Studying of the Covid-19 model by using the finite element method: Theoretical and numerical simulation

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Abstract This study simulates the start of coronavirus infection using a mathematical model based on ordinary differential equations (Covid-19). Additionally, provide the numerical treatment and simulation of this model using the finite element approach (FEM). The goal of this research is to stop and slow the spread of a sickness that is ravaging the globe. A susceptible person may also transfer immediately to the quarantined class after the exposed person has been quarantined or moved to one of the contaminated classes. This model was employed by the researchers to account for both asymptomatic and symptomatic infected people. The proposed model is reduced to a set of algebraic equations using the FEM. The resulting system is then created as an optimization problem with constraints, which is subsequently optimized to obtain the solution and the unknown coefficients. The obtained findings are compared to those produced using the fourth-order Runge-Kutta method (RK4). Finally, we calculate the residual error function of the approximation in order to validate the FEM, and it is presented in symmetric forms. MSC 2010: 34A12; 41A30; 47H10; 65N20.

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