A Study on Fractional SIR Epidemic Model with Vital Dynamics and Variable Population Size using the Residual Power Series Method

Abstract

In this paper, we develop an integer and fractional-order susceptible, infectious, and recovery (SIR) epidemic model based on vital dynamics, i.e., birth, death, immigration, and variable population size, including infection and recovery rates. We investigate the stability analysis for the fractional SIR model on the disease-free and endemic equilibrium points. The existence and uniqueness conditions of solutions for a stable model are also discussed. The residual power series (RPS) approach is used to get the semi-analytical solutions of the proposed model in the form of convergent fractional power series. The convergence analysis of the
RPS method is also discussed. Numerical results demonstrate the effect of distinct fractional orders α ∈ (0, 1] on the population density. The obtained results are exciting and may be beneficial for medical experts to control the epidemic disease.