Dynamic Analysis of a Stochastic Delayed SEIRS Epidemic Model with Lévy Jumps and the Impact of Public Health Education

This study presents a class of the stochastic time-delayed susceptible–educated–infective–recovered–susceptible (SEIRS) epidemic model incorporating both public health education and Lévy jumps. We prove that system has unique global positive solution. also provide derived conditions sufficient for extinction persistence in mean. The verification findings conclusions is performed through parameter sensitivity analysis numerical simulations. concludes education, noises, vaccination, increased disease recovery levels, reduced patient contact significantly contribute to prevention control.