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A positive-bounded explicit finite-difference method is presented to approximate the solutions of a biological system that describes the interaction between a microbial colony and a surrounding substrate.The mathematical model is a nonlinear parabolic partial differential equations system with nonlinear diffusion and reaction.The development process of a microbial colony is formed by an active portion,an inert component and the contribution of extra-cellular polymeric substances.Our novel finite-difference(FD)scheme is designed to transfer the nonlinear terms in the PDE into discrete sets of linear ones that can be solved very efficiently by computers,while ensuring positive and bounded numerical solution,provided that the initial solutions is positive and bounded.Our examples have shown the fact that the numerical solution can be ensured non-negative and bounded to simulate the actual physics.Numerical examples have also been presented to demonstrate the efficiency of the proposed scheme.