A Caputo power law model predicting the spread of the COVID-19 outbreak in Pakistan

Abstract

This work is devoted to establish a modified population model of susceptible and infected (SI) compartments to predict the spread of the infectious disease COVID-19 in Pakistan. We have formulated the model and derived its boundedness and feasibility. By using next generation matrices method we have derived some results for the global and local stability of different kinds of equilibrium points. Also, by using fixed point approach some results of existence of at least one solution are studied. Furthermore, the numerical simulations for various values of isolation parameters corresponding to different fractional order are investigated by using modified Euler’s method.

A multi-stage SEIR model to predict the potential of a new COVID-19 wave in KSA after lifting all travel restrictions

“…Based on WHO statistics, since its detection until December 25, 2020, the total number of confirmed cases worldwide is 80,133,093 and the number of deaths is 1,755,653. The considerable and continuous rise in the daily infected cases number all over the world is worrying, and many researchers are currently developing various mathematical and machine learning models to predict the future progress of this pandemic [1] , [2] , [3] , [4] , [5] , [6] , [7] . However, only few studies have discussed the possibility of the second surge of this SARS pandemic.…”

“…However, to continue imposing these policies it seems to be impossible now due to economic reasons [13] . Nevertheless, recent modeling studies have indicated that the relaxation of restrictions could have terrible penalties [4] , [14] , [15] , [16] .…”

A fractional-order model for CoViD-19 dynamics with reinfection and the importance of quarantine

“…Briefly, fractional order (FO) operators can be representative of memory functions, making the dynamics of variables more realistic [18] , [19] , [20] . Recent studies on CoViD-19 have incorporated FC [21] , [22] , [23] , [24] . Epidemiological and biomathematical models are two of several areas where FC is being applied [25] , [26] , [27] .…”

Stability analysis for a class of implicit fractional differential equations involving Atangana–Baleanu fractional derivative

“…Many researchers also examined the solutions of fractional models for stability analysis [ 2 ]. Some researchers also worked on COVID-19 model with the help of fractional calculus [ 3 , 4 ]. On the other hand, fixed point theory helps much in the development of the qualitative and computational concepts of FDEs and their related dynamic equations [ 5 – 11 ].…”