Gompertz law in simple computer model of aging of biological population

We propose a new deterministic growth model which captures certain features of both the Gompertz and Korf laws. We investigate its main properties, with special attention to the correction factor, the relative growth rate, the inflection point, the maximum specific growth rate, the lag time and the threshold crossing problem. Some data analytic examples and their performance are also considered. Furthermore, we study a stochastic counterpart of the proposed model, that is a l...

In this paper, we advance the network theory of aging and mortality by developing a causal mathematical model for the mortality rate. First, we show that in large networks, where health deficits accumulate at nodes representing health indicators, the modeling of network evolution with Poisson processes is universal and can be derived from fundamental principles. Second, with the help of two simplifying approximations, which we refer to as mean-field assumption and homogeneity...

Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which characterizes the dynamics of an evolving population with a given maximum age. Remarkably, while the spectrum of eigenvalues that govern the evolution depends on the fitness, how they change with the maximum age is independent of fitness. Thi...

Many cell populations, exemplified by certain tumors, grow approximately according to a Gompertzian growth model which has a slower approach to an upper limit than that of logistic growth. Certain populations of animals and other organisms have also recently been analyzed with the Gompertz model. This article addresses the question of how long it takes to reduce the population from one level to a lower one under a schedule of sudden decrements, each of which removes a given f...

What is aging? Mechanistic answers to this question remain elusive despite decades of research. Here, we propose a mathematical model of cellular aging based on a model gene interaction network. Our network model is made of only non-aging components - the biological functions of gene interactions decrease with a constant mortality rate. Death of a cell occurs in the model when an essential gene loses all of its interactions to other genes, equivalent to the deletion of an ess...

The chronological age used in demography describes the linear evolution of the life of a living being. The chronological age cannot give precise information about the exact developmental stage or aging processes an organism has reached. On the contrary, the biological age (or epigenetic age) represents the true evolution of the tissues and organs of the living being. Biological age is not always linear and sometimes proceeds by discontinuous jumps. These jumps can be positive...

The Penna model is a model of evolutionary ageing through mutation accumulation where traditionally time and the age of an organism are treated as discrete variables and an organism's genome by a binary bit string. We reformulate the asexual Penna model and show that, a universal scale invariance emerges as we increase the number of discrete genome bits to the limit of a continuum. The continuum model, introduced by Almeida and Thomas in [Int.J.Mod.Phys.C, 11, 1209 (2000)] ca...

This paper considers a nonlinear model for population dynamics with age structure. The fertility rate with respect to age is non constant and has the form proposed by [17]. Moreover, its multiplicative structure and the multiplicative structure of mortality makes the model separable. In this setting it is shown that the number of births in unit time is given by a system of nonlinear ordinary differential equations. The steady state solution together with the equilibrium solut...

Infant deaths and old age deaths are very different. The former are mostly due to severe congenital malformations of one or a small number of specific organs. On the contrary, old age deaths are largely the outcome of a long process of deterioration which starts in the 20s and affects almost all organs. In terms of age-specific death rates, there is also a clear distinction: the infant death rate falls off with age, whereas the adult and old age death rate increases exponenti...

Comment on "Classification Scheme for Phenomenological Universalities in Growth Problems in Physics and Other Sciences" by P. Castorina, P. P. Delsanto and C. Guiot, Phys. Rev. Lett. {\bf 96}, 188701 (2006) is presented. It has been proved that the West-like function of growth derived by the authors is incorrect and the approach does not take into account the growth of the biological systems undergoing atrophy or demographic and economic systems undergoing involution or regre...