The endocytosis of bacteria by mammalian cells is analogous process to endocytosis of chemical substances that bind the receptors on the mammalian cell surface. Therefore kinetic equation that describes endocytosis can be applied to the problem (Douglas A.Lauffenburger Jennifer J. Linderman, Receptors):

Rs - number of the free receptors on the cell surfsce
Cs – number of receptor ligand complexses on the cell surface
Rti – Total number of free and bound receptors In the endosome
Li - the amount of intracellular ligand per cell
fr – endocytosed receptors
fl – endocytosed ligands
L - ligand concentration In the medium
Vs - rate of the New receptor synthesis and expression on the cell surface

In case of endocytosis of bacteria by mammalian cells the ligand refers to a bacterial cell and fluid phase uptake ( kfpNavL-not included in the equation) is not relevant