We apply the POD-DEIM model order reduction to the propagation of the transmembrane potential along $1$D muscle fibers. This propagation is represented using the monodomain partial differential equation. The monodomain equation, which is a reaction-diffusion equation, is coupled through its reaction term with a set of ordinary differential equations, which provide the ionic current across the cell membrane. Due to the strong coupling of the transmembrane potential and ionic state variables, we reduce them all together proposing a total reduction strategy. We compare the current strategy with the conventional strategy of reducing the transmembrane potential. Considering the current approach, the discrete system matrix is slightly modified to adjust for the size. However, size of the precomputed reduced system matrix remains the same, which means the same computational cost. The current approach appears to be four orders of magnitude more accurate considering the equivalent number of modes on the same grid in comparison to the conventional approach. Moreover, it shows a faster convergence in the number of POD modes with respect to the grid refinement. Using the DEIM approximation of nonlinear functions in combination with the total reduction, the nonlinear functions corresponding to the ionic state variables are also approximated besides the nonlinear ionic current in the monodomain equation. For the current POD-DEIM approach, it appears that the same number of DEIM interpolation points as the number of POD modes is the optimal choice regarding stability, accuracy and runtime.