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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…
In the wake of epidemics, quarantine measures are typically recommended by health authorities or governments to help control the spread of the disease. Compared with mandatory quarantine, voluntary quarantine offers individuals the liberty…
At the time of writing, the ongoing COVID-19 pandemic, caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), had already resulted in more than thirty-two million cases infected and more than one million deaths worldwide.…
Several recent studies have tackled the issue of optimal network immunization by providing efficient criteria to identify key nodes to be removed in order to break apart a network, thus preventing the occurrence of extensive epidemic…
The death toll for Covid-19 may be reduced by dividing the population into two classes, the vulnerable and the fit, with different lockdown regimes. Instead of one reproduction number there now are four parameters. These make it possible to…
We study first order necessary conditions for an optimal control problem of a Susceptible-Infected-Recovered (SIR) model with limitations on the duration of the quarantine. The control is done by means of the reproduction number, i.e., the…
Drug resistance and strong contacts actually play crucial roles in epidemic spread in complex systems. Nevertheless, neither theoretical model or methodology is proposed to address this. We thus consider an edge-based epidemic spread model…
The Susceptible-Infected-Recovered (SIR) model has successfully mimicked the propagation of such airborne diseases as influenza A (H1N1). Although the SIR model has recently been studied in a multilayer networks configuration, in almost all…
The coronavirus disease 2019 (COVID-19) pandemic radically impacts our lives, while the transmission/infection and recovery dynamics of COVID-19 remain obscure. A time-dependent Susceptible, Exposed, Infectious, and Recovered (SEIR) model…
We introduce a system of differential equations to assess the impact of (self-)quarantine of symptomatic infectious individuals on disease dynamics. To this end we depart from using the classic bilinear infection process, but remain still…
Various measures have been taken in different countries to mitigate the Covid-19 epidemic. But, throughout the world, many citizens don't understand well how these measures are taken and even question the decisions taken by their…
Human diseases spread over networks of contacts between individuals and a substantial body of recent research has focused on the dynamics of the spreading process. Here we examine a model of two competing diseases spreading over the same…
We study the effectiveness of tracking and testing in mitigating or suppressing epidemic outbreaks, in combination with or as an alternative to quarantines and global lockdowns. We study these intervention methods on a network-based SEIR…
Epidemiological models are the mathematical models that capture the dynamics of epidemics. The spread of the virus has two routes - exogenous and endogenous. The exogenous spread is from outside the population under study, and endogenous…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
In this work we analyze mathematically the consequences and effectiveness of strategies to control an epidemic in the framework of classical SEIR models with multiple parallel infectious stages. We define the mathematical concept of a…
Current modeling of infectious diseases allows for the study of complex and realistic scenarios that go from the population to the individual level of description. However, most epidemic models assume that the spreading process takes place…
In the standard SIR model, infected vertices infect their neighbors at rate $\lambda$ independently across each edge. They also recover at rate $\gamma$. In this work we consider the SIR-$\omega$ model where the graph structure itself…
We study a susceptible-infected-recovered (SIR) epidemic model on a network of $n$ interacting subpopulations. We analyze the transient and asymptotic behavior of the infection dynamics in each node of the network. In contrast to the…
While many efforts are currently devoted to vaccines development and administration, social distancing measures, including severe restrictions such as lockdowns, remain fundamental tools to contain the spread of COVID-19. A crucial point…