# Control with uncertain data of socially structured compartmental epidemic models

@article{Albi2020ControlWU, title={Control with uncertain data of socially structured compartmental epidemic models}, author={Giacomo Albi and Lorenzo Pareschi and Mattia Zanella}, journal={medRxiv}, year={2020} }

The adoption of containment measures to reduce the amplitude of the epidemic peak is a key aspect in tackling the rapid spread of an epidemic. Classical compartmental models must be modified and studied to correctly describe the effects of forced external actions to reduce the impact of the disease. In addition, data are often incomplete and heterogeneous, so a high degree of uncertainty must naturally be incorporated into the models. In this work we address both these aspects, through an… Expand

#### 18 Citations

Modelling lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty.

- Medicine
- Mathematical biosciences and engineering : MBE
- 2021

After the introduction of drastic containment measures aimed at stopping the epidemic contagion from SARS-CoV2, many governments have adopted a strategy based on a periodic relaxation of such… Expand

Relaxing lockdown measures in epidemic outbreaks using selective socio-economic containment with uncertainty

- Biology, Mathematics
- medRxiv
- 2020

Starting from a compartmental model with a social structure, models with multiple feedback controls depending on the social activities that allow to assess the impact of a selective relaxation of the containment measures in the presence of uncertain data are derived. Expand

Kinetic models for epidemic dynamics with social heterogeneity

- Medicine
- Journal of mathematical biology
- 2021

The kinetic model allows to clarify how a selective control can be assumed to achieve a minimal lockdown strategy by only reducing individuals undergoing a very large number of daily contacts and conducts numerical simulations which confirm the ability of the model to describe different phenomena characteristic of the rapid spread of an epidemic. Expand

Social contacts and the spread of infectious diseases

- Physics, Biology
- 2020

A mathematical description of the impact of sociality in the spread of infectious diseases by integrating an epidemiological dynamic with a kinetic modeling of population-based contacts to clarify how a selective control can be assumed to achieve a minimal lockdown strategy. Expand

Hyperbolic compartmental models for epidemic spread on networks with uncertain data: application to the emergence of Covid-19 in Italy

- Biology, Computer Science
- Mathematical Models and Methods in Applied Sciences
- 2021

The ability of the model to correctly describe the spatial heterogeneity underlying the spread of an epidemic in a realistic city network is confirmed with a study of the outbreak of COVID-19 in Italy and its spread in the Lombardy Region. Expand

Universal Features of Epidemic Models Under Social Distancing Guidelines

- Biology, Psychology
- 2020

The main objective of this study is to reduce the disease burden in a population, here measured as the peak of the infected population, while simultaneously minimizing the length of time the population is socially distanced, utilizing both a single period of social distancing as well as periodic relaxation. Expand

Universal features of epidemic models under social distancing guidelines

- Computer Science, Medicine
- Annual Reviews in Control
- 2021

The main objective of this study is to reduce the disease burden in a population, here measured as the peak of the infected population, while simultaneously minimizing the length of time the population is socially distanced, utilizing both a single period of social distancing as well as periodic relaxation. Expand

Spatial spread of COVID-19 outbreak in Italy using multiscale kinetic transport equations with uncertainty

- Biology, Computer Science
- Mathematical biosciences and engineering : MBE
- 2021

A space-dependent multiscale model to describe the spatial spread of an infectious disease under uncertain data with particular interest in simulating the onset of the COVID-19 epidemic in Italy is introduced. Expand

Bi-fidelity stochastic collocation methods for epidemic transport models with uncertainties

- Computer Science, Mathematics
- ArXiv
- 2021

This paper introduces a bi-fidelity approach to quantify uncertainty in spatially dependent epidemic models and considers the class of multiscale transport models recently introduced in [6,10] as the high-f fidelity reference and uses simple two-velocity discrete models for low- fidelity evaluations. Expand

Modeling and simulating the spatial spread of an epidemic through multiscale kinetic transport equations

- Computer Science, Mathematics
- ArXiv
- 2020

A novel space-dependent multiscale model for the spread of infectious diseases in a two-dimensional spatial context on realistic geographical scenarios and an application to the initial spread of COVID-19 is presented. Expand

#### References

SHOWING 1-10 OF 56 REFERENCES

Time-optimal control strategies in SIR epidemic models

- Medicine, Mathematics
- Mathematical Biosciences
- 2017

It is proved that, for all the policies investigated, only bang–bang controls with at most one switch are admitted, and that, in a wide range of epidemiological circumstances, it may be impossible to minimize the total infectious burden while minimizing the epidemic duration. Expand

Optimal, near-optimal, and robust epidemic control

- Biology, Computer Science
- 2020

This work derives the optimal time-limited intervention for reducing peak epidemic prevalence in the standard Susceptible-Infectious-Recovered (SIR) model and shows that alternative, more practical interventions can perform nearly as well as the provably optimal strategy. Expand

Optimal control of a SIR epidemic model with general incidence function and a time delays

- Mathematics
- Cubo (Temuco)
- 2018

In this paper, we introduce an optimal control for a SIR model governed by an ODE system with time delay. We extend the stability studies of model (2.2) in section 2, by incorporating suitable… Expand

Modeling Optimal Age-Specific Vaccination Strategies Against Pandemic Influenza

- Medicine
- Bulletin of mathematical biology
- 2012

A mathematical model that incorporates age-structured transmission dynamics of influenza to evaluate optimal vaccination strategies in the epidemiological context of the Spring 2009 A (H1N1) pandemic in Mexico indicates that optimal age-specific vaccination rates are significantly associated with the amount of vaccines available and the timing of vaccination. Expand

Optimal control for pandemic influenza: the role of limited antiviral treatment and isolation.

- Medicine
- Journal of theoretical biology
- 2010

The implementation of optimal control strategies involving antiviral treatment and/or isolation measures can reduce significantly the number of clinical cases of influenza and can reduce the pressures placed on the health care infrastructure by a pandemic reducing the stress put on the system during epidemic peaks. Expand

Parameter estimation and uncertainty quantification for an epidemic model.

- Mathematics, Medicine
- Mathematical biosciences and engineering : MBE
- 2012

Estimation of the parameters of Susceptible-Infective-Recovered models in the context of least squares finds that estimates of different parameters are correlated, with the magnitude and sign of this correlation depending on the value of R0. Expand

Towards uncertainty quantification and inference in the stochastic SIR epidemic model.

- Mathematics, Computer Science
- Mathematical biosciences
- 2012

In this paper we address the problem of estimating the parameters of Markov jump processes modeling epidemics and introduce a novel method to conduct inference when data consists on partial… Expand

An optimal control theory approach to non-pharmaceutical interventions

- Medicine
- BMC infectious diseases
- 2010

This work applies optimal control on an epidemiologic compartmental model to develop triggers for NPI implementation to minimize expected person-days lost from influenza related deaths and NPI implementations for the model and indicates that linear cost leads to more costly implementation resulting in fewer deaths. Expand

A contribution to the mathematical theory of epidemics

- Biology
- 1927

The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection. Expand

Threshold behaviour of a SIR epidemic model with age structure and immigration

- Medicine, Mathematics
- Journal of mathematical biology
- 2008

A quasi-threshold theorem is proved, in the sense that, below the threshold, the density of infectives is close to 0, while it is away from 0, above the threshold; furthermore, conditions that guarantee uniqueness of steady states are obtained. Expand