Related papers: On characteristics of an ordinary differential equ…
This paper generalizes a previously published differential equation that describes the relation between the age-specific incidence, remission, and mortality of a disease with its prevalence. The underlying model is a simple compartment…
This paper descibes a new method for deriving incidence rates of a chronic disease from prevalence data. It is based on a new ordinary differential equation, which relates the change in the age-specific prevalence to the agespecific…
The illness-death model of a chronic disease consists of the states 'Normal', 'Disease' and 'Death'. In general, the transition rates between the states depend on three time scales: calendar time, age and duration of the chronic disease.…
We study the relation between the age-specific prevalence, incidence and mortality in an illness-death model consisting of the three states Healthy, Ill, Dead. The dependency on three different time scales (age, calendar time, disease…
Recently, we have shown that the age-specific prevalence of a disease can be related to the transition rates in the illness-death model via a partial differential equation (PDE). In case of a chronic disease, we show that the PDE can be…
Aggregated health data such as claims data from health insurances become more and more available for research purposes. Estimates of excess mortality from prevalence and incidence of a chronic condition have only been possible for ages 50…
This paper descibes a new method of calculating the mean duration and mean age of onset of a chronic disease from incidence and mortality rates. It is based on an ordinary differential equation resulting from a simple compartment model.…
The illness-death model for chronic conditions is combined with a renewal equation for the number of newborns taking into account possibly different fertility rates in the healthy and diseased parts of the population. The resulting boundary…
The aim of this article is relating the chemical master equation (CME) to the illness-death model for chronic diseases. We show that a recently developed differential equation for the prevalence directly follows from the CME. As an…
In this paper we introduce the functional framework and the necessary conditions for the well-posedness of an inverse problem arising in the mathematical modeling of disease transmission. The direct problem is given by an initial boundary…
We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the…
Recently, it has been shown that the transition rates of the illness-death model (IDM) for chronic conditions are related to the percentages of people in the states by a three-dimensional system of differential equations [Bri24]. The aim of…
We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…
We use historical data about breathlessness in British coal miners and recent data about diabetes in Germany to illustrate a method for deriving the age-specific incidence from aggregated current status data, i.e. age-specific prevalence…
Aging is thought to be a consequence of intrinsic breakdowns in how genetic information is processed. But mounting experimental evidence suggests that aging can be slowed. To help resolve this mystery, I derive a mortality equation which…
This paper describes types of errors arising in a recently proposed method of incidence estimation from prevalence data. The errors are illustrated by a simulation study about a hypothetical irreversible disease. In addition, a way of…
A compartment epidemic model for infectious disease spreading is investigated, where movement of individuals is governed by spatial diffusion. The model includes infection age of the infected individuals and assumes a logistic growth of the…
Background: A common modelling approach in public health and epidemiology divides the population under study into compartments containing persons that share the same status. Here we consider a three-state model with the compartments: A, B…
In usual demographic analysis, force of mortality is a function of one variable, that is, of age. In this article bi-variate and multivariate force of mortality functions are introduced for the first time to explain mortality differentials.…
It is emphasised that for epidemiological studies where disease incidence is rare, results from conventional proportional hazards models can often correctly estimate causal associations. The well-known "backdoor criteria" from…