Stability analysis of a fractional-order [formula omitted] epidemic model for the COVID-19 pandemic

Abstract

To explore the impact of the COVID-19 vaccination rate and immune loss rate on the pandemic, this paper proposes a fractional-order SIV1V2S epidemic model with vaccination ineffectiveness and infection differences. And we compare and analyze the dynamic differences between integer-order and Caputo fractional-order operators. First, we show the non-negativity and boundedness of solutions for the Caputo fractional-order model. Based on the basic reproduction number, we use the fractional-order matrix eigenvalue method and the Routh–Hurwitz criterion to determine the local asymptotic stability of disease-free equilibrium points and endemic equilibrium points, construct Lyapunov functions, and use the fractional-order Barbalat’s Lemma to prove the global asymptotic stability of the two equilibrium points. Second, real data from India were used to fit the model parameters and get the optimal fractional-order parameter, and then sensitivity analysis was performed on the basic reproduction number. Further, through numerical simulation of different fractional-order parameter epidemic models, we verify the global asymptotic stability of the equilibrium point of the fractional-order SIV1V2S COVID-19 model. The comparison shows that the fractional-order model is more closely related to actual virus transmission than the integer-order model. In the case of the SIV1V2S model, which only considers vaccination measures, simultaneously increasing the vaccination rate of susceptible individuals and reducing the rate of immunization loss can effectively control epidemic transmission.