Stability analysis of a solution for the fractional‐order model on rabies transmission dynamics using a fixed‐point approach

Abstract

Understanding the complex phenomena of rabies transmission dynamics requires effective tools. This research leverages the capabilities of the fixed‐point approach and employs the theoretical results to solve the model and extract meaningful insights from the results. So, a nonlinear ratio‐dependent incidence rate and a non‐integer Caputo‐Fabrizio derivative have been used to develop the rabies transmission dynamic model. The study investigated the results for the existence and uniqueness of the solution of the model (i.e., unique disease‐free equilibrium point) using Geraghty‐type contraction in b‐complete b‐dislocated quasi metric space. Additionally, determine the stability conditions for the disease‐free equilibrium point that the fixed point theorem provides by examining the range of the parameters. For this, we have established definitions, lemmas, and theorems that provide the conditions for the equilibrium point and its stability conditions for the model that contribute to a deeper understanding of the spread of infection. This research underscores the essential role played by the model and fixed‐point approach in advancing knowledge concerning rabies transmission dynamics.