Starting from a paper of M. E. Gurtin and R. C. MacCamy [1], Eqs. (S1)-(S5) are the mathematical model of the growth of a population depending on resources and pollution, ρ(a,t) being the number of individuals of age a at moment t: (S1) describes the variation of ρ postulated to be proportional to ρ itself; (S2) gives the total population at moment t; in (S3), B(t) is number of offspring at moment t, β being the birth modulus; finally, (S4)-(S5) describe the variation of resources and pollution degrees, depending on the number of individuals of all ages. Existence and uniqueness theorems are proved as well as-in certain restrictive situations-stability and asymptotic stability conditions. © 1979.
