A mathematical system of COVID-19 disease model:existence, uniqueness, numerical and sensitivity analysis

Abstract A compartmental mathematical model of spreading COVID-19 disease in Wuhan, China is applied to investigate the pandemic behaviour in Iran. This model is a system of seven ordinary differential equations including individual behavioural reactions, governmental actions, holiday extensions, travel restrictions, hospitalizations, and quarantine. We fit the Chinese model to the Covid-19 outbreak in Iran and estimate the values of parameters by trial-error approach. We use the Adams-Bashforth predictor-corrector method based on Lagrange polynomials to solve the system of ordinary differential equations. To prove the existence and uniqueness of solutions of the model we use Banach fixed point theorem and Picard iterative method. Also, we evaluate the equilibrium points and the stability of the system. With estimating the basic reproduction number R₀, we assess the trend of new infected cases in Iran. In addition, the sensitivity analysis of the model is assessed by allocating different parameters to the system. Numerical simulations are depicted by adopting initial conditions and various values of some parameters of the system

A B-Spline Quasi Interpolation Crank–Nicolson Scheme for Solving the Coupled Burgers Equations with the Caputo–Fabrizio Derivative

In this paper, a Crank–Nicolson finite difference scheme based on cubic B-spline quasi-interpolation has been derived for the solution of the coupled Burgers equations with the Caputo–Fabrizio derivative. The first- and second-order spatial derivatives have been approximated by first and second derivatives of the cubic B-spline quasi-interpolation. The discrete scheme obtained in this way constitutes a system of algebraic equations associated with a bi-pentadiagonal matrix. We show that the proposed scheme is unconditionally stable. Numerical examples are provided to verify the efficiency of the method

An Efficient Explicit Decoupled Group Method for Solving Two–Dimensional Fractional Burgers’ Equation and Its Convergence Analysis

In this paper, the Crank–Nicolson (CN) and rotated four-point fractional explicit decoupled group (EDG) methods are introduced to solve the two-dimensional time–fractional Burgers’ equation. The EDG method is derived by the Taylor expansion and 45° rotation of the Crank–Nicolson method around the x and y axes. The local truncation error of CN and EDG is presented. Also, the stability and convergence of the proposed methods are proved. Some numerical experiments are performed to show the efficiency of the presented methods in terms of accuracy and CPU time