Mathematical model based on the Jeffreys type equation for description of gene expression

The classical diffusion model widely used for description of transport processes results, in general, in an infinite velocity of particles propagation. It is hardly applicable to the description of protein transport in biological systems, containing heavy molecules. In the 1950s the Jeffreys type equation was applied to govern the motion of rheological substances. Later, using this equation, the transport problem statement was modified to consider the gene expression in fruit fly embryo, and the model equation for protein concentration was proposed. The numerical solution of the coupled Jeffreys type equations with nonlinear terms is found for description of gap gene expression in early Drosophila embryo development and compared with the experimental data.