A Detailed Analysis of Covid-19 Model with the Piecewise Singular and Non-Singular Kernels

In this article, we investigate the dynamics of COVID-19 with a new approach of piecewise global derivative in the sense of singular and non-singular kernels. The singular kernel operator is a Caputo derivative, whereas the non-singular operator is an Atangana-Baleanu Caputo operator. The said problem is investigated for the existence and uniqueness of a solution with a piecewise derivative. The approximate solution to the proposed problem has been obtained by the piecewise numerical iterative technique of Newton polynomials. The numerical scheme for piecewise derivatives in the sense of singular and non-singular kernels is also developed. The numerical simulation for the considered piecewise derivable problem has been drawn up against the available data for different fractional orders. This will be useful for easy understanding of the concept of piecewise global derivatives and the crossover problem dynamics.

A Restricted SIR Model with Vaccination Effect for the Epidemic Outbreaks Concerning COVID-19

This paper presents a restricted SIR mathematical model to analyze the evolution of a contagious infectious disease outbreak (COVID-19) using available data. The new model focuses on two main concepts: first, it can present multiple waves of the disease, and second, it analyzes how far an infection can be eradicated with the help of vaccination. The stability analysis of the equilibrium points for the suggested model is initially investigated by identifying the matching equilibrium points and examining their stability. The basic reproduction number is calculated, and the positivity of the solutions is established. Numerical simulations are performed to determine if it is multipeak and evaluate vaccination's effects. In addition, the proposed model is compared to the literature already published and the effectiveness of vaccination has been recorded.