In this paper, we use forecasting methods such as Euler’s iterative method and cubic spline interpolation to predict the total number of people infected and the number of active cases for COVID-19 propagation. We construct a novel iterative method, which is based on cubic spline interpolation and Euler’s method and it is an improvement over the two latter methods. The novel method is very efficient for forecasting and to describe the underlying dynamics of the pandemic. Our predicted results are also compared with an iterative method developed by Perc et al. (2020) [1]. Our study encompasses the following countries namely; South Korea, India, South Africa, Germany, and Italy. We use data from 15 February 2020 to 31 May 2020 in order to obtain graphs and then obtain predicted values as from 01 June 2020. We use two criteria to classify whether the predicted value for a certain day is effective or not.

In this paper, we construct four numerical methods to solve the Burgers-Huxley equation with specified initial and boundary conditions. The four methods are two novel versions of nonstandard finite difference schemes (NSFD1 and NSFD2), explicit exponential finite difference method (EEFDM) and fully implicit exponential finite difference method (FIEFDM). These two classes of numerical methods are popular in the mathematical biology community and it is the first time that such a comparison is made between nonstandard and exponential finite difference schemes. Moreover, the use of both nonstandard and exponential finite difference schemes are very new for the Burgers-Huxley equations. We considered eleven different combination for the parameters controlling diffusion, advection and reaction, which give rise to four different regimes. We obtained stability region or condition for positivity. The performances of the four methods are analysed by computing absolute errors, relative errors, L 1 and L ∞ errors and CPU time.Keywords: Burgers-Huxley equation; nonstandard finite difference method; explicit exponential finite difference method; fully implicit exponential finite difference method; absolute error; relative error.

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The study of biofilm formation is becoming increasingly important. Microbes that produce biofilms have complicated impact on medical implants. In this paper, we construct an unconditionally positive non-standard finite difference scheme for a mathematical model of biofilm formation on a medical implant. The unknowns in many applications reflect values that cannot be negative, such as chemical component concentrations or population numbers. The model employed here uses the bistable Allen-Cahn partial differential equation, which is a generalization of Fisher’s equation. We study consistency and convergence of the scheme constructed. We compare the performance of our scheme with a classical finite difference scheme using four numerical experiments. The technique used in the construction of unconditionally positive method in this study can be applied to other areas of mathematical biology and sciences. The results here elaborate the benefits of the non-standard approximations over the classical approximations in practical applications.

Purpose The purpose of this paper is to investigate the dynamical behavior of heat and mass transfer of non-Newtonian nanofluid flow through parallel horizontal sheet with heat-dependent thermal conductivity and magnetic field. The effects of thermophoresis and Brownian motion on the Eyring‒Powell nanofluid heat and concentration are also considered. The flow fluid is propelled by squeezing force and constant pressure gradient. The hydromagnetic fluid is induced by periodic time variations. Design/methodology/approach The dimensionless momentum, energy and species balance equations are solved by the spectral local linearization method that is employed to numerically integrate the coupled non-linear differential equations. Findings The response of the fluid flow, temperature and concentration to variational increase in the values of the parameters is graphically presented and discussed accordingly. Originality/value The validity of the method used was checked by comparing it with previous related article.