Modeling the Impact of Susceptibility Heterogeneity in Diphtheria Outbreaks within a Vaccinated Population Using Fractional-Order Dynamics
Keywords:
Fractional-order model , Stability analysis , Diphtheria, Vaccination effectsAbstract
The purpose of this paper is to study a fractional mathematical model of diphtheria infection spread, considering the susceptibility heterogeneity subpopulation based on vaccination effects and an asymptomatic infected subpopulation. Memory effects and long-range interactions in all compartments are represented by a Caputo fractional derivative. The mathematical analysis of boundedness, positivity, and existence and uniqueness are discussed. We investigate local and global stability existence by applying Matignon's theorem and constructing an appropriate Lyapunov function. The local stability for disease-free equilibrium point is proved by applying the Routh–Hurwitz criterion. The global asymptotic stability of the disease-free equilibrium is examined by applying the approach proposed by Castillo-Chavez et al. And the predictor-corrector technique is used for the numerical simulation. We found that our approach performs better in terms stability region as compared to based-line models. We also present the comparison result of root mean square error (RMSE) for varying fractional order alfa, and the alpha=0.8, give small RMSE, as to be considered by the government to reduce the Diphtheria outbreaks and to improve the vaccinated usage.
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