Stability and Stochastic Dynamics of an Extended SUC Epidemic Model With Delays via NSFD Scheme: Implications for Public Health Planning

As of April 11, 2025, the World Health Organization (WHO) reports that Pakistan has recorded 1,581,936 confirmed COVID-19 cases, with 30,664 deaths and 1,538,689 recoveries. Motivated by this context, we develop an extended Susceptible–Uninfected–Carrier (SUC) epidemic model incorporating both time delays and stochastic effects to capture more realistic disease dynamics. We perform a Lyapunov-based energy functional analysis to investigate the model’s stability and long-run dynamical behavior. The sensitivity analysis identifies the most influential parameters for transmission dynamics and threshold conditions for disease spread. To further consider randomness inherent in epidemic processes, we incorporate stochastic perturbations into the model framework. A new NSFD numerical scheme is proposed, which maintains the essential qualitative features of the model and is thus appropriate for reliable simulations of complex epidemiological dynamics. Extensive numerical experiments are carried out which demonstrate the model’s behavior under different parameter regimes and give insight into how delays and randomness can affect the development of a disease. It is expected that these findings can be used in advancing epidemiological modeling and supporting public health decision-making.