Related papers: Approximating reproduction numbers: a general nume…
The prediction of critical transitions, such as extinction events, is vitally important to preserving vulnerable populations in the face of a rapidly changing climate and continuously increasing human resource usage. Predicting such events…
The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to…
This paper investigates a nonlinear logistic model for age-structured population dynamics. The model incorporates interdependent fertility and mortality functions within a logistic framework, offering insights into stationary solutions and…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
Modifying the Redfield model of sexual reproduction and the Penna model of biological aging, we compare reproduction with and without recombination in age-structured populations. In contrast to Redfield and in agreement with Bernardes we…
A stochastic genetic model for biological aging is introduced bridging the gap between the bit-string Penna model and the Pletcher-Neuhauser approach. The phenomenon of exponentially increasing mortality function at intermediate ages and…
The basic reproduction number, $R_0$, is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating $R_0$ from incidence data early in the epidemic can lead to an over-estimation of this quantity. In…
For birth-and-death processes, we show that every initial distribution is reproduced from the first hitting time distribution. The reproduction is done by applying to the distribution function a differential operator defined through the…
In this paper, we propose a numerical scheme for structured population models defined on a separable and complete metric space. In particular, we consider a generalized version of a transport equation with additional growth and non-local…
Since the 1940s, population projections have in most cases been produced using the deterministic cohort component method. However, in 2015, for the first time, in a major advance, the United Nations issued official probabilistic population…
Finite mixture models are used in statistics and other disciplines, but inference for mixture models is challenging due, in part, to the multimodality of the likelihood function and the so-called label switching problem. We propose…
For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are…
Mathematical and computational modeling approaches are increasingly used as quantitative tools in the analysis and forecasting of infectious disease epidemics. The growing need for realism in addressing complex public health questions is…
Age-specific mortality rates are often disaggregated by different attributes, such as sex, state and ethnicity. Forecasting age-specific mortality rates at the national and sub-national levels plays an important role in developing social…
We consider a size-structured model for cell division and address the question of determining the division (birth) rate from the measured stable size distribution of the population. We formulate such question as an inverse problem for an…
The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to…
Ignoring the differences between countries, human reproductive and dispersal behaviors can be described by some standardized models, so whether there is a universal law of population growth hidden in the abundant and unstructured data from…
Epidemic models are a valuable tool in the decision making process. Once a mathematical model for an epidemics has been established, the very next step is calculating a mathematical expression for the basic reproductive number, $R_0$, which…
These notes provide a review of basic stochastic population models including branching processes and models of population genetics. Measure-valued population models including superprocesses and Fleming-Viot processes are also introduced…
We study a general class of birth-and-death processes with state space $\mathbb{N}$ that describes the size of a population going to extinction with probability one. This class contains the logistic case. The scale of the population is…