Related papers: An eradication time problem for the SIR model
As the COVID19 spreads across the world, prevention measures are becoming the essential weapons to combat the pandemic in the period of crisis. The lockdown measure is the most controversial one as it imposes an overwhelming impact on our…
A class of optimal control problems governed by linear fractional diffusion equation with control constraint is considered. We first establish some results on the existence of strong solution to the state equation and the existence of…
We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions, considering reinfection and post-exposure…
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
We consider here an extended SIR model, including several features of the recent COVID-19 outbreak: in particular the infected and recovered individuals can either be detected (+) or undetected (-) and we also integrate an intensive care…
We investigate methods to vaccinate contact networks -- i.e. removing nodes in such a way that disease spreading is hindered as much as possible -- with respect to their cost-efficiency. Any real implementation of such protocols would come…
During pandemic events, strategies such as social distancing can be fundamental to curb viral spreading. Such actions can reduce the number of simultaneous infections and mitigate the disease spreading, which is relevant to the risk of a…
When to initiate treatment on patients is an important problem in many medical studies such as AIDS and cancer. In this article, we formulate the treatment initiation time problem for time-to-event data and propose an optimal individualized…
In this study, we formulate a mathematical model incorporating age specific transmission dynamics of COVID-19 to evaluate the role of vaccination and treatment strategies in reducing the size of COVID-19 burden. Initially, we establish the…
We introduce a policy model coupled with the susceptible-infected-recovered (SIR) epidemic model to study interactions between policy-making and the dynamics of epidemics. We consider both single-region policies, as well as game-theoretic…
In this paper, we address a social planner's optimal control problem for a partially observable stochastic epidemic model. The control measures include social distancing, testing, and vaccination. Using a diffusion approximation for the…
Opposition to vaccination has long been a non-negligible public health phenomenon resulted from people's varied perceptions toward vaccination (e.g., vaccine-phobia). This paper investigates the voluntary vaccination behavior of a…
In general, the rates of infection and removal (whether through recovery or death) are nonlinear functions of the number of infected and susceptible individuals. One of the simplest models for the spread of infectious diseases is the SIR…
Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior.…
The crisis caused by the COVID-19 outbreak around the globe raised an increasing concern about the ongoing emergence of variants of SARS-CoV-2 that may evade the immune response provided by vaccines. New variants appear due to mutation, and…
In this paper, we consider an adaptive optimal control problem for an SIR/V epidemic model with human behavioral effects.We develop a model where effective management of infectious diseases are monitored by the means of non pharmaceutical…
The Susceptible-Infected-Recovered (SIR) model is the cornerstone of epidemiological models. However, this specification depends on two parameters only, which implies a lack of flexibility and the difficulty to replicate the volatile…
We develop a mathematical model for transferring the vaccine BNT162b2 based on the heat diffusion equation. Then, we apply optimal control theory to the proposed generalized SEIR model. We introduce vaccination for the susceptible…
This paper is concerned with the analysis of vaccination strategies in a stochastic SIR (susceptible $\to$ infected $\to$ removed) model for the spread of an epidemic amongst a population of individuals with a random network of social…
We propose a simple SIR model in order to investigate the impact of various confinement strategies on a most virulent epidemic. Our approach is motivated by the current COVID-19 pandemic. The main hypothesis is the existence of two…