Investigating epidemic model of infectious disease for stability analysis and approximation solution

Abstract

In the current work, we formulate a fractional order model via the use of fractional Mittag-Leffler derivative (FMD) to describe the dynamics of Chikungunya virus. We investigate existence, uniqueness, positivity and boundedness of the concerned model. We identify threshold conditions for the endogenous persistence vs eradication of the virus, and predict the potential for outbreaks by computing reproduction numbers $\left(R_0\right)$. Besides this, we also study the stability by determining the condition on which disease-free equilibrium stays stable. A comparative study and sensitivity analysis are also given in detail in the work. We conduct numerical simulations using a two-step Lagrange polynomial method that can efficiently investigate the dynamics of the specified model. Our findings highlight the role of fractional calculus (FC) in epidemiological models, which incorporate memory effects and genetic trait, and can lead to more accurate forecasts as well as efficacious public health policy. These findings not only support the theoretical foundation of infectious disease modeling, but also serve as a launching point for future research on other vector-borne diseases. We offer predictions of the model for different fractional orders, demonstrating how alterations in these orders affect the model predictions.