Related papers: Optimal management of the vaccination process in S…
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 investigates the optimal control of an epidemic governed by a SEIR model with an operational delay in vaccination. We address the mathematical challenge of imposing hard healthcare capacity constraints (e.g., ICU limits) over an…
This paper deals with an SIR model with saturated incidence rate affected by inhibitory effect and saturated treatment function. Two control functions have been used, one for vaccinating the susceptible population and other for the…
This research introduces a new approach utilizing optimal control theory (OCT) to assess the Social Optimum (SO) of a vaccination game, navigating the intricate considerations of cost, availability, and distribution policies. By integrating…
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…
We investigate the time-optimal control problem in SIR (Susceptible-Infected-Recovered) epidemic models, focusing on different control policies: vaccination, isolation, culling, and reduction of transmission. Applying the Pontryagin's…
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…
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…
The SEIR model is a compartmental model used to simulate the dynamics of an epidemic. In this chapter, we introduce two control functions in the compartmental SEIR model representing vaccination and plasma transfusion. Optimal control…
We present and compare two different optimal control approaches applied to SEIR models in epidemiology, which allow us to obtain some policies for controlling the spread of an epidemic. The first approach uses Dynamic Programming to…
This paper investigates optimal vaccination strategies in a metapopulation epidemic model. We consider a linear cost to better capture operational considerations, such as the total number of vaccines or hospitalizations, in contrast to the…
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…
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 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…
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…
The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem with SIR dynamics. The main feature of our study is the presence of state constraints (related to intensive care units ICU capacity) and…
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…
In this study, we present an epidemic-controlled SIRD model with two types of control strategies: mask wear and screening. The aim of this study is to minimize the number of deceased keeping a minimal cost of mask advertising and screening.…
We consider a susceptible, infected, and recovered infectious disease model which incorporates a vaccination rate. In particular, we study the problem of choosing the vaccination rate in order to reduce the number of infected individuals to…
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…