Related papers: Illness-death model with renewal

The mortality rate of many complex multicellular organisms increase with age, which suggests that net aging damage is accumulative, despite remodeling processes. But how exactly do little mishaps in the cellular level accumulate and spread…

We consider the well-posedness of models involving age structure and non-linear diffusion. Such problems arise in the study of population dynamics. It is shown how diffusion and age boundary conditions can be treated that depend…

A common problem in health research is that we have a large database with many variables measured on a large number of individuals. We are interested in measuring additional variables on a subsample; these measurements may be newly…

Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…

We consider a boundary value problem of the stationary transport equation with the incoming boundary condition in two or three dimensional bounded convex domains. We discuss discontinuity of the solution to the boundary value problem…

Semi-competing risks refers to the survival analysis setting where the occurrence of a non-terminal event is subject to whether a terminal event has occurred, but not vice versa. Semi-competing risks arise in a broad range of clinical…

We study a Neumann type initial-boundary value problem for strongly degenerate parabolic-hyperbolic equations under the nonlinearity-diffusivity condition. We suggest a notion of entropy solution for this problem and prove its uniqueness.…

In this work, we consider the problem of predicting the course of a progressive disease, such as cancer or Alzheimer's. Progressive diseases often start with mild symptoms that might precede a diagnosis, and each patient follows their own…

To better understand mortality change with age capturing the variability in individuals' rates of aging, we performed comprehensive analysis of statistical properties of a cumulative index of age-associated disorders (deficits), called a…

Compartmental models have long served as important tools in mathematical epidemiology, with their usefulness highlighted by the recent COVID-19 pandemic. However, most of the classical models fail to account for certain features of this…

In this article we study a class of generalised linear systems of difference equations with given boundary conditions and assume that the boundary value problem is non-consistent, i.e. it has infinite many or no solutions. We take into…

We deal with some generalizations on a Black--Scholes model arising in financial mathematics. As novelty in this paper, we consider a variable volatility and abstract functional boundary conditions, which allow us to treat a very large…

Stochastic modelling of fatigue (and other material's deterioration), as well as of cumulative damage in risk theory, are often based on compound sums of independent random variables, where the number of addends is represented by an…

We consider multiple diseases spreading in a static Configuration Model network. We make standard assumptions that infection transmits from neighbor to neighbor at a disease-specific rate and infected individuals recover at a…

The rise in chronic diseases over the last century presents a significant health and economic burden globally. Here we apply evolutionary medicine and life history theory to better understand their development. We highlight an imbalanced…

We investigate the global dynamics of a general Kermack-McKendrick-type epidemic model formulated in terms of a system of renewal equations. Specifically, we consider a renewal model for which both the force of infection and the infected…

In this paper, within scaling invariance theory, we define and apply to the numerical solution of a similarity boundary layer model an iterative transformation method. The boundary value problem to be solved depends on a parameter and is…

We collect examples of boundary-value problems of Dirichlet and Dirichlet-Neumann type which we found instructive when designing and analysing numerical methods for fully nonlinear elliptic partial differential equations. In particular, our…

In studies of recurrent events, joint modeling approaches are often needed to allow for potential dependent censoring by a terminal event such as death. Joint frailty models for recurrent events and death with an additional dependence…

We present some analytic results for the steady states of the Penna model of sen escence, generalised to allow genetically identical individuals to die at differ ent ages via an arbitrary survival function. Modelling this with a Fermi…