The present paper deals with the numerical solution for a general form of a system of nonlinear Volterra delay integro-differential equations (VDIDEs). The main purpose of this work is to provide a current numerical method based on the use of continuous collocation Taylor polynomials for the numerical solution of nonlinear VDIDEs systems. It is shown that this method is convergent. Numerical results will be presented to prove the validity and effectiveness of this convergent algorithm. We apply two models to the COVID-19 epidemic in China and one for the Predator-Prey model in mathematical ecology. Keywords Nonlinear Volterra delay integro-differential equations • Collocation method • Taylor polynomials • Epidemic mathematical model • Corona virus Mathematics Subject Classification (2010) 45G15 • 34K28 • 45D05 • 45L05 • 65L60
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