Use of the repeated integral transformation method to describe the transport of solute in soil.

Predicting the fate and transport of contaminants in soil or groundwater systems using analytical or numerical models is crucial for environmental researchers. While the analytical models are a flexible approach to quantifying the subsurface contamination and remediation because they are non-susceptible to numerical dispersions, economical and handier; two-dimensional analytical models that describe a bilateral flow coupled with both sink and decay factors are rarely reported. Motivated by the case of a non-bare soil ridge with constant point-solute source lying internally but parallel to the longitudinal flow direction, a (2 + 1) dimensional Advection-Diffusion-Reaction Equation (ADRE) of bilateral flow coupled with the linear sorption, decay, and sink is formulated to model the transport of dissolved solute in a homogenous and isotropic non-fractured porous medium.

A COVID-19 mathematical model of at-risk populations with non-pharmaceutical preventive measures: The case of Brazil and South Africa.

This work examines a mathematical model of COVID-19 among two subgroups: low-risk and high-risk populations with two preventive measures; non-pharmaceutical interventions including wearing masks, maintaining social distance, and washing hands regularly by the low-risk group. In addition to the interventions mentioned above, high-risk individuals must take extra precaution measures, including telework, avoiding social gathering or public places, etc. to reduce the transmission.

COVID-19 intervention models: An initial aggressive treatment strategy for controlling the infection.

The novel coronavirus (COVID-19) outbreak emerged in December 2019. The disease has caused loss of many lives and has become an unprecedented threat to public health worldwide. We develop simple COVID-19 epidemic models to study treatment strategies to control the pandemic.

On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media.

The paper presents a significant improvement to the implementation of the spectral relaxation method (SRM) for solving nonlinear partial differential equations that arise in the modelling of fluid flow problems. Previously the SRM utilized the spectral method to discretize derivatives in space and finite differences to discretize in time. In this work we seek to improve the performance of the SRM by applying the spectral method to discretize derivatives in both space and time variables.

A bivariate Chebyshev spectral collocation quasilinearization method for nonlinear evolution parabolic equations.

This paper presents a new method for solving higher order nonlinear evolution partial differential equations (NPDEs). The method combines quasilinearisation, the Chebyshev spectral collocation method, and bivariate Lagrange interpolation. In this paper, we use the method to solve several nonlinear evolution equations, such as the modified KdV-Burgers equation, highly nonlinear modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation, and the Fitzhugh-Nagumo equation.