On the growth of a population dependent on ages and involving resources and pollution
Haimovici, A.
Mathematical Biosciences 43(3-4): 213-238
1979
ISSN/ISBN: 0025-5564 DOI: 10.1016/0025-5564(79)90050-6Document Number: 372602
Gurtin and MacCamy (1974) gave 5 equations [(S1)-(S5)] are defining a mathematical model for growth of a population depending on resources and pollution. With .rho.(a,t) being the number of individuals of age a at moment t: (S1) describes the variation of .rho. postulated to be proportional to .rho. itself; (S2) gives the total population at moment t; (S3), gives the number of offspring B(t) at moment t, (.beta. being the birth modulus) and (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. In certain restrictive situations, stability and asymptotic stability conditions are also proved.