On the final size of epidemics within herds

We are concerned with an epidemic in a closed population under the assumption that the per capita number of contacts remains constant, when population size diminishes due to the fatal consequences of the disease. We focus on the final size as a function of the basic reproduction ratio $R_0$ (which now is independent of population size!) and the survival probability $f$. Mathematically the model is described by a nonlinear Volterra integral equation of convolution type, just as the general Kermack-McKendrick model