A fractional order Covid-19 epidemic model with Mittag-Leffler kernel

Abstract

In this article, we are studying fractional-order COVID-19 model for the analytical and computational aspects. The model consists of five compartments including; which denotes susceptible class, represents exposed population, is the class for infected people who have been developed with COVID-19 and can cause spread in the population. The recovered class is denoted by and is the concentration of COVID-19 virus in the area. The computational study shows us that the spread will be continued for long time and the recovery reduces the infection rate. The numerical scheme is based on the Lagrange’s interpolation polynomial and the numerical results for the suggested model are similar to the integer order which gives us the applicability of the numerical scheme and effectiveness of the fractional order derivative.

Fractional commensurate model on COVID‐19 with microbial co‐infection: An optimal control analysis

“…Motivated from the works of References 30,31 which explains the hesitation and threatening of virus, isolation effects, vaccination and environmental exposure, age factors, demographic changes, 32,33 symptomatic and asymptomatic carriers and mutations visualized in References 34,35, fear effects due to isolation and quarantine, vaccination, self‐precautionary measures, and associated coinfections studied in References 36–45. However, we present vaccine breakthrough infections, vaccine efficiency and microbial pathogen coinfections in a novel way on our proposed COVID‐19 coinfection model.…”

“…Several fractional studies of deterministic, stochastic and incommensurate models on COVID-19 illness were delved in the literature examining various fear factors, diagnosed, threatened, awareness of pathogen spread, vaccination schemes, vaccine hesitancy, vaccine inefficacy, treatment, isolation, exposure to the virulent environment, effective vaccination with self-precautions, vaccine breakthrough infections, symptomatic and asymptomatic carriers and mutant strains, and so on. [30][31][32][33][34][35][36][37][38][39][40][41][42] COVID-19-related coinfections were studied with other superinfections namely hepatitis-B, 43 Tuberculosis, 44 and diabetes mellitus. 45 Optimal control modeling analysis were very effective in epidemical studies implementing effective control measures for disease annihilation found in References 46-50.…”

“…(2 + 1)‐dimensional Hirota–Satsuma–Ito equation, 25 and Wu–Zhang system mounted for earthquake aftereffects (dispersive gravitation of ocean waves) 26 and epidemiological behaviors of influenza, cholera and dengue in References 27–30. Fractional modeling of COVID‐19 pandemic with various approaches, control practices and fractional operators are found in References 30–42.…”

“…Memory, encapsulated by the Mittag–Leffler function of the ABC derivative, recaptures the past historical evidence, which will perfectly match the immune history of mankind in response to epidemics or sudden pandemic breakouts. Several fractional studies of deterministic, stochastic and incommensurate models on COVID‐19 illness were delved in the literature examining various fear factors, diagnosed, threatened, awareness of pathogen spread, vaccination schemes, vaccine hesitancy, vaccine inefficacy, treatment, isolation, exposure to the virulent environment, effective vaccination with self‐precautions, vaccine breakthrough infections, symptomatic and asymptomatic carriers and mutant strains, and so on 30–42 . COVID‐19‐related coinfections were studied with other superinfections namely hepatitis–B, 43 Tuberculosis, 44 and diabetes mellitus 45 .…”

Solution of fractional Sawada–Kotera–Ito equation using Caputo and Atangana–Baleanu derivatives

“…This new ABC derivative has a great memory due to the existence of Mittag–Leffler function as its nonlocal kernel; eventually, it results in a better comparative performance as compared to other existing fractional derivative operators. Validation of the above claim is justified by applying ABC operator, instead of other operators, and solving various scientific models, namely, the general sequential hybrid class of FDEs [15, 16], controllability of neutral impulsive [17], Covid‐19 mathematical model [18, 19], fractional typhoid model [20], wireless sensor network as an application of the fuzzy fractional SIQR model [21], plasma particle model with circular LASER light polarization [22], Hepatitis B model [23], SEIR and blood coagulation technologies [24], a fractal‐fractional tuberculosis [25] and tobacco [26] mathematical model, a class of population growth model [27], and the fractional nonlinear logistic system [27].…”