scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

2021 ◽  
Author(s):  
Olaniyi Samuel Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Equilibrium Analysis ◽  
Complex Nature ◽  
Contact Rate ◽  
Uniqueness Of Solutions ◽  
Effective Contact ◽  
Proposed Model

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalization and deaths have been observed, and thousands of cases daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to understand the transmission of the disease better. Nonlocality involved in the model has made fractional differential equations appropriate for modeling the behavior. However, solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate (from exposed quarantine and recovered to susceptible and infected quarantined individuals), quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium analysis, and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam-Bashforth-Moulton method developed for the fractional order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19, especially quarantining exposed and infected individuals and the effective contact rate. Based on the results with different fractional order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is what is happening right now in many countries.

scholarly journals System of Time Fractional Models for COVID-19: Modeling, Analysis and Solutions

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 787
Author(s):  
Olaniyi Iyiola ◽  
Bismark Oduro ◽  
Trevor Zabilowicz ◽  
Bose Iyiola ◽  
Daniel Kenes
Keyword(s):  
Fractional Order ◽  
Recovery Rate ◽  
Death Rate ◽  
Numerical Solutions ◽  
Complex Nature ◽  
Uniqueness Of Solutions ◽  
Fractional Equations ◽  
Effective Contact ◽  
Proposed Model ◽  
Fractional Models

The emergence of the COVID-19 outbreak has caused a pandemic situation in over 210 countries. Controlling the spread of this disease has proven difficult despite several resources employed. Millions of hospitalizations and deaths have been observed, with thousands of cases occurring daily with many measures in place. Due to the complex nature of COVID-19, we proposed a system of time-fractional equations to better understand the transmission of the disease. Non-locality in the model has made fractional differential equations appropriate for modeling. Solving these types of models is computationally demanding. Our proposed generalized compartmental COVID-19 model incorporates effective contact rate, transition rate, quarantine rate, disease-induced death rate, natural death rate, natural recovery rate, and recovery rate of quarantine infected for a holistic study of the coronavirus disease. A detailed analysis of the proposed model is carried out, including the existence and uniqueness of solutions, local and global stability analysis of the disease-free equilibrium (symmetry), and sensitivity analysis. Furthermore, numerical solutions of the proposed model are obtained with the generalized Adam–Bashforth–Moulton method developed for the fractional-order model. Our analysis and solutions profile show that each of these incorporated parameters is very important in controlling the spread of COVID-19. Based on the results with different fractional-order, we observe that there seems to be a third or even fourth wave of the spike in cases of COVID-19, which is currently occurring in many countries.

Analysis of a New Class of Impulsive Implicit Sequential Fractional Differential Equations

2020 ◽  
Vol 21 (6) ◽  
pp. 571-587 ◽  
Author(s):  
Akbar Zada ◽  
Sartaj Ali ◽  
Tongxing Li
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Fractional Differential Equations ◽  
Sufficient Conditions ◽  
Uniqueness Of Solutions ◽  
Integer Order ◽  
New Class ◽  
Proposed Model ◽  
Fractional Differential ◽  
Sequential Fractional Differential Equations

AbstractIn this paper, we study an implicit sequential fractional order differential equation with non-instantaneous impulses and multi-point boundary conditions. The article comprehensively elaborate four different types of Ulam’s stability in the lights of generalized Diaz Margolis’s fixed point theorem. Moreover, some sufficient conditions are constructed to observe the existence and uniqueness of solutions for the proposed model. The proposed model contains both the integer order and fractional order derivatives. Thus, the exponential function appearers in the solution of the proposed model which will lead researchers to study fractional differential equations with well known methods of integer order differential equations. In the last, few examples are provided to show the applicability of our main results.

scholarly journals A predictive model for Covid-19 spread – with application to eight US states and how to end the pandemic

2020 ◽  
Vol 148 ◽  
Author(s):  
Z. S. Khan ◽  
F. Van Bussel ◽  
F. Hussain
Keyword(s):  
Predictive Model ◽  
Release Rate ◽  
Recovery Rate ◽  
Death Rate ◽  
Compartmental Model ◽  
Contact Rate ◽  
Reinfection Rate ◽  
Us States ◽  
Coupled Equations ◽  
The Us

