Fractional Order Model for the Role of Mild Cases in the Transmission of COVID-19

Fractional model analysis of COVID-19 spread based on big data platform

Based on the data of COVID-19, this paper establishes the FCSEIR model for the spread through data analysis and designs the related simulation software. Using the data from Shanghai, the spread of the virus was simulated and predicted, and the process from outbreak to control of this infectious disease was better analyzed.

A fractal-fractional COVID-19 model with a negative impact of quarantine on the diabetic patients

In this article, we consider a Covid-19 model for a population involving diabetics as a subclass in the fractal-fractional (FF) sense of derivative. The study includes: existence results, uniqueness, stability and numerical simulations. Existence results are studied with the help of fixed-point theory and applications. The numerical scheme of this paper is based upon the Lagrange’s interpolation polynomial and is tested for a particular case with numerical values from available open sources. The results are getting closer to the classical case for the orders reaching to 1 while all other solutions are different with the same behavior. As a result, the fractional order model gives more significant information about the case study.

On fractal-fractional Covid-19 mathematical model

In this article, we are studying a Covid-19 mathematical model in the fractal-fractional sense of operators for the existence of solution, Hyers-Ulam (HU) stability and computational results. For the qualitative analysis, we convert the model to an equivalent integral form and investigate its qualitative analysis with the help of iterative convergent sequence and fixed point approach. For the computational aspect, we take help from the Lagrange's interpolation and produce a numerical scheme for the fractal-fractional waterborne model. The scheme is then tested for a case study and we obtain interesting results.

Fractional dynamical model to assess the efficacy of facemask to the community transmission of COVID-19

The emergence of highly contagious Alpha, Beta, Gamma and Delta variants and strains of COVID-19 put healthy people on high risk of contracting the infection. In addition to the vaccination strategies, the nonpharmaceutical intervention use of face mask gives protection against the contraction of the virus. To understand the efficacy of such, we present a Caputo type fractional dynamical model to assess the efficacy of facemask to the community transmission of COVID-19. The existence and uniqueness of the solution was established, and subsequently, with the use of the generalized mean value theorem, the positivity and boundedness of the solutions were established. The disease free equilibrium (DFE) was found to be asymptotically stable when the basic reproduction number R0<1. By constructing quadratic Lyapunov function, the equilibria (DFE and Endemic) were found to be globally asymptotically stable.

A mathematical study on a fractional COVID-19 transmission model within the framework of nonsingular and nonlocal kernel

In this work, a mathematical model consisting of a compartmentalized coupled nonlinear system of fractional order differential equations describing the transmission dynamics of COVID-19 is studied. The fractional derivative is taken in the Atangana-Baleanu-Caputo sense. The basic dynamic properties of the fractional model such as invariant region, existence of equilibrium points as well as basic reproduction number are briefly discussed. Qualitative results on the existence and uniqueness of solutions via a fixed point argument as well as stability of the model solutions in the sense of Ulam-Hyers are furnished. Furthermore, the model is fitted to the COVID-19 data circulated by Nigeria Centre for Disease Control and the two-step Adams-Bashforth method incorporating the noninteger order parameter is used to obtain an iterative scheme from which numerical results for the model can be generated. Numerical simulations for the proposed model using Adams-Bashforth iterative scheme are presented to describe the behaviors at distinct values of the fractional index parameter for of each of the system state variables. It was shown numerically that the value of fractional index parameter has a significant effect on the transmission behavior of the disease however, the infected population (the exposed, the asymptomatic infectious, the symptomatic infectious) shrinks with time when the basic reproduction number is less than one irrespective of the value of fractional index parameter.

On study of fractional order epidemic model of COVID-19 under non-singular Mittag-Leffler kernel

This paper investigates the analysis of the fraction mathematical model of the novel coronavirus (COVID-19), which is indeed a source of threat all over the globe. This paper deals with the transmission mechanism by some affected parameters in the problem. The said study is carried out by the consideration of a fractional-order epidemic model describing the dynamics of COVID-19 under a non-singular kernel type of derivative. The concerned model examine via non-singular fractional-order derivative known as Atangana-Baleanu derivative in Caputo sense (ABC). The problem analyzes for qualitative analysis and determines at least one solution by applying the approach of fixed point theory. The uniqueness of the solution is derived by the Banach contraction theorem. For iterative solution, the technique of iterative fractional-order Adams-Bashforth scheme is applied. Numerical simulation for the proposed scheme is performed at various fractional-order lying between 0, 1 and for integer-order 1. We also compare the compartmental quantities of the said model at two different effective contact rates of β . All the compartments show convergence and stability with growing time. The simulation of the iterative techniques is also compared with the Laplace Adomian decomposition method (LADM). Good comparative results for the whole density have been achieved by different fractional orders and obtain the stability faster at the low fractional orders while slowly at higher-order.

Optimal control of a fractional order model for the COVID - 19 pandemic

In this paper a fractional optimal control problem was formulated for the outbreak of COVID-19 using a mathematical model with fractional order derivative in the Caputo sense. The state and co-state equations were given and the best strategy to significantly reduce the spread of COVID-19 infections was found by introducing two time-dependent control measures, u 1 ( t ) (which represents the awareness campaign, lockdown, and all other measures that reduce the possibility of contacting the disease in susceptible human population) and u 2 ( t ) (which represents quarantine, monitoring and treatment of infected humans). Numerical simulations were carried out using RK-4 to show the significance of the control functions. The exposed population in susceptible population is reduced by the factor ( 1 - u 1 ( t ) ) due to the awareness and all other measures taken. Likewise, the infected population is reduced by a factor of ( 1 - u 2 ( t ) ) due to the monitoring and treatment by health professionals.

Mathematical model to assess the imposition of lockdown during COVID-19 pandemic

Nigeria, like most other countries in the world, imposes lockdown as a measure to curtail the spread of COVID-19. But, it is known fact that in some countries the lockdown strategy could bring the desired results while in some the situation could worsen the spread of the virus due to poor management and lack of facilities, palliatives and incentives. To this regard, we feel motivated to develop a new mathematical model that assesses the imposition of the lockdown in Nigeria. The model comprises of a system of five ODE. Mathematical analysis of the model were carried out, where boundedness, computation of equilibria, calculation of the basic reproduction ratio and stability analysis of the equilibria were carried out. We finally study the numerical outcomes of the governing model in respect of the approximate solutions. To this aim, we employed the effective ODE45, Euler, RK-2 and RK-4 schemes and compare the results.