Related papers: An eradication time problem for the SIR model
The paper considers the problems of optimal vaccination control in the classical SIR model under constraints on the resource capabilities of the insurance medical system, in particular under constraints on the possible absolute rate of…
This paper presents a vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for…
We consider the problem of the optimal allocation of vaccination and protection measures for the Susceptible-Infected-Recovered-Infected (SIRI) epidemiological model, which generalizes the classical Susceptible-Infected-Recovered (SIR) and…
We propose and solve an optimal vaccination problem within a deterministic compartmental model of SIRS type: the immunized population can become susceptible again, e.g.\ because of a not complete immunization power of the vaccine. A social…
Understanding the dynamics of an epidemic spread is crucial for effective control measures. During the COVID-19 pandemic, quarantines were implemented to minimize infections while mitigating social and economic impacts, raising the question…
In this paper we investigate the asymptotic behavior of some SIR models incorporating demography, bounded random transmission coefficient and a time-dependent vaccination strategy targeting the susceptible population. In this setting, we…
We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available. At that stage, control is often limited to non-medical interventions like social distancing and…
This study aims to determine an optimal control strategy for vaccine scheduling in COVID-19 pandemic treatment by converting widely acknowledged infectious disease model named SEIR into an optimal control problem. The problem is augmented…
We consider a behavioral-feedback SIR epidemic model, in which the infection rate depends in feedback on the fractions of susceptible and infected agents, respectively. The considered model allows one to account for endogenous adaptation…
Given maximal social distancing duration and intensity, how can one minimize the epidemic final size, or equivalently the total number of individuals infected during the outbreak? A complete answer to this question is provided and…
Controlling and understanding epidemic outbreaks has recently drawn great interest in a large spectrum of research communities. Vaccination is one of the most well-established and effective strategies in order to contain an epidemic. In the…
This paper investigates a behavioral-feedback SIR model in which the infection rate adapts dynamically based on the fractions of susceptible and infected individuals. We introduce an invariant of motion and we characterize the peak of…
This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total…
This paper presents several simple linear vaccination-based control strategies for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population…
In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over…
Susceptible-Infected-Recovered (SIR) models have been used for decades to understand epidemic outbreak dynamics. We develop an SIR model specifically designed to study the effects of population behavior with respect to health and…
SIR models, also with age structure, can be used to describe the evolution of an infective disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered…
This work examines the discrete-time networked SIR (susceptible-infected-recovered) epidemic model, where the infection and recovery parameters may be time-varying. We provide a sufficient condition for the SIR model to converge to the set…
In the Susceptible-Infectious-Recovered (SIR) model of disease spreading, the time to extinction of the epidemics happens at an intermediate value of the per-contact transmission probability. Too contagious infections burn out fast in the…
Epidemics have shaped human history, often with devastating consequences, motivating the development of mathematical models to understand and control their dynamics. Among the many aspects of epidemic behavior, the conditions that lead to…