Abstract A compartmental model is proposed to predict the coronavirus 2019 (Covid-19) spread. It considers: detected and undetected infected populations, social sequestration, release from sequestration, plus reinfection. This model, consisting of seven coupled equations, has eight coefficients which are evaluated by fitting data for eight US states that make up 43% of the US population. The evolution of Covid-19 is fairly similar among the states: variations in contact and undetected recovery rates remain below 5%; however, variations are larger in recovery rate, death rate, reinfection rate, sequestration adherence and release rate from sequestration. Projections based on the current situation indicate that Covid-19 will become endemic. If lockdowns had been kept in place, the number of deaths would most likely have been significantly lower in states that opened up. Additionally, we predict that decreasing contact rate by 10%, or increasing testing by approximately 15%, or doubling lockdown compliance (from the current ~15% to ~30%) will eradicate infections in Texas within a year. Extending our fits for all of the US states, we predict about 11 million total infections (including undetected), and 8 million cumulative confirmed cases by 1 November 2020.

scholarly journals Numerical Solutions of a Heat Transfer for Fractional Maxwell Fluid Flow with Water Based Clay Nanoparticles; A Finite Difference Approach

2021 ◽  
Vol 5 (4) ◽  
pp. 242
Author(s):  
Arfan Ali ◽  
Muhammad Imran Asjad ◽  
Muhammad Usman ◽  
Mustafa Inc
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Finite Difference ◽  
Mathematical Modelling ◽  
Fractional Order ◽  
Numerical Solutions ◽  
Physical Modelling ◽  
Maxwell Fluid ◽  
Complex Nature ◽  
Physical Parameters

Fractional-order mathematical modelling of physical phenomena is a hot topic among various researchers due to its many advantages over positive integer mathematical modelling. In this context, the appropriate solutions of such fractional-order physical modelling become a challenging task among scientists. This paper presents a study of unsteady free convection fluid flow and heat transfer of Maxwell fluids with the presence of Clay nanoparticle modelling using fractional calculus. The obtained model was transformed into a set of linear nondimensional, partial differential equations (PDEs). The finite difference scheme is proposed to discretize the obtained set of nondimensional PDEs. The Maple code was developed and executed against the physical parameters and fractional-order parameter to explain the behavior of the velocity and temperature profiles. Some limiting solutions were obtained and compared with the latest existing ones in literature. The comparative study witnesses that the proposed scheme is a very efficient tool to handle such a physical model and can be extended to other diversified problems of a complex nature.

scholarly journals Controlling the Dynamical Spread of Coronavirus Disease (COVID-19) in a Population

2020 ◽  
Author(s):  
Akanni John Olajide
Keyword(s):  
Recovery Rate ◽  
Lyapunov Functions ◽  
Progression Rate ◽  
Contact Rate ◽  
Equilibrium Solutions ◽  
Centre Manifold ◽  
Effective Contact ◽  
Manifold Theory ◽  
Theoretical Results ◽  
Positivity And Boundedness

In the paper, a model governed by a system of ordinary differential equations was considered; the whole population was divided into Susceptible individuals (S), Exposed individuals (E), Infected individuals (I), Quarantined individuals (Q) and Recovered individuals (R). The well-posedness of the model was investigated by the theory of positivity and boundedness. Analytically, the equilibrium solutions were examined. A key threshold which measures the potential spread of the Coronavirus in the population is derived using the next generation method. Bifurcation analysis and global stability of the model were carried out using centre manifold theory and Lyapunov functions respectively. The effects of some parameters such as Progression rate of exposed class to infectious class, Effective contact rate, Modification parameter, Quarantine rate of infectious class, Recovery rate of infectious class and Recovery rate of quarantined class on R0 were explored through sensitivity analysis. Numerical simulations were carried out to support the theoretical results, to reduce the burden of COVID 19 disease in the population and significant in the spread of it in the population.

scholarly journals A simple mathematical model for Coronavirus (COVID-19)

2020 ◽  
Author(s):  
Said Melliani ◽  
Abdelati El Allaoui ◽  
Lalla Saadia Chadli
Keyword(s):  
Mathematical Model ◽  
Death Rate ◽  
Infected Individual ◽  
Viral Pneumonia ◽  
Contact Rate ◽  
Simple Mathematical Model ◽  
Proposed Model ◽  
The World ◽  
Per Capita ◽  
Novel Coronavirus

