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

Abstract

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 the system has a unique global positive solution. We also provide derived conditions sufficient for both extinction and persistence in the mean. The verification of the findings and conclusions is performed through parameter sensitivity analysis and numerical simulations. This study concludes that public health education, stochastic noises, vaccination, increased disease recovery levels, and reduced patient contact significantly contribute significantly to disease prevention and control.