Related papers: Delay differential equations for the spatially-res…
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…
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.…
The outbreak of COVID-19 in 2020 has led to a surge in interest in the mathematical modeling of infectious diseases. Such models are usually defined as compartmental models, in which the population under study is divided into compartments…
COVID-19 data released by public health authorities features the presence of notable time-delays, corresponding to the difference between actual time of infection and identification of infection. These delays have several causes, including…
It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on…
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…
Delayed processes are ubiquitous in biological systems and are often characterized by delay differential equations (DDEs) and their extension to include stochastic effects. DDEs do not explicitly incorporate intermediate states associated…
We study a simple realistic model for describing the diffusion of an infectious disease on a population of individuals. The dynamics is governed by a single functional delay differential equation, which, in the case of a large population,…
The outbreak of COVID-19 in 2020 has led to a surge in the interest in the mathematical modeling of infectious diseases. Disease transmission may be modeled as compartmental models, in which the population under study is divided into…
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…
The review is devoted to analysis of mathematical models used for describing epidemic processes. A main focus is done on the models that are based on partial differential equations (PDEs), especially those that were developed and used for…
Delay differential equations form the underpinning of many complex dynamical systems. The forward problem of solving random differential equations with delay has received increasing attention in recent years. Motivated by the challenge to…
Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics and engineering to medicine and economics. These systems cannot be properly modelled and simulated with standard…
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…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
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),…
The outbreaks of Coronavirus Disease 2019 (COVID-19) have impacted the world significantly. Modeling the trend of infection and real-time forecasting of cases can help decision making and control of the disease spread. However, data-driven…
Highly-interconnected societies difficult to model the spread of infectious diseases such as COVID-19. Single-region SIR models fail to account for incoming forces of infection and expanding them to a large number of interacting regions…
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…
The primary goal of this research is to investigate the impact of delay on the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and Susceptible (SEIRDS) model, to which we add a stochastic term to account for uncertainty in…