We prove existence of upper and lower solutions in reverse order with respect a part of the variables in a system of nonlinear ordinary dierential equations modelling acidogenesis in anaerobic digestion.The corresponding existence theorems are established.The upper and lower solutions are constructed analytically, by dening semi-trivial solutions for each of the variables in the model.We introduce the concept of indicator semi-trivial solutions.Finally, we numerically solve the system supported by the Matlab software and matching the graphs of the numerical solutions with analytical solutions is found.