Various swelling drug delivery devices are promising materials for control drug delivery because of their ability to swell and release entrapped therapeutics, in response to physiological stimuli. Previously, many mathematical models have been developed to predict the mechanism of drug release from a swelling device. However, some of these models do not consider the changes in diffusion behaviour as the device swells. Therefore, we used a two-phase approach to simplify the mathematical model considering the effect of swelling on the diffusion coefficient. We began by defining a moving boundary problem to consider the swelling process. Landau transformation was used for mitigating the moving boundary problem. The transformed problem was analytically solved using the separation of variables method. Further, the analytical solution was extended to include the drug release in two phases where each phase has distinct diffusion coefficient and continuity condition was applied. The newly developed model was validated by the experimental data of bacterial cellulose hydrogels using the LSQCURVEFIT function in MATLAB. The numerical test showed that the new model exhibited notable improvement in curve fitting, and it was observed that the initial effective diffusion coefficient of the swelling device was lower than the later effective diffusion coefficient.

The decision-making trial and evaluation laboratory (DEMATEL) has been used to solve numerous multicriteria decision-making (MCDM) problems, where real numbers are utilised in defining linguistic variables. Although the DEMATEL has shown its success in solving many decision-making problems, researchers have not fully understood how the DEMATEL works on non-real-number linguistic variables. Recent discovery of single-valued neutrosophic sets (SVNSs) can offer a new method to solve decision-making problems, where three memberships of SVNSs are used to define experts’ linguistic judgment. This paper aims to propose a novel MCDM method, where SVNSs and the DEMATEL are fully utilised. Different from the DEMATEL, which directly utilises real numbers, this proposed method introduces SVNSs to better deal with truth, indeterminacy, and falsity in solving MCDM problem. As an application of the proposed method, subcontractors’ selection problem is investigated using the proposed method, where four types of criteria are developed. A group of experts were invited to provide opinions and linguistic judgment regarding the degree of influence between criteria of subcontractors’ selection. The linguistic evaluations defined in SVNSs were computed using the eight-step procedures of the proposed method. Based on the degree of influence, the computational results successfully segregated all ten criteria into four types, in which two to three criteria are grouped in each type. The results also suggest that “Experience” and “Quality” are the most influential criteria in subcontractors’ selection. The segregation based on degree of influence would be greatly significant for the practical implementation of the subcontractors’ selection.

This paper discusses the development and the analytical solution of a mathematical model based on drug release system from a swelling delivery device. The mathematical model is represented by a one-dimensional advection-diffusion equation with nonhomogeneous moving boundary condition. The solution procedures consist of three major steps. Firstly, the application of steady state solution method, which is used to transform the nonhomogeneous moving boundary condition to homogeneous boundary condition. Secondly, the application of the Landau transformation technique that gives a significant impact in removing the advection term in the system of equation and transforming the moving boundary condition to a fixed boundary condition. Thirdly, the used of separation of variables method to find the analytical solution for the resulted initial boundary value problem. The results show that the swelling rate of delivery device and drug release rate is influenced by value of growth factor r.

Hydrogel is known as a good drug delivery material. The hydrogel characteristic of swelling upon contact with fluid helps in delivering the drug in a controlled manner. However this phenomenon makes the mathematical model more complicated. In this study, an analytical solution is discussed and tested in order to illustrate the drug release from a logistically swelling hydrogel. The model of drug release is developed using the advection-diffusion equation. The Landau transformation is used to simplify the model of drug release, and the separation of variables method is used to obtain the equation for the concentration of drug release from the swelling hydrogel. The result is illustrated by MATLAB software with various values of growth rates and diffusion coefficients.