Parabolic equations in which advection-diffusion transports are coupled to reactions termsarise in different science and engineering fields, including physical and biological systems.Usually, in practical applications the unknowns are concentration of chemical compounds orpopulation sizes being positive also from their physical nature as well. Widely used schemessuch as classical finite difference may produce numerical drawbacks such as spurious oscillationsand negative values in the solution because of truncation errors and may then becomeunstable. By using the nonstandard finite difference (NSFD) method, a better finite differencemodel is constructed. The proposed NSFD scheme, guarantees the positivity of the solutionsand returns spurious oscillations free, solutions.