An efficient technique to analyze the fractional model of vector-borne diseases

In the present work, we find and analyze the approximated analytical solution for the vector-borne diseases model of fractional order with the help of q-homotopy analysis transform method (q-HATM). Many novel definitions of fractional derivatives have been suggested and utilized in recent years to build mathematical models for a wide range of complex problems with nonlocal effects, memory, or history. The primary goal of this work is to create and assess a Caputo-Fabrizio fractional derivative model for Vector-borne diseases. In this investigation, we looked at a system of six equations that explain how vector-borne diseases evolve in a population and how they affect community public health. With the influence of the fixed-point theorem, we establish the existence and uniqueness of the models system of solutions. Conditions for the presence of the equilibrium point and its local asymptotic stability are derived. We discover novel approximate solutions that swiftly converge. Furthermore, the future technique includes auxiliary parameters that are both trustworthy and practical for managing the convergence of the solution found. The current study reveals that the investigated model is notably dependent on the time chronology and also the time instant, which can be effectively studied with the help of the arbitrary order calculus idea.