Analysis of SIQR type mathematical model under Atangana-Baleanu fractional differential operator.

In the given manuscript, the fractional mathematical model for the current pandemic of COVID-19 is investigated. The model is composed of four agents of susceptible (S), infectious (I), quarantined (Q) and recovered (R) cases respectively. The fractional operator of Atangana-Baleanu-Caputo (ABC) is applied to the considered model for the fractional dynamics. The basic reproduction number is computed for the stability analysis. The techniques of existence and uniqueness of the solution are established with the help of fixed point theory. The concept of stability is also derived using the Ulam-Hyers stability technique. With the help of the fractional order numerical method of Adams-Bashforth, we find the approximate solution of the said model. The obtained scheme is simulated on different fractional orders along with the comparison of integer orders. Varying the numerical values for the contact rate ζ, different simulations are performed to check the effect of it on the dynamics of COVID-19.

On nonlinear dynamics of COVID-19 disease model corresponding to nonsingular fractional order derivative.

This manuscript is devoted to investigate the mathematical model of fractional-order dynamical system of the recent disease caused by Corona virus. The said disease is known as Corona virus infectious disease (COVID-19). Here we analyze the modified SEIR pandemic fractional order model under nonsingular kernel type derivative introduced by Atangana, Baleanu and Caputo ([Formula: see text]) to investigate the transmission dynamics. For the validity of the proposed model, we establish some qualitative results about existence and uniqueness of solution by using fixed point approach. Further for numerical interpretation and simulations, we utilize Adams-Bashforth method. For numerical investigations, we use some available clinical data of the Wuhan city of China, where the infection initially had been identified. The disease free and pandemic equilibrium points are computed to verify the stability analysis. Also we testify the proposed model through the available data of Pakistan. We also compare the simulated data with the reported real data to demonstrate validity of the numerical scheme and our analysis.

Study of a COVID-19 mathematical model

In this chapter, we develop the mathematical model of four compartments including classes of susceptible, infected, recovered, and death of infected ones for the recent outbreak of a coronavirus infectious disease (COVID-19). The model is investigated for both integer-order and fractional-order derivatives. The integer-order model is analyzed for an approximate solution using the Taylor's series method along with the numerical simulation showing the validity of the obtained scheme. The fractional-order model is evaluated numerically by Euler's iterative techniques and its results are compared to that of the Taylor's series scheme. The numerical simulation is drawn against the available data at different fractional orders. The fractional-order model is also investigated for qualitative analysis using the well-known theorems of fixed-point theory. The said model is also checked for feasibility and stability by using the techniques of basic reproduction number.

Investigation of time-fractional SIQR Covid-19 mathematical model with fractal-fractional Mittage-Leffler kernel

In this manuscript, we investigate a nonlinear SIQR pandemic model to study the behavior of covid-19 infectious diseases. The susceptible, infected, quarantine and recovered classes with fractal fractional Atangana-Baleanu-Caputo (ABC) derivative is studied. The non-integer order ℘ and fractal dimension q in the proposed system lie between 0 and 1. The existence and uniqueness of the solution for the considered model are studied using fixed point theory, while Ulam-Hyers stability is applied to study the stability analysis of the proposed model. Further, the Adams-Bashforth numerical technique is applied to calculate an approximate solution of the model. It is observed that the analytical and numerical calculations for different fractional-order and fractal dimensions confirm better converging effects of the dynamics as compared to an integer order.

Numerical computations and theoretical investigations of a dynamical system with fractional order derivative

This manuscript is devoted to consider population dynamical model of non-integer order to investigate the recent pandemic Covid-19 named as severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) disease. We investigate the proposed model corresponding to different values of largely effected system parameter of immigration for both susceptible and infected populations. The results for qualitative analysis are established with the help of fixed-point theory and non-linear functional analysis. Moreover, semi-analytical results, related to series solution for the considered system are investigated on applying the transform due to Laplace with Adomian polynomial and decomposition techniques. We have also applied the non-standard finite difference scheme (NSFD) for numerical solution. Finally, both the analysis are supported by graphical results at various fractional order. Both the results are comparable with each other and converging quickly at low order. The whole spectrum and the dynamical behavior for each compartment of the proposed model lying between 0 and 1 are simulated via Matlab.

Investigation of fractal-fractional order model of COVID-19 in Pakistan under Atangana-Baleanu Caputo (ABC) derivative.

This manuscript addressing the dynamics of fractal-fractional type modified SEIR model under Atangana-Baleanu Caputo (ABC) derivative of fractional order y and fractal dimension p for the available data in Pakistan. The proposed model has been investigated for qualitative analysis by applying the theory of non-linear functional analysis along with fixed point theory. The fractional Adams-bashforth iterative techniques have been applied for the numerical solution of the said model. The Ulam-Hyers (UH) stability techniques have been derived for the stability of the considered model. The simulation of all compartments has been drawn against the available data of covid-19 in Pakistan. The whole study of this manuscript illustrates that control of the effective transmission rate is necessary for stoping the transmission of the outbreak. This means that everyone in the society must change their behavior towards self-protection by keeping most of the precautionary measures sufficient for controlling covid-19.

Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data.

We discuss a fractional-order SIRD mathematical model of the COVID-19 disease in the sense of Caputo in this article. We compute the basic reproduction number through the next-generation matrix. We derive the stability results based on the basic reproduction number. We prove the results of the solution existence and uniqueness via fixed point theory. We utilize the fractional Adams-Bashforth method for obtaining the approximate solution of the proposed model. We illustrate the obtained numerical results in plots to show the COVID-19 transmission dynamics. Further, we compare our results with some reported real data against confirmed infected and death cases per day for the initial 67 days in Wuhan city.

Fractal-Fractional Mathematical Model Addressing the Situation of Corona Virus in Pakistan.

This work is the consideration of a fractal fractional mathematical model on the transmission and control of corona virus (COVID-19), in which the total population of an infected area is divided into susceptible, infected and recovered classes. We consider a fractal-fractional order SIR type model for investigation of Covid-19. To realize the transmission and control of corona virus in a much better way, first we study the stability of the corresponding deterministic model using next generation matrix along with basic reproduction number. After this, we study the qualitative analysis using "fixed point theory" approach. Next, we use fractional Adams-Bashforth approach for investigation of approximate solution to the considered model. At the end numerical simulation are been given by matlab to provide the validity of mathematical system having the arbitrary order and fractal dimension.

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

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.

Investigating a nonlinear dynamical model of COVID-19 disease under fuzzy caputo, random and ABC fractional order derivative.

This paper is devoted to investigation of the fractional order fuzzy dynamical system, in our case, modeling the recent pandemic due to corona virus (COVID-19). The considered model is analyzed for exactness and uniqueness of solution by using fixed point theory approach. We have also provided the numerical solution of the nonlinear dynamical system with the help of some iterative method applying Caputo as well as Attangana-Baleanu and Caputo fractional type derivative. Also, random COVID-19 model described by a system of random differential equations was presented. At the end we have given some numerical approximation to illustrate the proposed method by applying different fractional values corresponding to uncertainty.