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

被引：0
|
作者：
Naz, Rahila [1 ]
Jan, Aasim Ullah [1 ]
Attaullah [2 ]
Boulaaras, Salah [3 ]
Guefaifia, Rafik [3 ]
机构：
[1] Department of Mathematics & Statistics, Bacha Khan University, KP, Charsadda,24461, Pakistan
[2] Department of Mathematics & Statistics, University of Chitral, KP, Chitral,17200, Pakistan
[3] Department of Mathematics, College of Science, Qassim University, Buraydah,51452, Saudi Arabia
来源：
Nonlinear Engineering | 2024年 / 13卷 / 01期
关键词：
Epidemiological models feature reliable and valuable insights into the prevention and transmission of lifethreatening illnesses. In this study; a novel SIRmathematical 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-generationmatrix approachwas used to calculate the reproduction number (R )0 . Both disease-free equilibrium (DFE) (E0) and the endemic equilibrium(E∗) points are derived for the proposed model. The stability analysis of the equilibrium points reveals that (E0) is locally asymptotically stable when R0 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 (R0) 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. © 2024 the author(s); published by De Gruyter;
D O I：
10.1515/nleng-2024-0028
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