Stability Analysis of a Fractional-Order SIVS Epidemic Model with Saturated Incidence Rate
In this paper,we construct a Caputo fractional-order SIVS epidemic model with infection difference and the saturated incidence rate.The disease-free equilibrium point and the basic reproduction number of the model are calculated,and the existence and uniqueness of the endemic equilibrium point are determined.The local asymptotic stability of the two equilibrium points is determined by using the fractional matrix eigenvalue method and the Routh-Hurwitz criterion.The sufficient conditions for the global asymptotic stability of two equilibrium points are obtained by using fractional Barbalat's lemma and constructing the Lyapunov function.Finally,the correctness of the theoretical results is verified by numerical simulations of different fractional-order values,and we found that the numerical solution of the fractional-order model has greater degrees of freedom.The increase of saturation constant in this model reflects the enhancement of protective measures for susceptible individuals,which can effectively ease the spread of disease.
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