Related papers: Illness-death model with renewal
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…
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…
In this article, we use the illness-death model to present a mathematical framework for studying the compression of morbidity (COM) hypothesis. It turns out that questions about COM are completely determined by the transition rates in the…
In this work we examine the properties of a recently described ordinary differential equation that relates the age-specific prevalence of a chronic disease with the incidence and mortalities of the diseased and healthy persons. The equation…
We present a unified framework ensuring well posedness and providing stability estimates to a class of Initial Boundary Value Problems for renewal equations comprising a variety of biological or epidemiological models. This versatility is…
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.…
During infectious disease outbreaks, estimates of time-varying pathogen transmissibility, such as the instantaneous reproduction number R(t) or epidemic growth rate r(t), are used to inform decision-making by public health authorities. For…
A widely-used model for determining the long-term health impacts of public health interventions, often called a "multistate lifetable", requires estimates of incidence, case fatality, and sometimes also remission rates, for multiple…
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…
This article proposes an age-structured compartment model for irreversible diseases with a pre-clinical state of undiagnosed cases that precedes the diagnosis. The model is able to cope with mortality rates differing between the…
Compartmental models are popular in the mathematics of epidemiology for their simplicity and wide range of applications. Although they are typically solved as initial value problems for a system of ordinary differential equations, the…
We prove existence and uniqueness of solutions, continuous dependence from the initial datum and stability with respect to the boundary condition in a class of initial--boundary value problems for systems of balance laws. The particular…
Relevant events in a three state illness-death model (IDM) of a chronic disease are the diagnosis of the disease and death with or without the disease. In this article a simulation framework for populations moving in the IDM is presented.…
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…
This article describes a method to estimate the mortality rate ratio R from current status data with duration in a chronic condition in case the general mortality of the overall population is known. Apart from the general mortality, the…
Recently, we have proposed a new illness-death model that comprises a state of undiagnosed chronic disease preceding the diagnosed disease. Based on this model, the question arises how case-finding can be assessed in the presence of…
This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly…
Recently, we proposed an state model (compartment model) to describe the progression of a chronic disease with an pre-clinical (undiagnosed) state before clinical diagnosis. It is an open question, if a sequence of cross-sectional studies…
The UK Biobank is a large-scale health resource comprising genetic, environmental and medical information on approximately 500,000 volunteer participants in the UK, recruited at ages 40--69 during the years 2006--2010. The project monitors…
The recent increase in morbidity is primarily due to chronic diseases including Diabetes, Heart disease, Lung cancer, and brain tumours. The results for patients can be improved, and the financial burden on the healthcare system can be…