Related papers: A nonstandard numerical scheme for a novel SECIR i…
The SIR model is one of the most prototypical compartmental models in epidemiology. Generalizing this ordinary differential equation (ODE) framework into a spatially distributed partial differential equation (PDE) model is a considerable…
We propose a numerical method for approximating integro-differential equations arising in age-of-infection epidemic models. The method is based on a non-standard finite differences approximation of the integral term appearing in the…
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…
In the wake of the 2020 COVID-19 epidemic, much work has been performed on the development of mathematical models for the simulation of the epidemic, and of disease models generally. Most works follow the susceptible-infected-removed (SIR)…
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…
This paper introduces a nonstandard finite difference (NSFD) approach to a reaction-diffusion SEIQR epidemiological model, which captures the spatiotemporal dynamics of infectious disease transmission. Formulated as a system of semilinear…
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…
In order to simulate the spread of infectious diseases, many epidemiological models use systems of ordinary differential equations (ODEs) to describe the underlying dynamics. These models incorporate the implicit assumption, that the stay…
By interpreting the forward dynamics of the latent representation of neural networks as an ordinary differential equation, Neural Ordinary Differential Equation (Neural ODE) emerged as an effective framework for modeling a system dynamics…
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…
Genetic variations in the COVID-19 virus are one of the main causes of the COVID-19 pandemic outbreak in 2020 and 2021. In this article, we aim to introduce a new type of model, a system coupled with ordinary differential equations (ODEs),…
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.…
A nonlinear partial differential equation (PDE) based compartmental model of COVID-19 provides a continuous trace of infection over space and time. Finer resolutions in the spatial discretization, the inclusion of additional model…
In this article, we construct a numerical method for a stochastic version of the Susceptible Infected Susceptible (SIS) epidemic model, expressed by a suitable stochastic differential equation (SDE), by using the semi-discrete method to a…
In this paper, we study an analytically tractable SIS model with a non-linear incidence rate for the number of infectious individuals described through a stochastic differential equation (SDE). We guarantee the existence of a positive…
We study an infection-age structured epidemic model in which both the infectivity and the rate of loss of immunity depend on the time-since-infection. The model can be equivalently viewed as a nonlinear renewal equation for the incidence of…
One of the most significant challenges in combating against the spread of infectious diseases was the difficulty in estimating the true magnitude of infections. Unreported infections could drive up disease spread, making it very hard to…
The SIR model is a classical model characterizing the spreading of infectious diseases. This model describes the time-dependent quantity changes among Susceptible, Infectious, and Recovered groups. By introducing space-depend effects such…
We propose a new model that describes the dynamics of epidemic spreading on connected graphs. Our model consists in a PDE-ODE system where at each vertex of the graph we have a standard SIR model and connexions between vertices are given by…
The spread of many infectious diseases is modeled using variants of the SIR compartmental model, which is a coupled differential equation. The coefficients of the SIR model determine the spread trajectories of disease, on whose basis…