Mathematical analysis of fractional-order Caputo’s derivative of coronavirus disease model via Laplace Adomian decomposition method

Abstract

Background The world's survival ability has been threatened by the COVID-19 outbreak. The possibility of the virus reemerging in the future should not be disregarded, even if it has been confined to certain areas of the world after wreaking such havoc. This is because it is impossible to prove that the virus has been totally eliminated. This research attempts to investigate the spread and control of the COVID-19 virus in Nigeria using the Caputo fractional order derivative in a proposed model. Results We proposed a competent nine-compartment model of Corona virus infection. It starts by demonstrating that the model is epidemiologically sound in terms of solution existence and uniqueness. The basic reproduction threshold R0 was determined using the next-generation matrix technique. We applied the Laplace-Adomian decomposition method to the fractional-order Caputo's derivative model of the Corona virus disease to produce the approximate solution of the model analytically. The obtained results, in the form of an infinite series, were simulated using the MAPLE 18 package to investigate the effect of fractional order derivative on the dynamics of COVID-19 transmission in the model and shed light on methods of eradication. The graphical interpretations of the simulation process were shown and discussed accordingly. Conclusions The study reveals the effect of the Caputo fractional order derivative in the transmission dynamics of the disease. Individual recovery was found to be greatest at an integer order, which represents the full implementation of other factors such as treatment, vaccination, and disease transmission reduction. Hence, we advised that researchers, government officials, and health care workers make use of the findings of this study to provide ways in which disease transmission will be reduced to a minimum to stop the prevalence of COVID-19 by applying the findings of this study.

The analysis of a novel COVID-19 model with the fractional-order incorporating the impact of the vaccination campaign in Nigeria via the Laplace-Adomian Decomposition Method

“…Definition 3 [18]. The Riemann-Liouville fractional integration of order ξ ≥ 0 for a real positive function is given by…”

“…These findings underscore the importance of addressing psychological factors related to vaccine efficacy and safety in vaccination promotion efforts. In the realm of epidemiology, fractional-order modeling has gained attention due to its ability to capture complex and nonlinear disease dynamics [18][19][20][21][22][23][24]. This approach offers an alternative to conventional integer-order models by considering memory effects, such as immunity among recovered individuals, and varying infection and recovery rates over time [25][26][27].…”

On new computations of the time-fractional nonlinear KdV-Burgers equation with exponential memory

“…Notable fractional operators that are used are the Caputo [11,12], Riemann-Liouville [13,14], Caputo-Fabrizo [15], and Atangana-Baleanu [16] operators. These operators are flexible tools for investigating chaotic and fractal events with non-local kernels [17]. The features, benefits, and drawbacks of these operators are covered in detail in [18], which also offers some interesting outcomes from investigations on a fractional optimum control issue in systems with time delay arguments.…”

An Approximate Solution of Fractional Order Epidemic Model of Typhoid using the Homotopy Perturbation Method

“…These models, usually based on compartmentalized models, may be rather simple, but studying them is crucial for gaining important knowledge of the underlying aspects of how infectious diseases spread [2]. The commonly used threshold value in epidemiology is probably the basic reproduction number [3,4]. The basic reproduction number, denoted by, is defined as the average number of secondary infections that occur when one infectious agent is introduced into a completely susceptible population.…”