Modified Predictor–Corrector Method for the Numerical Solution of a Fractional-Order SIR Model with 2019-nCoV

Abstract

In this paper, we analyzed and found the solution for a suitable nonlinear fractional dynamical system that describes coronavirus (2019-nCoV) using a novel computational method. A compartmental model with four compartments, namely, susceptible, infected, reported and unreported, was adopted and modified to a new model incorporating fractional operators. In particular, by using a modified predictor–corrector method, we captured the nature of the obtained solution for different arbitrary orders. We investigated the influence of the fractional operator to present and discuss some interesting properties of the novel coronavirus infection.

Model Development and Prediction of Covid-19 Pandemic in Bangladesh with Nonlinear Incident

“…Mathematical models were developed by several researchers (Gao et al 2022 , Srinivasa et al 2021 , Javeed et al 2021 , etc.) and analyzed the nature of Covid-19, and these models used a single pattern of disease transmission.…”

“…Gao et al ( 2020 ) investigated and simulated the dynamical behavior of Covid-19 using the mathematical model from the reservoir to people using variational iteration method. Gao et al ( 2022 ) analyzed a fractional order model of Covid-19 and showed that the projected solution technique was highly efficient in solving a nonlinear system of fractional differential equations describing dynamics of Covid-19. On the other hand, Srinivasa et al ( 2021 ) concluded that the numerical solution using HWM computational method was very close to the results of the RK method for the SEIQR compartmental model.…”

On the Modeling of COVID-19 Transmission Dynamics with Two Strains: Insight through Caputo Fractional Derivative

“…Since COVID-19 was declared by the WHO as a global pandemic, a number of mathematical models have been elaborated to conceive the spread of COVID-19. Some of the research work done in the field of mathematical modeling related to the COVID-19 problem applied both integer [13][14][15][16][17][18][19][20] and fractional order in their modeling frameworks [21][22][23][24][25][26][27]. Fractional calculus, which uses fractional derivatives (FD), is a new rapidly growing area in mathematical science that picks up a memory effect and hereditary characteristics of various physical and natural phenomena occurring in engineering, technology, physical and natural sciences [28][29][30].…”

Regarding Deeper Properties of the Fractional Order Kundu-Eckhaus Equation and Massive Thirring Model

“…On the other hand, the following recent research work helps us to understand the essence of generalizing the concept with fractional order. For instance, the author in [21] derived the two Fibonacci operational matrix pseudo-spectral schemes to investigate the physical model, the researchers in [22] studied the SIR model of the current 2019-nCoV with Caputo operator, the complex nature of the Gross-Pitaevskii equations derived with the help of fractional derivative. Further, many scholars employed different fractional operators to analyze real-world problems and study the physical phenomena [23][24][25][26][27][28], for instance, COVID-19 in India [29], biological pest control in tea plants [30], and many others.…”