  In this manuscript, we develop a novel single-strain dengue model with
fractional-order transmission and recovery from a stochastic process. A
fractional derivative that appeared in the disease transmission and recovery
processes is known as a tempered fractional (TF) derivative. We showed that if
a function satisfying certain conditions, then the TF derivative of that
function is proportional to the function itself. By utilizing this result, we
investigated the local and global stability of various equilibrium solutions
(disease-free and endemic) related to the novel fractional-order dengue model
in terms of the basic reproduction number R0. Additionally, we developed an
optimal control problem for the extended fractional-order dengue system with
control to study the effect of three different interventions: reduction of
mosquito recruitment rate, adult vector control, and individual protection.
Furthermore, we derived a sufficient condition for the existence of a solution
to the optimal control problem. Finally, numerical experiments suggest that
policymakers may focus on fractional-order parameters that represent the
mechanisms of disease transmission and recovery in addition to the two vector
controls to reduce dengue spreading in a location.
