Investigation of COVID-19 Mathematical Model Under Fractional Order Derivative

The given article is devoted to presentation of some results regarding existence and uniqueness of solution to a fractional order model that addressing the effect of immigration on the transmission dynamics of a population model. Further, in view of this investigation the effect of immigration have been checked on transmission of recent pandemic known as Corona virus COVID-19. The concerned results have been established by using fixed point theory approach. After investigation qualitative analysis of the considered model, by applying Laplace transform along with decomposition method, we have calculated some series type results for the concerned model. The unknown quantities of each equation have been decomposed into small quantities to calculate each small quantity very easily for the series solution by adding first few terms of the said quantities. Approximate results of some testing data with different cases are given to illustrate the results.

[1]  Manar A. Alqudah,et al.  Semi-analytical study of Pine Wilt Disease model with convex rate under Caputo–Febrizio fractional order derivative , 2020 .

[2]  Devendra Kumar,et al.  A reliable algorithm for the approximate solution of the nonlinear Lane‐Emden type equations arising in astrophysics , 2018 .

[3]  C. Cattani,et al.  Legendre spectral method for the fractional Bratu problem , 2020, Mathematical Methods in the Applied Sciences.

[4]  Harendra Singh,et al.  Analysis for fractional dynamics of Ebola virus model , 2020, Chaos, Solitons & Fractals.

[5]  Harendra Singh,et al.  Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients , 2019, Physica A: Statistical Mechanics and its Applications.

[6]  Potent binding of 2019 novel coronavirus spike protein by a SARS coronavirus-specific human monoclonal antibody , 2020, Emerging microbes & infections.

[7]  Ai-Min Yang,et al.  INITIAL BOUNDARY VALUE PROBLEM FOR FRACTAL HEAT EQUATION IN THE SEMI-INFINITE REGION BY YANG-LAPLACE TRANSFORM , 2014 .

[8]  H. M. Baskonus,et al.  New approach for the model describing the deathly disease in pregnant women using Mittag-Leffler function , 2020 .

[9]  K. Shah,et al.  Solution of fractional order heat equation via triple Laplace transform in 2 dimensions , 2017 .

[10]  C. Dolea,et al.  World Health Organization , 1949, International Organization.

[11]  Zhanbing Bai,et al.  On positive solutions of a nonlocal fractional boundary value problem , 2010 .

[12]  H. Srivastava,et al.  Numerical Simulation for Fractional-Order Bloch Equation Arising in Nuclear Magnetic Resonance by Using the Jacobi Polynomials , 2020, Applied Sciences.

[13]  Hongzhou Lu,et al.  Outbreak of pneumonia of unknown etiology in Wuhan, China: The mystery and the miracle , 2020, Journal of medical virology.

[14]  Harendra Singh,et al.  A reliable method based on second kind Chebyshev polynomial for the fractional model of Bloch equation , 2017, Alexandria Engineering Journal.

[15]  Yongli Cai,et al.  A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action , 2020, International Journal of Infectious Diseases.

[16]  Mehdi Dalir,et al.  Applications of Fractional Calculus , 2010 .

[17]  Hassan Eltayeb,et al.  A note on solutions of wave, Laplace's and heat equations with convolution terms by using a double Laplace transform , 2008, Appl. Math. Lett..

[18]  Dumitru Baleanu,et al.  A new fractional SIRS-SI malaria disease model with application of vaccines, antimalarial drugs, and spraying , 2019, Advances in Difference Equations.

[19]  Devendra Kumar,et al.  An efficient computational technique for local fractional Fokker Planck equation , 2020 .

[20]  Dumitru Baleanu,et al.  A new analysis of fractional fish farm model associated with Mittag-Leffler-type kernel , 2020 .

[21]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[22]  H. Srivastava,et al.  Solving Non-Linear Fractional Variational Problems Using Jacobi Polynomials , 2019, Mathematics.

[23]  Devendra Kumar,et al.  An efficient computational approach for local fractional Poisson equation in fractal media , 2020, Numerical Methods for Partial Differential Equations.

[24]  Harendra Singh.  Operational matrix approach for approximate solution of fractional model of Bloch equation , 2017 .

[25]  M. Shitikova,et al.  Applications of Fractional Calculus to Dynamic Problems of Linear and Nonlinear Hereditary Mechanics of Solids , 1997 .

[26]  Two-Dimensional Transient Solutions for Crossflow Heat Exchangers With Neither Gas Mixed , 1987 .

[27]  A. J. Lotka.  Contribution to the Theory of Periodic Reactions , 1909 .

[28]  Yong Zhou,et al.  Study in Fractional Differential Equations by Means of Topological Degree Methods , 2012 .

[29]  Jagdev Singh.  Analysis of fractional blood alcohol model with composite fractional derivative , 2020 .

[30]  O. P. Singh,et al.  Numerical Method Based on Galerkin Approximation for the Fractional Advection-Dispersion Equation , 2015, 1504.08178.

[31]  KAMAL SHAH,et al.  EXISTENCE AND UNIQUENESS OF SOLUTIONS TO FRACTIONAL ORDER MULTI-POINT BOUNDARY VALUE PROBLEMS , 2015 .

[32]  M. Goyal,et al.  An efficient technique for a time fractional model of lassa hemorrhagic fever spreading in pregnant women , 2019, The European Physical Journal Plus.

[33]  K. Shah,et al.  Existence of Positive Solution to a Class of Fractional Differential Equations with Three Point Boundary Conditions , 2016 .

[34]  H. Srivastava,et al.  Numerical Investigation of the Fractional-Order Liénard and Duffing Equations Arising in Oscillating Circuit Theory , 2020, Frontiers in Physics.

[35]  Bashir Ahmad,et al.  On four-point nonlocal boundary value problems of nonlinear integro-differential equations of fractional order , 2010, Appl. Math. Comput..

[36]  C. Althaus,et al.  Pattern of early human-to-human transmission of Wuhan 2019 novel coronavirus (2019-nCoV), December 2019 to January 2020 , 2020, Euro surveillance : bulletin Europeen sur les maladies transmissibles = European communicable disease bulletin.

[37]  J. Epstein,et al.  Isolation and characterization of a bat SARS-like coronavirus that uses the ACE2 receptor , 2013, Nature.

[38]  Devendra Kumar,et al.  A computational study of fractional model of atmospheric dynamics of carbon dioxide gas , 2020 .

[39]  Hammad Khalil,et al.  Analytical Solutions of Fractional Order Diffusion Equations by Natural Transform Method , 2018 .

[40]  T. Kaczorek,et al.  Fractional Differential Equations , 2015 .

[41]  R. Hilfer.  Applications Of Fractional Calculus In Physics , 2000 .