Related papers: An eradication time problem for the SIR model
This paper introduces a spatiotemporal SEIQR epidemic model governed by a system of reaction-diffusion partial differential equations that incorporates optimal control strategies. The model captures the transmission dynamics of an…
This paper presents a discrete time probabilistic dynamic for simulating a contact-based epidemic spreading based on discrete time Markov chain process, in particular the attention is addressed to the susceptible-infectious-removed (SIR)…
We consider the interplay of vaccination and migration rates on disease persistence in epidemiological systems. We show that short-term and long-term migration can inhibit disease persistence. As a result, we show how migration changes how…
We analyze a periodically-forced dynamical system inspired by the SIR model with impulsive vaccination. We fully characterize its dynamics according to the proportion $p$ of vaccinated individuals and the time $T$ between doses. If 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…
Motivated by the issue of COVID-19 mitigation, in this work we tackle the general problem of optimally controlling an epidemic outbreak of a communicable disease structured by time since exposure, by the aid of two types of control…
This study presents a mathematical model for optimal vaccination strategies in interconnected metropolitan areas, considering commuting patterns. It is a compartmental model with a vaccination rate for each city, acting as a control…
An integrable discretization of the SIR model with vaccination is proposed. The conserved quantities of the continuous model are inherited to the discrete model through the discretization, since the discretization is based on the…
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…
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 propose an SIR epidemic model coupled with opinion dynamics to study an epidemic and opinions spreading in a network of communities. Our model couples networked SIR epidemic dynamics with opinions towards the severity of the epidemic,…
A pulse vaccination SIR model with periodic infection rate $\beta (t)$ have been proposed and studied. The basic reproductive number $R_0$ is defined. The dynamical behaviors of the model are analyzed with the help of persistence,…
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…
In this work, we investigate a VS-EIAR epidemiological model that incorporates vaccinated individuals $\{V_i : i = 1, \ldots, n\}$, where $n \in \mathbb{N}^{*}$. The dynamics of the VS-EIAR model are governed by a system of ordinary…
This paper utilizes a stochastic Susceptible-Infected-recovered (SIR) model with a non-linear incidence rate to perform a detailed mathematical study of optimal lock-down intensity and vaccination rate under the COVID-19 pandemic…
The problem of targeted network immunization can be defined as the one of finding a subset of nodes in a network to immunize or vaccinate in order to minimize a tradeoff between the cost of vaccination and the final (stationary) expected…
An age-dependent SIR model is considered with the aim to develop a state-feedback vaccination law in order to eradicate a disease. A dynamical analysis of the system is performed using the principle of linearized stability and shows that,…
We study the susceptible-infective-recovered (SIR) epidemic on a random graph chosen uniformly subject to having given vertex degrees. In this model infective vertices infect each of their susceptible neighbours, and recover, at a constant…
The Susceptible-Infectious-Recovered (SIR) model is the canonical model of epidemics of infections that make people immune upon recovery. Many of the open questions in computational epidemiology concern the underlying contact structure's…
Recent Covid-19 pandemic has demonstrated the need of efficient epidemic outbreak management. We study the optimal control problem of minimizing the fraction of infected population by applying vaccination and treatment control strategies,…