Related papers: Illness-death model with renewal
The paper studies some inverse boundary value problem for simplest parabolic equations such that the homogenuous Cauchy condition is ill posed at initial time. Some regularity of the solution is established for a wide class of boundary…
Chronic diseases are long-lasting conditions that require lifelong medical attention. Using big EMR data, we have developed early disease risk prediction models for five common chronic diseases: diabetes, hypertension, CKD, COPD, and…
We study an S--I type epidemic model in an age-structured population, with mortality due to the disease. A threshold quantity is found that controls the stability of the disease-free equilibrium and guarantees the existence of an endemic…
We develop a well-posedness theory for second order systems in bounded domains where boundary phenomena like glancing and surface waves play an important role. Attempts have previously been made to write a second order system consisting of…
Clinical prognostic models help inform decision-making by estimating a patient's risk of experiencing an outcome in the future. The net benefit is increasingly being used to assess the clinical utility of models. By calculating an…
The number of recurrent events before a terminating event is often of interest. For instance, death terminates an individual's process of rehospitalizations and the number of rehospitalizations is an important indicator of economic cost. We…
Medical investigations focusing on patient survival often generate not only a failure time for each patient but also a sequence of measurements on patient health at annual or semi-annual check-ups while the patient remains alive. Such a…
A model describing the dynamics related to the spreading of non-lethal infectious diseases in a fixed-size population is proposed. The model consists of a non-linear delay-differential equation describing the time evolution of the increment…
We propose a tractable dynamic framework for the joint determination of optimal consumption, portfolio choice, and healthcare irreversible investment. Our model is based on a Merton's portfolio and consumption problem, where, in addition,…
Designing proper treatment plans to manage diabetes requires health practitioners to pay heed to the individuals remaining life along with the comorbidities affecting them. Older adults with Type 2 Diabetes Mellitus (T2DM) are prone to…
A parameter-dependent model involving nonlinear diffusion for an age-structured population is studied. The parameter measures the intensity of the mortality. A bifurcation approach is used to establish existence of positive equilibrium…
Undulation of infection levels, usually called waves, are not well understood. In this paper we propose a mathematical model that exhibits undulation and decay towards a stable state. The model is a re-interpretation of the original…
To explore the mechanistic relationships between ageing, frailty and mortality, we developed a computational model in which possible health attributes are represented by the nodes of a complex network. Each node can be either damaged (i.e.…
We study the boundary regularity properties and derive a priori pointwise supremum estimates of weak solutions and their derivatives in terms of suitable weighted $L^2$-norms for a class of degenerate parabolic equations that satisfy…
We consider a mixed type boundary value problem for a class of degenerate parabolic-hyperbolic equations. Namely, we consider a Cartesian product domain and split its boundary into two parts. In one of them we impose a Dirichlet boundary…
Multimorbidity, the co-occurrence of two or more chronic diseases such as diabetes, obesity or cardiovascular diseases in one patient, is a frequent phenomenon. To make care more efficient, it is of relevance to understand how different…
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…
\noindent We formulate an age-structured three-staged nonlinear partial differential equation model that features {\it nonlinear} recidivism to the infected ({\it infectious}) class from the {\it temporarily} recovered class. Equilibria are…
We consider the existence and uniqueness of solutions of an initial-boundary value problem for a coupled system of PDE's arising in a model for Alzheimer's disease. Apart from reaction diffusion equations, the system contains a transport…
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…