Fractional Order Dynamical Behavior of Dengue Hemorrhagic Fever with Saturation Factor

Abstract

In this study, we propose a modified fractional order derivative in the scope of Caputo to investigate the dynamics of Dengue fever transmission. The existence, uniqueness and boundedness of the fractional model were established using a fixed-point approach. The stability analysis of the model was done with respect to the reproduction number which was found to be stable locally and globally at infection free and endemic state respectively. The fractional order (DHF) model was estimated using the fractional Adams-Bashforth predictor-corrector technique. Additionally, the numerical validation was done to ascertain the impact of various parameters on the dynamics as a whole, as well as the effect of vaccines on the model. The graphical solutions show that the fractional order $(α)$ and vaccinations affect the dynamics of the model when they are varied within the model. The findings indicate that saturation of infectious individuals in the system helps to flatten out the infection transmission.