Related papers: A simplified drift-diffusion model for pandemic pr…
We introduce the concept of epidemic-fitted wavelets which comprise, in particular, as special cases the number $I(t)$ of infectious individuals at time $t$ in classical SIR models and their derivatives. We present a novel method for…
Computational multi-scale pandemic modelling remains a major and timely challenge. Here we identify specific requirements for a new class of models simulating pandemics across three scales: (1) pathogen evolution, often punctuated by the…
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…
The ubiquity of oscillations in epidemics presents a long standing challenge for the formulation of epidemic models. Whether they are external and seasonally driven, or arise from the intrinsic dynamics is an open problem. It is known that…
Students develop and test simple models of the spread of COVID-19. Microsoft Excel is used as the modeling platform because it's non-threatening to students and because it's widely available. Students develop finite difference models and…
We introduce a digital twin of the classical compartmental SIR (Susceptible, Infected, Recovered) epidemic model and study the interrelation between the digital twin and the system. In doing so, we use Stieltjes derivatives to feed the data…
The present paper introduces a data-driven framework for describing the time-varying nature of an SIRD model in the context of COVID-19. By embedding a rolling regression in a mixed integer bilevel nonlinear programming problem, our aim is…
This research presents an advanced fractional-order compartmental model designed to delve into the complexities of COVID-19 transmission dynamics, specifically accounting for the influence of environmental pathogens on disease spread. By…
We study evolution equations of drift-diffusion type when various parameters are random. Motivated by applications in pedestrian dynamics, we focus on the case when the total mass is, due to boundary or reaction terms, not conserved. After…
Population-wide vaccination is critical for containing the SARS-CoV-2 (Covid-19) pandemic when combined with restrictive and prevention measures. In this study, we introduce SAIVR, a mathematical model able to forecast the Covid-19 epidemic…
A model of reactive social distancing in epidemics is proposed, in which the infection rate changes with the number infected. The final-size equation for the total number that the epidemic will infect can be derived analytically, as can the…
The COVID-19 pandemic has presented unprecedented challenges worldwide, necessitating effective modelling approaches to understand and control its transmission dynamics. In this study, we propose a novel approach that integrates…
The unprecedented coronavirus disease 2019 (COVID-19) pandemic is still a worldwide threat to human life since its invasion into the daily lives of the public in the first several months of 2020. Predicting the size of confirmed cases is…
Diffusion models have emerged as powerful generative frameworks by progressively adding noise to data through a forward process and then reversing this process to generate realistic samples. While these models have achieved strong…
Compartmental models are a tool commonly used in epidemiology for the mathematical modelling of the spread of infectious diseases, with their most popular representative being the Susceptible-Infected-Removed (SIR) model and its…
We present a phenomenological procedure of dealing with the COVID--19 data provided by government health agencies of eleven different countries. Instead of using the (exact or approximate) solutions to the SIR (or other) model(s) to fit the…
We show that the mean field equations for the SIR epidemic can be exactly solved for a network with arbitrary degree distribution. Our exact solution consists of reducing the dynamics to a lone first order differential equation, which has a…
Epidemic models currently play a central role in our attempts to understand and control infectious diseases. Here, we derive a model for the diffusion limit of stochastic susceptible-infectious-removed (SIR) epidemic dynamics on a…
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…
When fitting a multi-parameter model to a data set, computer algorithms may suggest that a range of parameters provide equally reasonable fits, making the parameter estimation difficult. Here, we prove this fact for an SIR model. We say a…