics and the potential limitations of conventional modeling methods in predicting sudden outbreaks or disease persistence. Conclusion: The methodology enhances both theoretical understanding and practical prediction of complex epidemic behavior, offering valuable insights for public health planning and intervention strategies.