Modeling mosquito-borne disease dynamics via stochastic differential equations and generalized tempered stable distribution

In this study, we introduce an enhanced stochastic model for mosquito-borne diseases that incorporates quarantine measures and employs Lévy jumps with the generalized tempered stable (GTS) distribution. Our proposed model lacks both endemic and disease-free states, rendering the conventional approach of assessing disease persistence or extinction based on asymptotic behavior inapplicable. Instead, we adopt a novel stochastic analysis approach to demonstrate the potential for disease eradication or continuation. Numerical examples validate the accuracy of our results and compare the outcomes of our model with the GTS distribution against the standard system using basic Lévy jumps. By accounting for the heavy-tailed nature of disease incidence or vector abundance, the GTS distribution enhances the precision of epidemiological models and predictions.