  We study the movement of the living organism in a band form towards the
presence of chemical substrate based on a system of partial differential
evolution equations. We incorporate the Einstein's method of Brownian motion to
deduce the chemotactic model exhibiting travelling band. It is the first time
that Einstein method has been used to motivate equations describing mutual
interaction of chemotactic system. In addition to considering chemotactic
response and the random motion of organism, we also consider the formation of
crowd by organism via interactions within or between the community. This crowd
effect can also be seen as any organism travel or migrate in a herd or group in
search of food. We have shown that in the presence of limited and unlimited
substrate traveling bands are achievable and it has been explained accordingly.
