Summary
It is well known that the partial differential equation of the traditional model describing the dynamics of an age-dependent population is of the first order hyperbolic type. An equation of that type cannot simultaneously accommodate a renewal type birth boundary condition and a death boundary condition by old age (accumulation of aging injury) and thus lacks biological realism (mortality by old age). In this paper a governing equation of a parabolic type is derived to represent the expected size of a stochastically maturing population. Using techniques well known for the solution of parabolic partial differential and Volterra integral equations, the asymptotic behaviour of such a maturing population is discussed. Due to a non-local boundary condition, the boundary value problem encountered appears to be new.
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Gopalsamy, K. Dynamics of maturing populations and their asymptotic behaviour. J. Math. Biology 5, 383–398 (1977). https://doi.org/10.1007/BF00276108
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DOI: https://doi.org/10.1007/BF00276108