Related papers: Approximating reproduction numbers: a general nume…
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…
This study introduces a novel epidemiological model that expands upon the Kermack-McKendrick model by incorporating the age of infection and reinfection. By including infection age, we can classify participants, which enables a more…
We develop a linear one-sex dynamical model of human population reproduction through marriage. In our model, a woman may marry and divorce multiple times; however, only women who are currently married are assumed to bear children. The…
This article presents a comprehensive study of the continuous McKendrick model, which serves as a foundational framework in population dynamics and epidemiology. The model is formulated through partial differential equations that describe…
Renewal models are widely used in statistical epidemiology as semi-mechanistic models of disease transmission. While primarily used for estimating the instantaneous reproduction number, they can also be used for generating projections,…
The simple (linear) birth-and-death process is a widely used stochastic model for describing the dynamics of a population. When the process is observed discretely over time, despite the large amount of literature on the subject, little is…
The basic reproduction number, $R_0$ is an important and widely used concept in the study of infectious diseases. We briefly review the recent trend of calculating the average of various $R_0$ estimates in systematic reviews aimed at…
A new age-structured diffusive model for the mathematical modelling of epidemics is suggested. The model can be considered as a generalization of two models suggested earlier for the same purposes. The Lie symmetry classification of the…
The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak.…
In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and…
Inference of the reproduction number through time is of vital importance during an epidemic outbreak. Typically, epidemiologists tackle this using observed prevalence or incidence data. However, prevalence and incidence data alone is often…
Matrix population models have proved popular and useful for studying stage-structured populations in quantitative ecology. The goal of this paper is to develop and analyze a general matrix population model that is applicable to the…
What is a population? This review considers how a population may be defined in terms of understanding the structure of the underlying genetics of the individuals involved. The main approach is to consider statistically identifiable groups…
We study a linear model of McKendrick-von Foerster-Keyfitz type for the temporal development of the age structure of a two-sex human population. For the underlying system of partial integro-differential equations, we exploit the semigroup…
This paper aims to develop practical applications of the model for the highly technical measure-valued populations developed by the authors in \cite{FanEtal20}. We consider the problem of estimation of parameters in the general age and…
We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a…
During an epidemic outbreak, decision makers crucially need accurate and robust tools to monitor the pathogen propagation. The effective reproduction number, defined as the expected number of secondary infections stemming from one…
In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective…
We study the population profile in a simple discrete time model of population dynamics. Our model, which is closely related to certain ``bit-string'' models of evolution, incorporates competition for resources via a population dependent…
Fertility differentials by urban-rural residence and nativity of women in Australia significantly impact population composition at sub-national levels. We aim to provide consistent fertility forecasts for Australian women characterized by…