AbstractA novel coronavirus (COVID-19) was identified in Wuhan, China in the end of 2019, it causing an outbreak of viral pneumonia. It caused to the death rate of 4.63% among 571, 678 confirmed cases around the world to the March 28th, 2020. In this brief currentstudy, we will present a simple mathematical model where we show how the probability of successfully getting infected when coming into contact with an infected individual and the per-capita contact rate affect the healthy and infected population with time. The proposed model is used to offer predictions about the behavior of COVID-19 for a shorter period of time.

scholarly journals A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

2020 ◽  
Author(s):  
Zhenzhen Lu ◽  
Yongguang Yu ◽  
YangQuan Chen ◽  
Guojian Ren ◽  
Conghui Xu ◽  
...  
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Least Squares Method ◽  
Real Data ◽  
Order System ◽  
Coupling Effects ◽  
Order Model ◽  
The Real ◽  
Proposed Model ◽  
City Network

AbstractA novel coronavirus, designated as COVID-19, emerged in Wuhan, China, at the end of 2019. In this paper, a mathematical model is proposed to analyze the dynamic behavior of COVID-19. Based on inter-city networked coupling effects, a fractional-order SEIHDR system with the real-data from 23 January to 18 March, 2020 of COVID19 is discussed. Meanwhile, hospitalized individuals and the mortality rates of three types of individuals (exposed, infected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during incubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numerical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stimulated by using the real-data from 23 January to 18 − m March, 2020 where m is equal to the number of prediction days. Compared with integer-order system (α = 0), the fractional-order model without network is validated to have a better fitting of the data on Beijing, Shanghai, Wuhan, Huanggang and other cities. In contrast to the case without network, the results indicate that the inter-city network system may be not a significant case to virus spreading for China because of the lock down and quarantine measures, however, it may have an impact on cities that have not adopted city closure. Meanwhile, the proposed model better fits the data from 24 February to 31, March in Italy, and the peak number of confirmed people is also predicted by this fraction-order model. Furthermore, the existence and uniqueness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic reproduction number R0 is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymptotically stable when R0 ≤ 1, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future.

scholarly journals Mathematical modeling and analysis of fractional-order brushless DC motor

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Zain Ul Abadin Zafar ◽  
Nigar Ali ◽  
Cemil Tunç
Keyword(s):  
Fractional Order ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Approximate Solutions ◽  
Dc Motor ◽  
Brushless Dc Motor ◽  
Uniqueness Of Solutions ◽  
Product Integration ◽  
Modeling And Analysis ◽  
Brushless Dc

AbstractIn this paper, we consider a fractional-order model of a brushless DC motor. To develop a mathematical model, we use the concept of the Liouville–Caputo noninteger derivative with the Mittag-Lefler kernel. We find that the fractional-order brushless DC motor system exhibits the character of chaos. For the proposed system, we show the largest exponent to be 0.711625. We calculate the equilibrium points of the model and discuss their local stability. We apply an iterative scheme by using the Laplace transform to find a special solution in this case. By taking into account the rule of trapezoidal product integration we develop two iterative methods to find an approximate solution of the system. We also study the existence and uniqueness of solutions. We take into account the numerical solutions for Caputo Liouville product integration and Atangana–Baleanu Caputo product integration. This scheme has an implicit structure. The numerical simulations indicate that the obtained approximate solutions are in excellent agreement with the expected theoretical results.

scholarly journals Numerical Analysis of Viscoelastic Rotating Beam with Variable Fractional Order Model Using Shifted Bernstein–Legendre Polynomial Collocation Algorithm

2021 ◽  
Vol 5 (1) ◽  
pp. 8
Author(s):  
Cundi Han ◽  
Yiming Chen ◽  
Da-Yan Liu ◽  
Driss Boutat
Keyword(s):  
Numerical Analysis ◽  
Fractional Order ◽  
Governing Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Matrix Product ◽  
Algebraic Equations ◽  
Rotating Beam ◽  
The Matrix ◽  
The Time Domain

This paper applies a numerical method of polynomial function approximation to the numerical analysis of variable fractional order viscoelastic rotating beam. First, the governing equation of the viscoelastic rotating beam is established based on the variable fractional model of the viscoelastic material. Second, shifted Bernstein polynomials and Legendre polynomials are used as basis functions to approximate the governing equation and the original equation is converted to matrix product form. Based on the configuration method, the matrix equation is further transformed into algebraic equations and numerical solutions of the governing equation are obtained directly in the time domain. Finally, the efficiency of the proposed algorithm is proved by analyzing the numerical solutions of the displacement of rotating beam under different loads.

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