Related papers: Bifurcation Thresholds and Optimal Control in Tran…
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…
A malaria model is formulated which includes the enhanced attractiveness of infectious humans to mosquitoes, as result of host manipulation by malaria parasite, and the human behavior, represented by insecticide-treated bed nets usage. The…
We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This…
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 investigate an epidemiological model that incorporates waning of immunity at the individual level and boosting of the immune system upon re-exposure to the pathogen. When immunity is fully restored upon boosting, the system can be…
The reproduction number of deterministic models is an essential quantity to predict whether an epidemic will spread or die out. Thresholds for disease extinction contribute crucial knowledge on disease control, elimination, and mitigation…
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…
A heroin epidemic mathematical model with prevention information and treatment, as control interventions, is analyzed, assuming that an individual's behavioral response depends on the spreading of information about the effects of heroin.…
This study presents a seasonally forced cholera model that incorporates imperfect vaccination as a control strategy. The model captures the temporal dynamics of susceptible, vaccinated, infected, and recovered individuals, as well as the…
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 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…
Motivated by the increasing number of COVID-19 cases that have been observed in many countries after the vaccination and relaxation of non-pharmaceutical interventions, we propose a mathematical model on time-varying networks for the spread…
We analyze a class of general nonlinear epidemic models with age and space structure, including a nonlocal infection term depending on age and space. After establishing the well-posedness of the state partial differential equation, we…
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 devise a theoretical model for the optimal dynamical control of an infectious disease whose diffusion is described by the SVIR compartmental model. The control is realized through implementing social rules to reduce the disease's spread,…
We examine here the effects of recurrent vaccination and waning immunity on the establishment of an endemic equilibrium in a population. An individual-based model that incorporates memory effects for transmission rate during infection and…
Treatment rate has always been one of the most important factors affecting the spread of infectious diseases. In this paper, we study a treatment function SIR model with treatment rate related to the maximum treatment capacity, whose…
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…
Optimal control of interdependent epidemics spreading over complex networks is a critical issue. We first establish a framework to capture the coupling between two epidemics, and then analyze the system's equilibrium states by categorizing…
In this paper, we study optimal control problems associated with a scalar hyperbolic conservation law modeling the development of ovarian follicles. Changes in the age and maturity of follicular cells are described by a 2D conservation law,…