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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.…

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, 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…

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…

We study a stochastic epidemic model with multiple patches (locations), where individuals in each patch are categorized into three compartments, Susceptible, Infected and Recovered/Removed, and may migrate from one patch to another in any…

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.…

This paper introduces a novel hybrid model combining Partial Differential Equations (PDEs) and Ordinary Differential Equations (ODEs) to simulate infectious disease dynamics across geographic regions. By leveraging the spatial detail of…

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 an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet…

Partial differential equation (PDE) models for infectious diseases, while less common than their ordinary differential equation (ODE) counterparts, have found successful applications for many years. Such models are typically of…

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…

This paper presents a hybrid modeling approach that couples an Agent-Based Model (ABM) with a partial differential equation (PDE) model in an epidemic setting to simulate the spatial spread of infectious diseases using a compartmental…

We present a unifying, tractable approach for studying the spread of viruses causing complex diseases requiring to be modeled using a large number of types (e.g., infective stage, clinical state, risk factor class). We show that recording…

We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states…

Survival models are a popular tool for the analysis of time to event data with applications in medicine, engineering, economics, and many more. Advances like the Cox proportional hazard model have enabled researchers to better describe…

We propose a compartmental model for epidemiology wherein the population is split into groups with either comply or refuse to comply with protocols designed to slow the spread of a disease. Parallel to the disease spread, we assume that…

We present a simple model for the spread of an infection that incorporates spatial variability in population density. Starting from first principle considerations, we explore how a novel PDE with state-dependent diffusion can be obtained.…

Mathematical models of epidemics often use compartmental models dividing the population into several compartments. Based on a microscopic setting describing the temporal evolution of the subpopulation sizes in the compartments by stochastic…

Partial differential equation (PDE) models for infectious disease have received renewed interest in recent years. Most models of this type extend classical compartmental formulations with additional terms accounting for spatial dynamics,…