An effective transport-related SVIR stochastic epidemic model with media coverage and Lévy noise

Effective disease control measures are necessary because epidemics have a serious threat to public health. To address this, we propose a novel SVIR epidemic model that highlights the impact of transport-related infection and media coverage, with the inclusion of Lévy noise. With the help of Lyapunov functions and stopping time, we investigate the existence of a positive global solution for the new model. We also derive sufficient conditions for disease extinction as well as persistence. For the validation of our theoretical findings, we develop a numerical scheme to analyze the influence of various parameters on the model's dynamics. Our findings provide important insight into the science of epidemiology and provide a groundwork for better methods of preventing the spread of disease.