Related papers: SIR dynamics with Vaccination in a large Configura…
When modelling epidemics or spread of information on online social networks, it is crucial to include not just the density of the connections through which infections can be transmitted, but also the variability of susceptibility. Different…
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…
Spreading processes represent a very efficient tool to investigate the structural properties of networks and the relative importance of their constituents, and have been widely used to this aim in static networks. Here we consider simple…
In this paper, we extend the classical SIRS (Susceptible-Infectious-Recovered-Susceptible) model from mathematical epidemiology by incorporating a vaccinated compartment, V, accounting for an imperfect vaccine with waning efficacy over…
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…
Non-pharmacological interventions (NPIs), and in particular social distancing, in conjunction with the advent of effective vaccines at the end of 2020, aspired for the development of a protective immunity shield against the spread of…
With the invention of the COVID-19 vaccine, shipping and distributing are crucial in controlling the pandemic. In this paper, we build a mean-field variational problem in a spatial domain, which controls the propagation of pandemic by the…
Modeling human behavior is essential to accurately predict epidemic spread, with behaviors like vaccine hesitancy complicating control efforts. While epidemic spread is often treated as a simple contagion, vaccine uptake may follow complex…
We consider the spread of infectious diseases through a Mean Field Game version of a SIR compartmental model with social structure, in which individuals are grouped by their age class and interact together in different settings. In our game…
In this paper, we study the dynamics of the susceptible-infected-recovered (SIR) model on a network with community structure, namely the stochastic block model (SBM). As usual, the SIR model is a stochastic model for an epidemic where…
Networks of contacts capable of spreading infectious diseases are often observed to be highly heterogeneous, with the majority of individuals having fewer contacts than the mean, and a significant minority having relatively very many…
Modelling epidemics via classical population-based models suffers from shortcomings that so-called individual-based models are able to overcome, as they are able to take heterogeneity features into account, such as super-spreaders, and…
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 the context of the recent COVID-19 outbreak, quarantine has been used to "flatten the curve" and slow the spread of the disease. In this paper, we show that this is not the only benefit of quarantine for the mitigation of an SIR epidemic…
Until a vaccine or therapy is found against the SARS-CoV-2 coronavirus, reaching herd immunity appears to be the only mid-term option. However, if the number of infected individuals decreases and eventually fades only beyond this threshold,…
We consider the problem of optimal allocation strategies for a (perfect) vaccine in an infinite-metapopulation model (including SIS, SIR, SEIR,. . .), when the loss function is given by the effective reproduction number Re, which is defined…
We give the explicit solution of the optimal control problem which consists in minimizing the epidemic peak in the SIR model when the control is an attenuation factor of the infectious rate, subject to a L 1 budget constraint. The optimal…
In this work, to support decision making of immunisation strategies, we propose the inclusion of two vaccination doses in the SEIR model considering a stochastic cellular automaton. We analyse three different scenarios of vaccination: $i)…
We consider the optimal allocation of (perfect) vaccine in an heterogeneous SIS model. Using a coupling approach, we explain how different models for the heterogeneity of the population lead to the same Pareto frontier in the cost/loss…
We study in a general mathematical framework the optimal allocation of vaccine in an heterogeneous population. We cast the problem of optimal vaccination as a bi-objective minimization problem min(C($\eta$),L($\eta$)), where C and L stand…