Taylor collocation method for a system of nonlinear Volterra delay integro-differential equations with application to COVID-19 epidemic

References

• S. Abbasbandy and A. Taati, Numerical solution of the system of nonlinear Volterra integro-differential equations with nonlinear differential part by the operational Tau method and error estimation, J. Comput. Appl. Math. 231(1) (2009), pp. 106–113.
   Web of Science ®Google Scholar
• A. Abdi, J.P. Berrut, and S.A. Hosseini, The linear barycentric rational method for a class of delay Volterra integro-differential equations, J. Sci. Comput. 75(3) (2018), pp. 1757–1775.
   Web of Science ®Google Scholar
• G. Adomian, A review of the decomposition method and some recent results for nonlinear equations, Math. Comput. Model. 13(7) (1990), pp. 17–43.
   Web of Science ®Google Scholar
• R.P. Agarwal, Difference Equations and Inequalities: Theory, Methods, and Applications, CRC Press, Boca Raton, 2000.
   Google Scholar
• A. Arikoglu and I. Ozkol, Solutions of integral and integro-differential equation systems by using differential transform method, Comput. Math. Appl. 56(9) (2008), pp. 2411–2417.
   Web of Science ®Google Scholar
• A. Bellour and M. Bousselsal, A Taylor collocation method for solving delay integral equations, Numer. Algorithms. 65 (2014), pp. 843–857.
   Web of Science ®Google Scholar
• A. Bellour and M. Bousselsal, Numerical solution of delay integro-differential equations by using Taylor collocation method, Math. Methods Appl. Sci. 37 (2014), pp. 1491–1506.
   Web of Science ®Google Scholar
• J. Biazar, H. Ghazvini, and M. Eslami, Hes homotopy perturbation method for systems of integro-differential equations, Chaos Solitons Fractals. 39(3) (2009), pp. 1253–1258.
   Web of Science ®Google Scholar
• M.H.A. Biswas, L.T. Paiva, and M.D.R. De Pinho, A SEIR model for control of infectious diseases with constraints, Math. Biosci. Eng. 11(4) (2014), pp. 761–784.
   Web of Science ®Google Scholar
• H. Brunner, Collocation Methods for Volterra Integral and Related Functional Differential Equations, Cambridge University Press, Cambridge, 2004.
   Google Scholar
• T.A. Burton, Volterra Integral and Differential Equations, Academic Press, New York, 1983.
   Google Scholar
• Chinese Center for Disease Control and Prevention, Availalbe at http://www.chinacdc.cn/jkzt/crb/zl/szkb_11803/jszl_11809/.
   Google Scholar
• J.M. Cushing, Integrodifferential Equations and Delay Models in Population Dynamics, Vol. 20, Springer Verlag, Berlin Heidelberg New York, 1977.
   Google Scholar
• P. Darania, Multistep collocation method for nonlinear delay integral equations, Sahand Commun. Math. Anal. (SCMA). 3 (2016), pp. 47–65.
   Web of Science ®Google Scholar
• P. Darania and S. Pishbin, High-order collocation methods for nonlinear delay integral equation, J. Comput. Appl. 326 (2017), pp. 284–295.
   Web of Science ®Google Scholar
• S. Fazeli and G. Hojjati, Numerical solution of Volterra integro-differential equations by superimplicit multistep collocation methods, Numer. Algorithms. 68 (2015), pp. 741–768.
   Web of Science ®Google Scholar
• M. Gülsu and M. Sezer, Taylor collocation method for solution of systems of high-order linear Fredholm-Volterra integro-differential equations, Int. J. Comput. 83 (2006), pp. 429–448.
   Web of Science ®Google Scholar
• Z. Gu, Chebyshev spectral collocation method for system of nonlinear Volterra integral equations, Numer. Algorithms 83(1) (2020), pp. 243–263.
   Web of Science ®Google Scholar
• E. Hairer, C. Lubich, and S.P. Nørsett, Order of convergence of one-step methods for Volterra integral equations of the second kind, SIAM J. Numer. Anal. 20 (1983), pp. 569–579.
   Web of Science ®Google Scholar
• A. Harir, S. Melliani, H. El Harfi, and L.S. Chadli, Variational iteration method and differential transformation method for solving the SEIR epidemic model, Int. J. Differ. Equ. 2020 (2020), pp. 00–00.
   Google Scholar
• J.H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Comput. Methods Appl. Mech. Eng. 167 (1998), pp. 69–73.
   Web of Science ®Google Scholar
• Italian Civil Protection Department, Available at https://github.com/pcm-dpc/COVID-19 with licence CC-BY-4.0.
   Google Scholar
• A.J. Jerri, Introduction to Integral Equations with Applications, John Wiley and Sons, INC, New York, 1999.
   Google Scholar
• H. Laib, A. Bellour, and M. Bousselsal, Numerical solution of high-order linear Volterra integro-differential equations by using Taylor collocation method, Int. J. Comput. Math. 96(5) (2019), pp. 1066–1085.
   Web of Science ®Google Scholar
• Z. Liu, P. Magal, O. Seydi, and G. Webb, A COVID-19 epidemic model with latency period, Infect. Dis. Model. 5 (2020), pp. 323–337.
   PubMedGoogle Scholar
• Z. Liu, P. Magal, O. Seydi, and G. Webb, A model to predict COVID-19 epidemics with applications to South Korea, Italy, and Spain, medRxiv, 2020.
