An epidemic equation with immigration

Abstract We formulate a model of single-species population growth in which there is immigration into the population at any prescribed rate and with any prescribed age distribution. Births are assumed to be density-dependent but not dependent on the age distribution in the population. Deaths may be according to any age distribution. The model results in a non-linear, non-homogeneous integral equation with delay. This equation is also shown to be a model for growth of capital and for certain epidemics. Behavior of solutions as t tends to infinity is investigated, with the aid of theorems of Levin, Shea, Londen, and Karlin, when the forcing term tends to a constant limit.