Analysis and numerical simulation of novel coronavirus (COVID‐19) model with Mittag‐Leffler Kernel

Abstract

Every now and then, there has been natural or man-made calamities. Such adversities instigate various institutions to find solutions for them. The current study attempts to explore the disaster caused by the micro enemy called coronavirus for the past few months and aims at finding the solution for the system of nonlinear ordinary differential equations to which q−homotopy analysis transform method (q−HATM) has been applied to arrive at effective results. In this paper, there are eight nonlinear ordinary differential equations considered and to solve them the advanced fractional operator Atangana-Baleanu (AB) fractional derivative has been applied to produce better understanding. The outcomes have been presented in terms of plots. Ultimately, the present study assists in examining the real-world models and aids in predicting their behavior corresponding to the parameters considered in the models. KEYWORDS Atangana-Baleanu fractional derivative, coronavirus epidemic model, nonlinear differential equations, q−homotopy analysis transform method MSC CLASSIFICATION 37M05; 34F05; 92D30 1 INTRODUCTION Human history is facing a strange time, fighting with an invisible enemy called the novel coronavirus (COVID-19). This pandemic virus disease found in Wuhan, China. 1 It ensured where the animals and sea meat were sold and named as coronavirus on 31st of December, 2019. The Chinese Government and its health organization together insisted about its transformation from animals to human. 2,3 Coronavirus spread is rapidly increasing in all over the countries. Large number of people are affected by this deadly disease. The current status of coronavirus (COVID-19) is unimaginable, because enormous people have been suffered so far. Though people are recovering from this COVID-19, simultaneously the death ratio is increasing rapidly. World health organization is giving awareness among people through various factors. Scientist are also insisting its importance. The entire nation is joining together to overcome the disease, because even the developed countries couldn't get solution for this virus. This disease threat the people all over the world mentally, because vaccine didn't find yet for this dreadful disease. This study is not only on anticipating the results of the spread but also analyzing the spread of various disease. The study also focuses on to control the disease as possible. 1,4-8 In this paper, we are applying q-homotopy analysis transformation method (q-HATM) to the system of nonlinear equations and find suitable solution for this crucial disease. In order to consider the new fractional operator called

Numerical analysis of fractional coronavirus model with Atangana-Baleanu derivative in Liouville-Caputo sense

“…Padmavathi et al . [ 74 ] developed this model as a fractional model. The memory in time is significant for the coronavirus model which makes its fractional modeling appropriate.…”

“… is the order of AB derivative. The full model information is available in [ 74 ]. Amouch and Karim [ 75 ] computed the basic reproduction number of the COVID-19 model and studied the local stability of the disease-free equilibrium in terms of basic reproduction number.…”

“…As a result, operator W is a contraction. It illustrates that the presented system has a unique set of solutions [ 74 ]. Since Eq.…”

The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations

“…We rank according to the degree of resistance. At the same time, we can obtain the index of the affected categories of each influencing factor in the initial state of reverse psychological performance [8]. We then obtained the reverse psychological performance states for different influence categories.…”

“…We assume that the probability of occurrence of k kinds of different mental performance state sequences is 1 2 , , , k P P P  , then, according to the form of Shannon entropy, the probability of reverse mental state sequence is sorted. We use formula (8) to define the permutation entropy 1 ( )…”