   Google Scholar
• Z. Mahmoodi, Collocation method for solving systems of Fredholm and Volterra integral equations, Int. J. Comput. Math. 91(8) (2014), pp. 1802–1816.
   Web of Science ®Google Scholar
• F. Mirzaee, S. Alipour, and N. Samadyar, Numerical solution based on hybrid of block-pulse and parabolic functions for solving a system of nonlinear stochastic Itô-Volterra integral equations of fractional order, J. Comput. Appl. Math. 349 (2019), pp. 157–171.
   Web of Science ®Google Scholar
• F. Mirzaee and N. Samadyar, Parameters estimation of HIV infection model of CD4+ T-cells by applying orthonormal Bernstein collocation method, Int. J. Biomath. 11(02) (2018), pp. 1850020.
   Google Scholar
• F. Mirzaee and N. Samadyar, Application of hat basis functions for solving two-dimensional stochastic fractional integral equations, Comput. Appl. Math. 37(4) (2018), pp. 4899–4916.
   Google Scholar
• F. Mirzaee and N. Samadyar, On the numerical solution of stochastic quadratic integral equations via operational matrix method, Math. Methods Appl. Sci. 41(12) (2018), pp. 4465–4479.
   Web of Science ®Google Scholar
• F. Mirzaee and N. Samadyar, Application of Bernoulli wavelet method for estimating a solution of linear stochastic Itô-Volterra integral equations, Multidiscipline Model. Mater. Struct. 15(3) (2019), pp. 575–598.
   Web of Science ®Google Scholar
• F. Mirzaee and N. Samadyar, Implicit meshless method to solve 2D fractional stochastic Tricomi-type equation defined on irregular domain occurring in fractal transonic flow, Numer. Methods Partial Differ. Equ. 37(2) (2021), pp. 1781–1799.
   Web of Science ®Google Scholar
• National Epidemiology Center, Available at https://cnecovid.isciii.es/covid19/.
   Google Scholar
• F.A. Rihan, E.H. Doha, M. Hassan, and N.M. Kamel, Numerical treatments for volterra delay integro-differential equations, Comput. Methods Appl. Math. 9(3) (2009), pp. 292–308.
   Google Scholar
• Y. Rostami, Operational matrix of two dimensional Chebyshev wavelets and its applications in solving nonlinear partial integro-differential equations, Eng. Comput. 38(2) (2020), pp. 745–761.
   Google Scholar
• Y. Rostami and K. Maleknejad, Numerical solution of partial integro-differential equations by using projection method, Mediterranean J. Math. 3(14) (2017), pp. 1–16.
   Google Scholar
• Y. Rostami and K. Maleknejad, Solving Fredholm integral equations of the first kind by using wavelet bases, Hacettepe J. Math. Stat. 48(6) (2019), pp. 1729–1743.
   Web of Science ®Google Scholar
• J. Saberi-Nadjafi and M. Tamamgar, The variational iteration method: A highly promising method for solving the system of integro-differential equations, Comput. Math. Appl. 56(2) (2008), pp. 346–351.
   Web of Science ®Google Scholar
• N. Samadyar and F. Mirzaee, Numerical scheme for solving singular fractional partial integro-differential equation via orthonormal Bernoulli polynomials, Int. J. Numer. Model. Electron. Netw. Devices Fields 32(6) (2019), p. e2652
   Web of Science ®Google Scholar
• N. Samadyar and F. Mirzaee, Orthonormal Bernoulli polynomials collocation approach for solving stochastic Itô-Volterra integral equations of Abel type, Int. J. Numer. Model. Electron. Netw. Devices Fields 33(1) (2020), p. e2688
   Web of Science ®Google Scholar
• N. Samadyar, Y. Ordokhani, and F. Mirzaee, Hybrid Taylor and block-pulse functions operational matrix algorithm and its application to obtain the approximate solution of stochastic evolution equation driven by fractional Brownian motion, Commun. Nonlinear Sci. Numer. Simul. 90 (2020), pp. 105346
   Google Scholar
• F. Shakeri and M. Dehghan, Solution of a model describing biological species living together using the variational iteration method, Math. Comput. Model. 48 (2008), pp. 685–699.
   Google Scholar
• M. Shakourifar and W. Enright, Superconvergent interpolants for collocation methods applied to Volterra integro-differential equations with delay, BIT Numer. Math. 52(3) (2012), pp. 725–740.
   Web of Science ®Google Scholar
• V. Volterra, Variazioni e fluttuazioni del numero d'individui in specie animali conviventi, C. Ferrari, 1927, p. 142.
   Google Scholar
• K. Wang and Q. Wang, Taylor collocation method and convergence analysis for the Volterra-Fredholm integral equations, J. Comput. Appl. 260 (2014), pp. 294–300.
   Web of Science ®Google Scholar
• A.M. Wazwaz, Linear and Nonlinear Integral Equations, Vol. 639, Springer, Berlin, 2011.
   Google Scholar
• S. Yuzbasi and M. Sezer, An exponential approach for the system of nonlinear delay integro-differential equations describing biological species living together, Neural Comput. Appl. 27(3) (2016), pp. 769–779.
   Web of Science ®Google Scholar
• M. Zarebnia and J. Rashidinia, Approximate solution of systems of Volterra integral equations with error analysis, Int. J. Comput. Math. 87(13) (2010), pp. 3052–3062.
   Web of Science ®Google Scholar