Mathematical analysis of dengue fever outbreak by novel fractional operators with field data

Abstract

An epidemiological model is proposed for three different types of novel fractional-order derivative operators known as the Caputo, the Caputo–Fabrizio, and the Atangana–Baleanu–Caputo operators. The classical model is fractionalized while taking care of the dimensional consistency for each ordinary differential equation of the model. The true field data, obtained through some authentic sources, for the dengue fever outbreak in Cape Verde islands in 2009 is the major motivation behind analysis of the present research study. The proposed model, being nonlinear, possesses the possibility of having no closed form solution. It is, therefore, existence and uniqueness for the solutions of the models are investigated via fixed point theory. The residuals computed via least-squares approach for all types of cases under consideration reveal the better performance of the models under fractional-order derivative operators proving that the dynamics of the disease (dengue virus) can be well understood if non-local effects are taken into consideration within the model. Based upon the results obtained, the efficiency rates of the fractional-order operators under the Caputo, Caputo–Fabrizio and the Atangana–Baleanu–Caputo are higher than that of the existing classical model.