  The rampant phenomenon of overpopulation and the remarkable increase of human
movements over the last decade have caused an aggressive re-emergence of dengue
fever, which made it the subject of several research fields. In this regard,
mathematical modeling, and notably through compartmental systems, is considered
as an eminent tool to obtain a clear overview of this disease's prevalence
behavior. In reality, and like all epidemics, the dengue spread phenomenon is
often subject to some randomness due to the different natural environment
fluctuations. For this reason, a mathematical formulation that considers
suitably as much as possible the external stochasticity is indeed required. By
this token, we strive in this work to present and analyze a generalized
stochastic dengue model that incorporates both slight and huge environmental
perturbations. More precisely, our proposed model is represented under the form
of an It\^o-L\'evy stochastic differential equations system that we demonstrate
its mathematical well-posedness and biological significance. Based on some
novel analytical techniques, we prove, and under appropriate hypothetical
frameworks, of course, two important asymptotic properties, namely: extinction
and persistence in the mean. The theoretical findings show that the dynamics of
our disturbed dengue model are mainly determined by the parameters that are
narrowly related to the small perturbations' intensities and the jumps
magnitudes. In the end, we give certain numerical illustrative examples to
support our theoretical findings and to highlight the effect of the adopted
mathematical techniques on the results.
