  The present study focuses on the receptor driven endocytosis typical of viral
entry into a cell. A locally increased density of receptors at the time of
contact between the cell and the virus is necessary in this case. The virus is
considered as a substrate with fixed receptors on its surface, whereas the
receptors of the host cell are free to move over its membrane, allowing a local
change in their concentration. In the contact zone the membrane inflects and
forms an envelope around the virus. The created vesicle imports its cargo into
the cell. This paper assumes the diffusion equation accompanied by boundary
conditions requiring the conservation of binders to describe the process.
Moreover, it introduces a condition defining the energy balance at the front of
the adhesion zone. The latter yields the upper limit for the size of virus
which can be engulfed by the cell membrane. The described moving boundary
problem in terms of the binder density and the velocity of the adhesion front
is well posed and numerically solved by using the finite difference method. The
illustrative examples have been chosen to show the influence of the process
parameters on the initiation and the duration of the process.
