Non-linear age-dependent population dynamics

where P( t ) is the total population at time t and 5 is the growth modulus. This law is clearly inapplicable to situations in which the population competes for resources (e.g., space and food), for in these situations 5 should depend on the size of the population: the larger the population, the slower should be its rate of growth. To overcome this deficiency in the Malthusian law, VERHULST [1845, 1847] assumed that f i= (6o-co0 P ) P (5o, COo=constant). (1.2)