The profile of each state variable and the fitted values of the parameters were used to illustrate the spread of the disease. In addition, the equilibrium points showed that E ¯ 0 was locally and globally asymptotically stable depending on R 0 1. According to the results, the model had two equilibrium points: the endemic equilibrium point E ¯ 1 and the disease-free equilibrium point E ¯ 0. The presentation of the qualitative examination of the model was given particular importance. The system was then stated as a constrained optimization problem, and the problem was then optimized to find the unknown coefficients for the approximate solution. The model was turned into an algebraic system of equations using the suggested method and this approximation for a formula. With the aid of the characteristics of the shifted Chebyshev polynomials, a rough formula for the Caputo fractional derivative was presented with a particular focus. We used the proposed method to simulate the COVID-19 model in this work. In addition, we compared the solution generated by the proposed method with the generalized Runge-Kutta method of the fourth-order (GRK4). In addition, the residual error function was introduced to estimate the error of the solution. Finally, we gave a numerical simulation of the model under study using the proposed method with different values for the initial values, the various natality rate values, and the distinct values of the fractional derivative. The model was turned into an algebraic system of equations using the suggested method and this approximation of a formula. A particular focus was placed on providing a rough formula for the Caputo fractional (CF) derivative with the use of the shifted Chebyshev polynomials. The qualitative analysis of the proposed model is presented and concerns the locally asymptotically stable endemic equilibrium point, the locally stable disease-free equilibrium, and the globally asymptotically stable endemic equilibrium. This study’s main objective was to offer a theoretical and numerical simulation of the proposed COVID-19 system. Hence, local fractional calculus is a fascinating concept that merits more study. In addition, the majority of α-differentiation results are trivially inferable from the conventional ones. In actuality, the first-order derivative of a function multiplied by a continuous function is the α-derivative of that function. Existing ideas on local fractional derivatives have some strong connections to the standard derivative function. These derivatives, which are local in nature, are helpful for researching the fractional differentiability characteristics of extremely irregular and nowhere-differentiable functions. Recent literature has introduced local fractional derivative operators. The concept of fractional differential equations (FDEs) in general, and ordinary differential equations (ODEs) in particular, has gained a lot of interest due to its wide-ranging improvements to and numerous applications in several disciplines. These differential operators have memory qualities, allowing them to be utilized to demonstrate a wide range of scientific phenomena and facts involving dynamics. Results acquired with the achieved results were contrasted with those obtained using the generalized Runge-Kutta method.Īll of the models described in the preceding investigations usually used known derivatives. The researchers adopted this strategy and considered both asymptomatic and symptomatic infected patients. A susceptible person may be moved immediately into the confined class after being initially quarantined or an exposed person may be transferred to one of the infected classes. The objective of this research was to halt the global spread of a disease. To evaluate the effectiveness and accuracy of the suggested scheme, the residual error function was computed. To identify the unknown coefficients of the approximate solution, the proposed problem was transformed into a system of algebraic equations, which was then transformed into a restricted optimization problem. Here, the third-kind Chebyshev approximations of the spectral collocation method (SCM) were used. Initially, a rough approximation formula was created for the fractional derivative of t p. A mathematical model of this system is provided, based on a collection of fractional differential equations (in the Caputo sense). We give a theoretical and numerical analysis of a coronavirus (COVID-19) infection model in this research.
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