A Mathematical Model for Weight Gain in Farm Animals Based on Feed Diffusion and Digestibility

Abstract

This study introduces a spatio-temporal mathematical model to predict weight gain in farm animals based on the diffusion and assimilation of feed within the organism. The model is formulated using a modified form of Fick’s second law, incorporating spatially and temporally varying diffusion coefficient D(x,T) and feed digestibility parameter K(x,T), while accounting for the nonlinearity of the biological process and the influence of body temperature. An analytical solution is developed employing the method of averaging of function corrections up to the second-order approximation. This approach enables the determination of the spatio-temporal distribution of feed concentration, the mass of digested and undigested feed, and the portion of assimilated nutrients allocated to body weight increase versus maintenance requirements. The model successfully reproduces typical growth curves and demonstrates that increasing the diffusion coefficient or digestibility parameter enhances weight gain. Conditions for accelerating or decelerating the fattening process are formulated, offering a useful tool for optimizing feeding strategies and improving the efficiency of livestock production.