Modeling and simulation results of a fractional dengue model

Dengue fever is a vector-borne disease and is still epidemic in most countries of the world by providing so many outbreaks. The present paper investigates the dengue dynamics for the real cases reported in Pakistan in the period 2003–2015. The model is formulated and the associated properties are presented. We show, for the given period, a basic reproduction, R= 3. 8. The parameters are parameterized for model simulation by using the leaset square curve fitting in MATLAB. We use the Caputo derivative and formulate the fractional dengue model. The stability analysis for the fractional dengue model in both disease-free and endemic cases is presented. We show that, in the disease-free case, the fractional dengue model is locally and globally stable when R< 1. Then, we prove the model stability in the endemic case and present the results for R> 1 . We provide some graphical illustrations and show that the dengue model with fractional derivative is more useful than that of the integer order model.