A new numerical method based on the approximation of polynomials is here proposed for solving the one dimensional parabolic partial differential equation arising from unsteady state flow of heat subject to initial and boundary conditions. The method results from discretization of the parabolic partial differential equation which leads to the production of a system of algebraic equations. By solving the system of algebraic equations we obtain the problem approximate solutions.

Differential Transformation Method (DTM) is a very effective tool for solving linear and non-linear ordinary differential equations. This paper uses DTM to solve the mathematical model for the dynamics of Dengue fever in a population. The graphical profiles for human population are obtained using Maple software. The solution profiles give the long term behavior of Dengue fever model which shows that treatment plays a vital role in reducing the disease burden in a population.

A new continuous numerical method based on polynomials approximation is here proposed for solving the equation arising from heat transfer along a copper rod and a hollow tube subject to initial and boundary conditions. The method results from discretization of the heat equation which leads to the production of a system of algebraic equations. By solving the system of algebraic equations we obtain the problem approximate solutions.

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The different definitions of efficiency (in their medical meanings) are presented as the result of metareviews found in scientific databases. Efficacy and efficiency are often mismatched with effectiveness in the research of healthcare systems in different countries.In addition to the classic Bismarck's and Beveridge's models the modern concepts of health systems include personalized medicine, recognition of health as economic value. However, the basic problem in the Polish healthcare system is the low quality of overly specific and often changed legislation COJ Biomed Sci & Res