Related papers: Revisiting SIR in the age of COVID-19: Explicit So…
In this paper, we study the effectiveness of the modelling approach on the pandemic due to the spreading of the novel COVID-19 disease and develop a susceptible-infected-removed (SIR) model that provides a theoretical framework to…
The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures.…
The current COVID-19 pandemic and subsequent lockdowns have highlighted the close and delicate relationship between a country's public health and economic health. Macroeconomic models that use preexisting epidemic models to calculate the…
In this paper, we conduct mathematical and numerical analyses to address the following crucial questions for COVID-19: (Q1) Is it possible to contain COVID-19? (Q2) When will be the peak and the end of the epidemic? (Q3) How do the…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
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…
We consider the problem of controlling an SIR-model epidemic by temporarily reducing the rate of contact within a population. The control takes the form of a multiplicative reduction in the contact rate of infectious individuals. The…
The growing literature on the propagation of COVID-19 relies on various dynamic SIR-type models (Susceptible-Infected-Recovered) which yield model-dependent results. For transparency and ease of comparing the results, we introduce a common…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
Although modeling studies are focused on the control of SIR-based systems describing epidemic data sets (particularly the COVID-19), few of them present a formal dynamic characterization in terms of equilibrium sets and stability. Such…
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…
The SIR model is a three-compartment model of the time development of an epidemic. After normalizing the dependent variables, the model is a system of two non-linear differential equations for the susceptible proportion $S$ and the infected…
The current global health emergency triggered by the pandemic COVID-19 is one of the greatest challenges mankind face in this generation. Computational simulations have played an important role to predict the development of the current…
In this paper, an SIR epidemic model with variable size of population is considered. We study optimal control problem for an SIR model with "vaccination" and "treatment" as controls. It is shown that an optimal control exists. We have…
Transmission rates in epidemic outbreaks may vary over time depending on the societal response. Non-pharmacological mitigation strategies such as social distancing and the adoption of protective equipment aim precisely at reducing…
In the recent COVID-19 pandemic we assisted at a sequence of epidemic waves intertwined by anomalous fade-outs with periods of low but persistent epidemic prevalence. These long-living epidemic states complicate epidemic control and…
Social distancing has been enacted in order to mitigate the spread of COVID-19. Like many authors, we adopt the classic epidemic SIR model, where the infection rate is the control variable. Its differential flatness property yields ele…
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…
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…
The recent COVID-19 pandemic highlighted the need of non-pharmaceutical interventions in the first stages of a pandemic. Among these, lockdown policies proved unavoidable yet extremely costly from an economic perspective. To better…