Abstract
Within a very short period, the corona infection virus (COVID-19) has created a global emergency situation by spreading worldwide. This virus has dissimilar effects in different geographical regions. In the beginning of the spread, the number of new cases of active corona virus has shown exponential growth across the globe. At present, for such infection, there is no vaccination or anti-viral medicine specific to the recent corona virus infection. Mathematical formulation of infection models is exceptionally successful to comprehend epidemiological models of ailments, just as it causes us to take vital proportions of general wellbeing interruptions to control the disease transmission and the spread. This work based on a new mathematical model analyses the dynamic behaviour of novel corona virus (COVID-19) using Caputo–Fabrizio fractional derivative. A new modified SEIRQ compartment model is developed to discuss various dynamics. The COVID-19 transmission is studied by varying reproduction number. The basic number of reproduction \(R_{0}\) is determined by applying the next generation matrix. The equilibrium points for disease-free and endemic states are computed with the help of basic reproduction number \(R_{0}\) to check the stability property. The Picard approximation and Banach’s fixed point theorem based on iterative Laplace transform are useful in establishing the existence and stability behaviour of the fractional-order system. Finally, numerical computations of the COVID-19 fractional-order system are presented to analyse the dynamical behaviour of the solutions of the model. Also, a fractional-order SEIRQ COVID-19 model with vaccinated people has also been formulated and its dynamics with impact on the propagation behaviour is studied.KeywordsMathematical modellingCaputo–Fabrizio derivativeCorona virusBasic reproduction numberExistence and stabilityFixed point theoryNumerical simulation2010 Mathematics Subject Classifications34A0834A2534D2035A2035A22
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