$$\mathscr {S}\mathscr {E}\mathscr {I}\mathscr {A}\mathscr {R}\mathscr {S}$$ model for analyzing $$\mathscr {C}\mathscr {O}\mathscr {V}\mathscr {I}\mathscr {D}$$-19 pandemic process via $$\uppsi $$-Caputo fractional derivative and numerical simulation

Abstract

AbstractThe objective of this study is to develop the $$\mathscr {S}\mathscr {E}\mathscr {I}\mathscr {A}\mathscr {R}\mathscr {S}$$ S E I A R S epidemic model for $$\mathscr {C}\mathscr {O}\mathscr {V}\mathscr {I}\mathscr {D}$$ C O V I D -$${\textbf {19}}$$ 19 utilizing the $$\uppsi $$ ψ -Caputo fractional derivative. The reproduction number ($$\breve{\mathscr {R}}_0$$ R ˘ 0 ) is calculated utilizing the next generation matrix method. The equilibrium points of the model are computed, and both the local and global stability of the disease-free equilibrium point are demonstrated. Sensitivity analysis is discussed to describe the importance of the parameters and to demonstrate the existence of a unique solution for the model by applying a fixed point theorem. Utilizing the fractional Euler procedure, an approximate solution to the model is obtained. To study the transmission dynamics of infection, numerical simulations are conducted by using MatLab. Both numerical methods and simulations can provide valuable insights into the behavior of the system and help in understanding the existence and properties of solutions. By placing the values $$\texttt{t}$$ t , $$\ln (\texttt{t})$$ ln ( t ) and $$\sqrt{\texttt{t}}$$ t instead of $$\uppsi $$ ψ , the derivatives of the Caputo and Caputo–Hadamard and Katugampola appear, respectively, to compare the results of each with real data. Besides, these simulations specifically with different fractional orders to examine the transmission dynamics. At the end, we come to the conclusion that the simulation utilizing Caputo derivative with the order of 0.95 shows the prevalence of the disease better. Our results are new which provide a good contribution to the current research on this field of research.