Related papers: Approximating reproduction numbers: a general nume…
We analyse the infection-age-dependent SIR model from a numerical point of view. First, we present an algorithm for calculating the solution the infection-age-structured SIR model without demography of the background host. Second, we…
In this paper, we consider the infection-age-dependent Kermack--McKendrick model in which host individuals are distributed in a continuous state space. To provide a mathematical foundation for the heterogeneous model, we develop a…
The United Nations (UN) issued official probabilistic population projections for all countries to 2100 in July 2015. This was done by simulating future levels of total fertility and life expectancy from Bayesian hierarchical models, and…
We introduce a model-agnostic procedure to construct prediction intervals for the age distribution of deaths. The age distribution of deaths is an example of constrained data, which are nonnegative and have a constrained integral. A…
In this paper we consider epidemic models of directly transmissible SIR (susceptible $\to$ infective $\to$ recovered) and SEIR (with an additional latent class) infections in fully-susceptible populations with a social structure, consisting…
We numerically address the stability analysis of linear age-structured population models with nonlocal diffusion, which arise naturally in describing dynamics of infectious diseases. Compared to Laplace diffusion, models with nonlocal…
The time varying effective reproduction number is an important parameter for communication and policy decisions during an epidemic. In this paper, we present new statistical methods for estimating the reproduction number based on the…
The United Nations released official probabilistic population projections (PPP) for all countries for the first time in July 2014. These were obtained by projecting the period total fertility rate (TFR) and life expectancy at birth ($e_0$)…
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 propose a new regularization technique based on a…
Infection can spread easily on networks with heterogeneous degree distribution. Here, we considered targeted immunization on such networks, wherein a fraction of individuals with the highest connectivity are immunized. To quantify the…
A probability model is presented for the dynamics of mutation-selection balance in a haploid infinite-population infinite-sites setting sufficiently general to cover mutation-driven changes in full age-specific demographic schedules. The…
The basic and effective reproduction numbers are widely used metrics for characterizing the dynamics of infectious disease epidemics. However, the interpretation of these numbers is based on the assumption of homogeneous mixing and may not…
This article reviews quantitative methods to estimate the basic reproduction number of pandemic influenza, a key threshold quantity to help determine the intensity of interventions required to control the disease. Although it is difficult…
We formulate a general age-of-infection epidemic model with two pathways: the symptomatic infections and the asymptomatic infections. We then calculate the basic reproduction number $\mathcal{R}_0$ and establish the final size relation. It…
The probability of the survival of the population of individuals of both sexes of given mature age, procreation rate and structure stability has been searched in the numerical experiment. The populations with long period of reproduction and…
We consider a nonlinear structured population model with a distributed recruitment term. The question of the existence of non-trivial steady states can be treated (at least!) in three different ways. One approach is to study spectral…
A general multi-type population model is considered, where individuals live and reproduce according to their age and type, but also under the influence of the size and composition of the entire population. We describe the dynamics of the…
We develop a general modelling framework for compartmental epidemiological systems structured by continuous variables which are linked to the levels of expression of compartment-specific traits. We start by formulating an individual-based…
We are interested in a stochastic model of trait and age-structured population undergoing mutation and selection. We start with a continuous time, discrete individual-centered population process. Taking the large population and rare…
This paper is concerned with the evolution of haploid organisms that reproduce asexually. In a seminal piece of work, Eigen and coauthors proposed the quasispecies model in an attempt to understand such an evolutionary process. Their work…