Abstract:In this paper, A Chebyshev spectral method is presented to study the deals with the fractional SIRC model associated with the evolution of influenza A disease in human population. The properties of the Chebyshev polynomials are used to derive an approximate formula of the Caputo fractional derivative. This formula reduces the SIRC model to the solution of a system of algebraic equations which is solved using Newton iteration method. The convergence analysis and an upper bound of the error of the derived formula are given. We compared our numerical solutions with those numerical solutions using fourth-order Runge-Kutta method. The obtained results of the SIRC model show the simplicity and the efficiency of the proposed method. Also, illustration for propagation of influenza A virus and the relation between the four cases of it along the time at the fractional derivative are given.
In this paper, estimators for the parameters of the Kumaraswamy-inverse Rayleigh distribution based on record values are obtained. These estimators are derived using the maximum likelihood and Bayesian methods. The Bayesian estimators are derived under the well-known squared error (SE) loss function. Prediction of the future sth record value is derived using the maximum likelihood and Bayesian methods. Simulation study is conduct to illustrate the findings.
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