Qualitative and quantitative analysis of vector-borne infection through fractional framework

Vector-borne infections are a class of human diseases resulting from the transmission of pathogenic microorganisms, including bacteria, viruses, and parasites, through various vectors. Yellow fever, prevalent in both the American and African continents, stands as a prominent example of vector-borne infections. In this paper, we structure the transmission dynamics of yellow fever with vaccine and treatment through non-integer derivative. The fixed point theorem introduced by Banach and Schaefer is utilized to examine the existence and uniqueness of solutions for the proposed yellow fever system. The sufficient conditions of the Ulam-Hyers stability has been established for our system. The solution routes are highlighted using the Laplace Adomian decomposition method to show the influence of input factors on yellow fever. In order to visualise the impacts of fractional-order, vaccine, biting rate, and treatment on the infection level, numerical simulations are performed. We proposed the most attractive parameters of the system for the prevention and control of the infection. Furthermore, it is proposed that the biting rate of mosquitoes is dangerous and can increase the possibility of infection in the community. We suggest that the index of memory, treatment and vaccination are attractive parameters which can reduce the level of infection.