Clustering of independently diffusing individuals by birth and death processes

We study analytically a model for the dynamics of populations and epidemics that includes birth and death processes in a system of independently diffusing individuals. When birth and death rates are close to each other, the individuals tend to cluster around their center of mass and the population (disease) territory migrates as a whole. The clustering phenomenon is caused by the natural asymmetry between birth and death processes, and does not require any communication among the individuals or between the individuals and the substrate.