Enhancing epidemic modeling: exploring heavy-tailed dynamics with the generalized tempered stable distribution

The generalized tempered stable (GTS) distribution is an optimal choice for modeling disease propagation, as it effectively captures the heavy-tailed nature of such events. This attribute is crucial for evaluating the impact of large-scale outbreaks and formulating effective public health interventions. In our study, we introduce a comprehensive stochastic epidemic model that incorporates various intervention strategies and utilizes Lévy jumps characterized by the GTS distribution. Notably, our proposed stochastic system does not exhibit endemic or disease-free states, challenging the conventional approach of assessing disease persistence or extinction based on asymptotic behavior. To address this, we employed a novel stochastic analysis approach to demonstrate the potential for disease eradication or continuation. We provide numerical examples to highlight the importance of incorporating the GTS distribution in epidemiological modeling. These examples validate the accuracy of our results and compare our model's outcomes with those of a standard system using basic Lévy jumps. The purposeful use of the GTS distribution accounts for the heavy-tailed nature of disease incidence or vector abundance, enhancing the precision of models and predictions in epidemiology.