Related papers: Modeling Infectious Diseases: From SIR Models to D…
We study the qualitative properties of a spatial diffusive heterogeneous SIR model, that appears in mathematical epidemiology to describe the spread of an infectious disease in a population. The model we consider consists in a system of…
Multiple-type branching processes that model the spread of infectious diseases are investigated. In these stochastic processes, the disease goes through multiple stages before it eventually disappears. We mostly focus on the critical…
The SIR model is the cornerstone model for mathematical epidemiology, explaining key epidemic features such as the second-order transition between disease-free and epidemic states, the initial exponential growth of outbreaks or the…
In this work, we have described the mathematical modeling of COVID-19 transmission using fractional differential equations. The mathematical modeling of infectious disease goes back to the 1760s when the famous mathematician Daniel…
For preventing the spread of epidemics such as the coronavirus disease COVID-19, social distancing and the isolation of infected persons are crucial. However, existing reaction-diffusion equations for epidemic spreading are incapable of…
Pandemics can cause immense disruption and damage to communities and societies. Thus far, modeling of pandemics has focused on either large-scale difference equation models like the SIR and the SEIR models, or detailed micro-level…
Intent of this research is to explore how mathematical models, specifically Susceptible-Infected-Removed (SIR) model, can be utilized to forecast peak outbreak timeline of COVID-19 epidemic amongst a population of interest starting from the…
We investigate an epidemic model based on Bailey's continuous differential system. In the continuous time domain, we extend the classical model to time-dependent coefficients and present an alternative solution method to Gleissner's…
We present an approach to studying and predicting the spatio-temporal progression of infectious diseases. We treat the problem by adopting a partial differential equation (PDE) version of the Susceptible, Infected, Recovered, Deceased…
Motivated by analogies between the spreading of human-to-human infections and of chemical processes, we develop a comprehensive model that accounts both for infection and for transport. In this analogy, the three different populations of…
Compartmental transmission models have become an invaluable tool to study the dynamics of infectious diseases. The Susceptible-Infectious-Recovered (SIR) model is known to have an exact semi-analytical solution. In the current study, the…
We provide an overview of the methods that can be used for prediction under uncertainty and data fitting of dynamical systems, and of the fundamental challenges that arise in this context. The focus is on SIR-like models, that are being…
Understanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In…
This paper gives an introduction to rule-based modelling applied to topics in infectious diseases. Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in…
This article explores mathematical models for understanding the evolution of contagious diseases. The most widely known set of models are the compartmental ones, which are based on a set of differential equations. But these are not the only…
The SIR-compartment model is among the simplest models that describe the spread of a disease through a population. The model makes the unrealistic assumption that the population through which the disease is spreading is well-mixed. Although…
Fractional-order SIR models have become increasingly popular in the literature in recent years, however unlike the standard SIR model, they often lack a derivation from an underlying stochastic process. Here we derive a fractional-order…
In this study, we present an integro-differential model to simulate the local spread of infections. The model incorporates a standard susceptible-infected-recovered (\textit{SIR}-) model enhanced by an integral kernel, allowing for…
Social distancing strategies have been adopted by governments to manage the COVID-19 pandemic, since the first outbreak began. However, further epidemic waves keep out the return of economic and social activities to their standard levels of…
Different countries -- and sometimes different regions within the same countries -- have adopted different strategies in trying to contain the ongoing COVID-19 epidemic; these mix in variable parts social confinement, early detection and…