Related papers: Revisiting the Linear Chain Trick in epidemiologic…
Mathematical modelers have long known of a "rule of thumb" referred to as the Linear Chain Trick (LCT; aka the Gamma Chain Trick): a technique used to construct mean field ODE models from continuous-time stochastic state transition models…
The well-known Linear Chain Trick (LCT) allows modelers to derive mean field ODEs that assume gamma (Erlang) distributed passage times, by transitioning individuals sequentially through a chain of sub-states. The time spent in these states…
Our paper investigates distributions of exposed and infectious time periods in an epidemic model and how applying a disease control strategy affects the model's accuracy. While ordinary differential equations are widely used for their…
Ordinary differential equations (ODE) are a popular tool to model the spread of infectious diseases, yet they implicitly assume an exponential distribution to describe the flow from one infection state to another. However, scientific…
Ordinary differential equations (ODE) models have a wide variety of applications in the fields of mathematics, statistics, and the sciences. Though they are widely used, these models are sometimes viewed as inflexible with respect to the…
This paper is concerned with a stochastic model for the spread of an SEIR (susceptible -> exposed (=latent) -> infective -> removed) epidemic with a contact tracing scheme, in which removed individuals may name some of their infectious…
Reproduction numbers, like the basic reproduction number $\mathcal{R}_0$, play an important role in the analysis and application of dynamic models, including contagion models and ecological population models. One difficulty in deriving…
We study the dynamics of a spatially structured model of worldwide epidemics and formulate predictions for arrival times of the disease at any city in the network. The model is comprised of a system of ordinary differential equations…
This study investigates the utilization of various mathematical models for comprehending and managing outbreaks of infectious diseases, with a specific focus on how different distributions of incubation times influence predictions regarding…
The interplay between disease spreading and personal risk perception is of key importance for modelling the spread of infectious diseases. We propose a planar system of ordinary differential equations (ODEs) to describe the co-evolution of…
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…
We design a linear chain trick algorithm for dynamical systems for which we have oscillatory time histories in the distributed time delay. We make use of this algorithmic framework to analyse memory effects in disease evolution in a…
We design a Linear Chain Trick (LCT)-algorithm for dynamical systems with distributed time delay where the time histories contain temporal oscillations. The methodology is illustrated by means of an example in population dynamics.
The spread of infectious diseases crucially depends on the pattern of contacts among individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. Few empirical studies are however available that…
In most models of the spread of disease over contact networks it is assumed that the probabilities per unit time of disease transmission and recovery from disease are constant, implying exponential distributions of the time intervals for…
Objective: COVID-19 has spread worldwide and made a huge influence across the world. Modeling the infectious spread situation of COVID-19 is essential to understand the current condition and to formulate intervention measurements.…
This paper is devoted to the study of a stochastic epidemiological model which is a variant of the SIR model to which we add an extra factor in the transition rate from susceptible to infected accounting for the inflow of infection due to…
The paradigm for compartment models in epidemiology assumes exponentially distributed incubation and removal times, which is not realistic in actual populations. Commonly used variations with multiple exponentially distributed variables are…
We study the spread of susceptible-infected-recovered (SIR) infectious diseases where an individual's infectiousness and probability of recovery depend on his/her "age" of infection. We focus first on early outbreak stages when stochastic…
Dynamic properties of spreading infection through a heterogeneous population are studied numerically and analytically using a dynamic variant of Watts and Strogatz Small World Network-based stochastic Susceptible-Exposed-Infectious-Removed…