Differential order analysis and sensitivity analysis of a CoVID-19 infection system with memory effect

The paper deals with numerical analysis of solutions for state variables of a CoVID-19 model in integer and fractional order. The solution analysis for the fractional order model is done by the new generalized Caputo-type fractional derivative and Predictor-Corrector methodology, and that for the integer order model is carried out by Multi-step Differential Transformation Method. We have performed sensitivity analysis of the basic reproduction number with the help of a normalized forward sensitivity index. The Arzelá-Ascoli theorem and Fixed point theorems with other important properties are used to establish a mathematical analysis of the existence and uniqueness criteria for the solution of the fractional order. The obtained outcomes are depicted with the help of diagrams, narrating the nature of the state variables. According to the results, the Predictor-Corrector methodology is favorably unequivocal for the fractional model and very simple in administration for the system of equations that are non-linear. The research done in this manuscript can assure the execution and relevance of the new generalized Caputo-type fractional operator for mathematical physics.