Modeling Rift Valley fever transmission: insights from fractal-fractional dynamics with the Caputo derivative

Abstract

The infection caused by Rift Valley fever (RVF) virus is a dangerous vector-borne disease found in humans, domestic, and wild animals. It is transferred through insect vectors to ruminant host and then spread through direct contact of infected animals with their body fluid or organs. In this paper, a fractal-fractional model for the transmission of RVF in the Caputo's sense was presented. We analyzed the model and determined the basic reproduction number through the next-generation matrix technique, indicated by $ \mathcal{R}_0 $. The global sensitivity technique is used for the sensitivity test of $ \mathcal{R}_0 $ to find out the most sensitive input-factors to the reproduction parameter $ \mathcal{R}_0 $. The existence and uniqueness results of the proposed fractal-fractional model were established. Then, we presented the fractal-fractional dynamics of the proposed RVF model through a novel numerical scheme under the fractal-fractional Caputo operator. In the end, the recommended model of RVF was highlighted numerically with the variation of different input parameters of the system. The key factors of the system were highlighted to the policymakers for the control and prevention of the infection.

Keywords

• rift valley fever
• fractal-fractional operator
• mathematical model
• sensitivity analysis
• numerical analysis