Related papers: Accurately summarizing an outbreak using epidemiol…
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…
Accurate forecasts of disease outbreaks are critical for effective public health responses, management of healthcare surge capacity, and communication of public risk. There are a growing number of powerful forecasting methods that fall into…
In the face of an infectious disease, a key epidemiological measure is the basic reproduction number, which quantifies the average secondary infections caused by a single case in a susceptible population. In practice, the effective…
Mathematical models of epidemiological systems enable investigation of and predictions about potential disease outbreaks. However, commonly used models are often highly simplified representations of incredibly complex systems. Because of…
Epidemic propagation on networks represents an important departure from traditional massaction models. However, the high-dimensionality of the exact models poses a challenge to both mathematical analysis and parameter inference. By using…
This contribution analyzes the COVID-19 outbreak by comparably simple mathematical and numerical methods. The final goal is to predict the peak of the epidemic outbreak per country with a reliable technique. This is done by an algorithm…
Towards the end of an infectious disease outbreak, when a period has elapsed without new case notifications, a key question for public health policy makers is whether the outbreak can be declared over. This requires the benefits of a…
Practical parameter identifiability in ODE-based epidemiological models is a known issue, yet one that merits further study. It is essentially ubiquitous due to noise and errors in real data. In this study, to avoid uncertainty stemming…
We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number $\mathcal{R}(t)$. We discuss the estimation of the underlying SIR parameters with a…
The estimation of unknown parameters in simulations, also known as calibration, is crucial for practical management of epidemics and prediction of pandemic risk. A simple yet widely used approach is to estimate the parameters by minimizing…
Epidemic models and self-exciting processes are two types of models used to describe diffusion phenomena online and offline. These models were originally developed in different scientific communities, and their commonalities are…
This paper introduces a new approach to describe the spread of research topics across disciplines using epidemic models. The approach is based on applying individual-based models from mathematical epidemiology to the diffusion of a research…
When an infectious disease strikes a population, the number of newly reported cases is often the only available information that one can obtain during early stages of the outbreak. An important goal of early outbreak analysis is to obtain a…
Multiple epidemiological models have been proposed to predict the spread of Ebola in West Africa. These models include consideration of counter-measures meant to slow and, eventually, stop the spread of the disease. Here, we examine one…
Epidemiological models are an important tool in coping with epidemics, as they offer a forecast, even if often simplistic, of the behavior of the disease in the population. This allows responsible health agencies to organize themselves and…
The Time Since Infection (TSI) models, which use disease surveillance data to model infectious diseases, have become increasingly popular due to their flexibility and capacity to address complex disease control questions. However, a notable…
We present a detailed set-based analysis of the well-known SIR and SEIR epidemic models subjected to hard caps on the proportion of infective individuals, and bounds on the allowable intervention strategies, such as social distancing,…
The possibility to analyze, quantify and forecast epidemic outbreaks is fundamental when devising effective disease containment strategies. Policy makers are faced with the intricate task of drafting realistically implementable policies…
Mathematical modeling of disease outbreaks can infer the future trajectory of an epidemic, which can inform policy decisions. Another task is inferring the origin of a disease, which is relatively difficult with current mathematical models.…
In Part 1, we introduced a stochastic model of an infectious disease, based on the BDI (birth and death with immigration) process. We showed that random processes defined by this model can capture the essence of the stochastic, often…