Related papers: An eradication time problem for the SIR model

We study the minimum eradication time problem for controlled Susceptible-Infected-Recovered (SIR) epidemic models that incorporate vaccination control and time-varying infected and recovery rates. Unlike the SIR model with constant rates,…

We study an optimal control problem where the objective is to find the best vaccine allocation during an epidemic outbreak. The epidemic dynamics is described by an age-structured SIR model with nonlocal interactions. Both the infection and…

In this paper, we study the optimal control for an SEIR model adapted to the vaccination strategy of susceptible individuals. There are factors associated with a vaccination campaign that make this strategy not only a public health issue…

There are often multiple diseases with cross immunity competing for vaccination resources. Here we investigate the optimal vaccination program in a two-layer Susceptible-Infected-Removed (SIR) model, where two diseases with cross immunity…

To understand the impact of vaccination, we consider a SIVR (susceptible-infected-vaccinated-recovered) model which combines impulsive vaccination into the classical SIR model. The final size is firstly defined and estimated, and then the…

Real-time vaccination following an outbreak can effectively mitigate the damage caused by an infectious disease. However, in many cases, available resources are insufficient to vaccinate the entire at-risk population, logistics result in…

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…

We analyze an optimal control version of a simple SIRS epidemiology model. The policy maker can adopt policies to diminish the contact rate between infected and susceptible individuals, at a specific economic cost. The arrival of a vaccine…

This paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the ICU (intensive care unit) capacity. The…

This paper analyses the optimal control of infectious disease propagation using a classic susceptible-infected-recovered (SIR) model characterised by permanent immunity and the absence of available vaccines. The control is performed over a…

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…

We consider a SIR model with temporary immunity and time dependent transmission rate. We assume time dependent vaccination which confers the same immunity as natural infection. We study two types of vaccination strategies: i) optimal…

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…

We analyze an optimal control version of a simple SIR epidemiology model that includes a partially specified vaccination policy and takes into account fatigue from protracted application of social distancing measures. The model assumes…

The Susceptible-Infected-Susceptible (SIS) model is a widely used model for the spread of information and infectious diseases, particularly non-immunizing ones, on a graph. Given a highly contagious disease, a natural question is how to…

In this paper we introduce an approach to the management of infectious disease diffusion through the formulation of a controlled compartmental SVIR (Susceptible-Vaccinated-Infected-Recovered) model. We consider a cost functional…

We study an optimal control problem for a non-autonomous SEIRS model with incidence given by a general function of the infective, the susceptible and the total population, and with vaccination and treatment as control variables. We prove…

We consider the SIR model and study the first time the number of infected individuals begins to decrease and the first time this population is below a given threshold. We interpret these times as functions of the initial susceptible and…

We consider a SIR model with vaccination strategy on a sparse configuration model random graph. We show the convergence of the system when the number of nodes grows and characterize the scaling limits. Then, we prove the existence of…

Developing robust, quantitative methods to optimize resource allocations in response to epidemics has the potential to save lives and minimize health care costs. In this paper, we develop and apply a computationally efficient algorithm that…