R0R_0 and the global behavior of an age-structured SIS epidemic model with periodicity and vertical transmission

In this paper, we study an age-structured SIS epidemic model with periodicity and vertical transmission. We show that the spectral radius of the Frechet derivative of a nonlinear integral operator plays the role of a threshold value for the global behavior of the model, that is, if the value is less than unity, then the disease-free steady state of the model is globally asymptotically stable, while if the value is greater than unity, then the model has a unique globally asymptotically stable endemic (nontrivial) periodic solution. We also show that the value can coincide with the well-know epidemiological threshold value, the basic reproduction number $\mathcal{R}_0$

Population dynamics and conservation biology of over-exploited Mediterranean red coral.

Abstract The main goal of ecologists is nowadays to foster habitat and species conservation. Life-history tables and Leslie-Lewis transition matrices of population growth can be powerful tools suitable for the study of age-structured over harvested and/or endangered species dynamics. Red coral (Corallium rubrum L 1758) is a modular anthozoan endemic to the Mediterranean Sea. This slow growing, long lived species has been harvested since ancient times. In the last decades harvesting pressure increased and the overall Mediterranean yield reduced by 2 3 . Moreover, mass mortality (putatively-linked to global warming) recently affected some coastal populations of this species. Red coral populations are discrete genetic units, gonochoric, composed by several overlapping generations and provided of a discrete (annual) reproduction. A population of this precious octocoral was studied in detail and its static life table was compiled. In order to simulate the trends overtime of the population under different environmental conditions and fishing pressures, a discrete, non-linear model, based on Leslie-Lewis transition matrix, was applied to the demographic data. In this model a bell-shaped curve, based on experimental data, representing the dependence of recruitment on adult colonies density was included. On these bases the stability of the population under different density, reproduction and mortality figures was analysed and simulations of the population trends overtime were set out. Some simulations were also carried out applying to the studied population the mortality values measured during the anomalous mass mortality event which really affected some red coral populations in 1999. The population under study showed high stability and a strong resilience capability, surviving to a 61% reduction of density, to a 27.7% reduction of reproduction rate and to an unselective harvesting affecting 95% of the reproductive colonies.

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states

The basic approach to age-structured population dynamics: models, methods and numerics

This book provides an introduction to age-structured population modeling which emphasises the connection between mathematical theory and underlying biological assumptions. Through the rigorous development of the linear theory and the nonlinear theory alongside numerics, the authors explore classical equations that describe the dynamics of certain ecological systems. Modeling aspects are discussed to show how relevant problems in the fields of demography, ecology, and epidemiology can be formulated and treated within the theory. In particular, the book presents extensions of age-structured modelling to the spread of diseases and epidemics while also addressing the issue of regularity of solutions, the asymptotic behaviour of solutions, and numerical approximation. With sections on transmission models, non-autonomous models and global dynamics, this book fills a gap in the literature on theoretical population dynamics. The Basic Approach to Age-Structured Population Dynamics will appeal to graduate students and researchers in mathematical biology, epidemiology and demography who are interested in the systematic presentation of relevant models and mathematical methods

Asynchronous growth and competition in a two-sex age-structured population model

Asynchronous exponential growth has been extensively studied in population dynamics. In this paper we find out the asymptotic behaviour in a non-linear age-dependent model which takes into account sexual reproduction interactions. The main feature of our model is that the non-linear process converges to a linear one as the solution becomes large, so that the population undergoes asynchronous growth. The steady states analysis and the corresponding stability analysis are completely made and are summarized in a bifurcation diagram according to the parameter R0. Furthermore the effect of intraspecific competition is taken into account, leading to complex dynamics around steady states