Flowers of immortality

Traditionally, population models distinguish individuals on the basis of their current state. Given a distribution, a discrete time model then specifies (precisely in deterministic models, probabilistically in stochastic models) the population distribution at the next time point. The renewal equation alternative concentrates on newborn individuals and the model specifies the production of offspring as a function of age. This has two advantages: (i) as a rule, there are far fe...

This paper presents an age structured problem modelling mosquito blood-feeding plasticity in a natural environment. We first investigate the analytical asymptotic solution through studying the spectrum of an operator $\mathbb{A}$ which is the infinitesimal generator of a $C_0$-semigroup. Indeed, the study of the spectrum of $\mathbb{A}$ {\it per se} is interesting. Additionally, we get the existence and nonexistence of nonnegative steady solutions under some conditions.

Economic and ecological models can be extremely complex, with a large number of agents/species each featuring multiple dynamical quantities. In an attempt to understand the generic stability properties of such systems, we define and study an interesting new matrix ensemble with extensive correlations. We find analytically the boundary of its eigenvalue spectrum in the complex plane, as a function of the correlations determined by the model at hand. We solve numerically our eq...

A population is considered stationary if the growth rate is zero and the age structure is constant. It thus follows that a population is considered non-stationary if either its growth rate is non-zero and/or its age structure is non-constant. We propose three properties that are related to the stationary population identity (SPI) of population biology by connecting it with stationary populations and non-stationary populations which are approaching stationarity. One of these i...

In a complex network, different groups of nodes may have existed for different amounts of time. To detect the evolutionary history of a network is of great importance. We present a general method based on spectral analysis to address this fundamental question in network science. In particular, we argue and demonstrate, using model and real-world networks, the existence of positive correlation between the magnitudes of eigenvalues and node ages. In situations where the network...

Complex systems, in many different scientific sectors, show coarse-grain properties with simple growth laws with respect to fundamental microscopic algorithms. We propose a classification scheme of growth laws which includes human aging, tumor (and/or tissue) growth, logistic and generalized logistic growth and the aging of technical devices. The proposed classification permits to evaluate the aging/failure of combined new bio-technical "manufactured products", where part of ...

Lifespan distributions of populations of quite diverse species such as humans and yeast seem to surprisingly well follow the same empirical Gompertz-Makeham law, which basically predicts an exponential increase of mortality rate with age. This empirical law can for example be grounded in reliability theory when individuals age through the random failure of a number of redundant essential functional units. However, ageing and subsequent death can also be caused by the accumula...

Author's early work on aging is developed to yield a relationship between life spans and the velocity of aging. The mathematical analysis shows that the mean extent of the advancement of aging throughout one's life is conserved, or equivalently, the product of the mean life span, and the mean rate of aging is constant. The result is in harmony with our experiences: It accounts for the unlimited replicability of tumor cells, and predicts the prolonged life spans of hibernating...

Infinite Leslie matrices, introduced by Demetrius forty years ago are mathematical models of age-structured populations defined by a countable infinite number of age classes. This article is concerned with determining solutions of the discrete dynamical system in finite time. We address this problem by appealing to the concept of kneading matrices and kneading determinants. Our analysis is applicable not only to populations models, but to models of self-reproducing machines a...

We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak assumptions, and deduce from it the long-time convergence. The main difficulty comes from natural degeneracy of birth terms that we overcome with a regularization technique. We then extend the results to the case with several parameters and recall ...