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The COronaVIrus Disease 2019 (COVID-19) pandemic that has had the world in its grip from the beginning of 2020, has resulted in an unprecedented level of public interest and media attention on the field of mathematical epidemiology. Ever…
We propose an SEIR-type meta-population model to simulate and monitor the Covid-19 epidemic evolution. The basic model consists of seven compartments, namely susceptible (S), exposed (E), three infective classes, recovered (R), and deceased…
Based on the classical SIR model, we derive a simple modification for the dynamics of epidemics with a known incubation period of infection. The model is described by a system of integro-differential equations. Parameters of our model…
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)…
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…
Recent outbreak of the novel coronavirus COVID-19 has affected all of our lives in one way or the other. While medical researchers are working hard to find a cure and doctors/nurses to attend the affected individuals, measures such as…
The main focus of this chapter is on public health control strategies which are currently the main way to mitigate COVID-19 pandemic. We introduce and compare compartmental models of increasing complexity for COVID-19 transmission to…
Understanding the spatio-temporal patterns of the coronavirus disease 2019 (COVID-19) is essential to construct public health interventions. Spatially referenced data can provide richer opportunities to understand the mechanism of the…
There is increasing evidence that one of the most difficult problems in trying to control the ongoing COVID-19 epidemic is the presence of a large cohort of asymptomatic infectives. We develop a SIR-type model taking into account the…
The emergence of coronavirus disease 2019 (COVID-19) in the United States has forced federal and local governments to implement containment measures. Moreover, the severity of the situation has sparked engagement by both the research and…
The last decade saw the advent of increasingly realistic epidemic models that leverage on the availability of highly detailed census and human mobility data. Data-driven models aim at a granularity down to the level of households or single…
The most important features to assess the severity of an epidemic are its size and its timescale. We discuss these features in a systematic way in the context of SIR and SIR-type models. We investigate in detail how the size and timescale…
We investigate adaptive strategies to robustly and optimally control the COVID-19 pandemic via social distancing measures based on the example of Germany. Our goal is to minimize the number of fatalities over the course of two years without…
Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible $S$, infected $I$, removed $R$ and dead people $D$. In order to have…
We introduce a methodology to guarantee safety against the spread of infectious diseases by viewing epidemiological models as control systems and by considering human interventions (such as quarantining or social distancing) as control…
A growing number of universities worldwide use various forms of online and blended learning as part of their academic curricula. Furthermore, the recent changes caused by the COVID-19 pandemic have led to a drastic increase in importance…
This work provides an overview on deterministic and stochastic models that have previously been proposed by us to study the transmission dynamics of the Coronavirus Disease 2019 (COVID-19) in Europe and USA. Briefly, we describe realistic…
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…
In this study, we address three important challenges related to disease transmissions such as the COVID-19 pandemic, namely, (a) providing an early warning to likely exposed individuals, (b) identifying individuals who are asymptomatic, and…
As COVID-19 is rapidly spreading across the globe, short-term modeling forecasts provide time-critical information for decisions on containment and mitigation strategies. A main challenge for short-term forecasts is the assessment of key…