Aggregating pattern dynamics in a chemotaxis model including growth

A population model including diffusion, chemotaxis and growth is studied. Assuming that the diffusion rate and the chemotactic rate are both very small compared with the growth rate, we derive a new equation to describe the time-evolution of the aggregating region of biological individuals and show the conditions for the existence and stability of radially symmetric equilibrium solutions of the equation, which indicate the aggregation of individuals.