In this work, we have used the infinity-norm penalty function to select the best-fit model parameters which define a system of first order ordinary differential equations that describe the interaction between two corrosion penetration data over a time interval. For this particular problem, the estimated best-fit model parameters are the intrinsic growth rate of the first corrosion population which has the value of -0.5092 followed by the intraspecific coefficient which has the value of -0.1570. The other model parameters are estimated under some simplifying assumptions. The precise steady-state solutions are (0,0), (0, 0.3500), (3.2433, 0) and (1.2817, 2.5664).