Computational analysis of the Covid-19 model using the continuous Galerkin-Petrov scheme

Epidemiological models feature reliable and valuable insights into the prevention and transmission of life- threatening illnesses. In this study, a novel SIR mathematical model for COVID-19 is formulated and examined. The newly developed model has been thoroughly explored through theoretical analysis and computational methods, specifically the continuous Galerkin-Petrov (cGP) scheme. The next-generation matrix approach was used to calculate the reproduction number (R-0). Both disease-free equilibrium (DFE) (E-0) and the endemic equilibrium (E*) points are derived for the proposed model. The stability analysis of the equilibrium points reveals that (E-0) is locally asymptotically stable when R-0 < 1 , while E-* is globally asymptotically stable when R-0 > 1 . We have examined the model's local stability (LS) and global stability (GS) for endemic equilibrium and DFE based on the number (R0). To ascertain the dominance of the parameters, we examined the sensitivity of the number (R-0) to parameters and computed sensitivity indices. Additionally, using the fourth-order Runge-Kutta (RK4) and Runge-Kutta-Fehlberg (RK45) techniques implemented in MATLAB, we determined the numerical solutions. Furthermore, the model was solved using the continuous cGP time discretization technique. We implemented a variety of schemes like cGP(2), RK4, and RK45 for the COVID-19 model and presented the numerical and graphical solutions of the model. Furthermore, we compared the results obtained using the above-mentioned schemes and observed that all results overlap with each other. The significant properties of several physical parameters under consideration were discussed. In the end, the computational analysis shows a clear image of the rise and fall in the spread of this disease over time in a specific location.