Dynamical analysis of the transmission of dengue fever via Caputo-Fabrizio fractional derivative

Abstract

In this work, we develop a sophisticated mathematical model for dengue transmission dynamics based on vaccination, reinfection and carrier class assumptions. We utilize Caputo-Fabrizio fractional framework to represent the transmission phenomena of dengue. For the model analysis, the basic theory and findings of the Caputo-Fabrizio fractional operator are provided. We utilize the next-generation approach to calculate the threshold parameter $R_0$ for our proposed dengue infection model. We have shown that the disease-free steady-state of the hypothesized dengue system is locally asymptotically stable if $R_0<1$ and is unstable in other conditions. The reproduction number of the system of dengue infection is investigated numerically. Furthermore, under the Caputo-Fabrizio approach, we offer a numerical approach for solving our fractional-order problem. We obtain the solution pathways of our system with various values of fractional-order $\vartheta$ and other input values in order to illustrate the effects of fractional-order $\vartheta$ and other input values on our system. Based on our findings, we forecast the most essential system factors for eradicating dengue infections.