Related papers: Illness-death model with renewal
We study initial boundary value problems for linear scalar partial differential equations with constant coefficients, with spatial derivatives of {\em arbitrary order}, posed on the domain $\{t>0, 0<x<L\}$. We first show that by analysing…
The existence and local stability of some non-negative equilibrium points of a class of SIRS infectious disease models with non-linear infection and treatment rates are investigated under the condition that the total population is a…
Solutions of boundary value problems for a diffusion equation of fractional and variable order in differential and difference settings are studied. It is shown that the method of energy inequalities is applicable to obtaining a priori…
Currently emerging "big data" techniques are reshaping medical science into a data science. Medical claims data allow assessing an entire nation's health state in a quantitative way, in particular with regard to the occurrences and…
Healthiness is a good old question in program logics that dates back to Dijkstra. It asks for an intrinsic characterization of those predicate transformers which arise as the (backward) interpretation of a certain class of programs. There…
An initial boundary value problem of the nonlinear diffusion equation with a dynamic boundary condition is treated. The existence problem of the initial-boundary value problem is discussed. The main idea of the proof is an abstract approach…
This paper deals with the Darcy-Forchheimer problem with two kinds of boundary conditions. We discretize the system by using the finite element methods and we propose two iterative schemes to solve the discrete problems. The well-posedness…
We study the mathematical properties of a general model of cell division structured with several internal variables. We begin with a simpler and specific model with two variables, we solve the eigenvalue problem with strong or weak…
Many infectious diseases are comprised of multiple strains with examples including Influenza, tuberculosis, and Dengue virus. The time evolution of such systems is linked to a complex landscape shaped by interactions between competing…
Type 2 diabetes mellitus (T2DM) is a chronic disease that often results in multiple complications. Risk prediction and profiling of T2DM complications is critical for healthcare professionals to design personalized treatment plans for…
The time-dependent reproduction number Rt can be used to track pathogen transmission and to assess the efficacy of interventions. This quantity can be estimated by fitting renewal equation models to time series of infectious disease case…
A major challenge of climate change adaptation is to assess the effect of changing weather on human health. In spite of an increasing literature on the weather-related health subject, many aspect of the relationship are not known, limiting…
The problem of unicellular-multicellular transition is one of the main issues that is discussing in evolutionary biology. In [1] the fitness of a colony of cells is considered in terms of its two basic components, viability and fecundity.…
To capture the dependences of a disease on several risk factors, a challenge is to combine model-based estimation with evidence-based arguments. Standard case-control methods allow estimation of the dependences of a rare disease on several…
Chronic diseases, such as cardiovascular disease, diabetes, chronic kidney disease, and thyroid disorders, are the leading causes of premature mortality worldwide. Early detection and intervention are crucial for improving patient outcomes,…
The three state illness death model has been established as a general approach for regression analysis of semi competing risks data. For observational data the marginal structural models (MSM) are a useful tool, under the potential outcomes…
Causal inference and model interpretability research are gaining increasing attention, especially in the domains of healthcare and bioinformatics. Despite recent successes in this field, decorrelating features under nonlinear environments…
In the paper, we investigate a local boundary value problem with transmitting condition of the integral form for mixed parabolic-hyperbolic equation with non-characteristic line of type changing. Two theorems on strong solvability and the…
We consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infection-induced mortality. We derive an infinite system of differential equations that provides an…
We use limit cycle oscillators to model Bipolar II disorder, which is characterized by alternating hypomanic and depressive episodes and afflicts about one percent of the United States adult population. We consider two nonlinear oscillator…