Numerical analysis of Atangana-Baleanu fractional model to understand the propagation of a novel corona virus pandemic

Abstract

In this manuscript, we formulated a new nonlinear SEIQR fractional order pandemic model for the Corona virus disease (COVID-19) with Atangana-Baleanu derivative. Two main equilibrium points of the proposed model are stated. Threshold parameter for the model using next generation technique is computed to investigate the future dynamics of the disease. The existence and uniqueness of solution is proved using a fixed point theorem. For the numerical solution of fractional model, we implemented a newly proposed Toufik-Atangana numerical scheme to validate the importance of arbitrary order derivative and our obtained theoretical results. It is worth mentioning that fractional order derivative provides much deeper information about the complex dynamics of Corona model. Results obtained through the proposed scheme are dynamically consistent and good in agreement with the analytical results. To draw our conclusions, we explore a complete quantitative analysis of the given model for different quarantine levels. It is claimed through numerical simulations that pandemic could be eradicated faster if a human community selfishly adopts mandatory quarantine measures at various coverage levels with proper awareness. Finally, we have executed the joint variability of all classes to understand the effectiveness of quarantine policy on human population.

Optimal control strategies for the reliable and competitive mathematical analysis of Covid-19 pandemic model

“…Since S(0) ≥ 0, so (9) implies that S( t) > 0 for all t ∈ [0, t]. In the same way, we can prove that all the other state variables are positive.…”

“…Disease is pandemic only in the case if R 0 > 1. The number is computed using the next generation matrix method [9,30,31]. It is actually a spectral radius of F V −1 , where F is the jacobian of the rate of recruitment of new infections and V is the jacobian of the rate of the other transmission terms in equations involving infections.…”

On the Stability and Numerical Scheme of Fractional Differential Equations with Application to Biology

“…For other recent developments in the literature on theoretical and numerical studies of FDEs, see for example [10][11][12] for the inverse problem associated with FDEs, ref. [13] for Hermite-Hadamard-type inequalities, [14][15][16] for numerical methods of FDEs, and [17][18][19] for analytical and numerical solutions of some FDEs.…”

Optimal control strategies for the reliable and competitive mathematical analysis of Covid‐19 pandemic model

“…In the field of mathematical modeling and optimal control design, researchers are continuously trying to develop different mathematical models of Covid‐19 according to physical situations or requirements and are presenting a variety of control strategies for disease control. 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 In this study, we design a new Covid‐19 model termed as SEIAPHR where the infectious humans are placed in three compartments such as symptomatic infected , asymptomatic , and super‐spreaders . The division of infectious individuals in three compartments makes the model more realistic for the sake of analysis and control of disease.…”