An optimal control theory approach to non-pharmaceutical interventions

Lin, Frank Yeong-Sung; Muthuraman, Kumar; Lawley, Mark

doi:10.1186/1471-2334-10-32

Cited by 75 publications

(77 citation statements)

References 41 publications

(56 reference statements)

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“…in agreement with the fitting procedure obtained from the lower bounds of the uncertain initial data. In Figure 7 we represent the evolution of the expected value of the number of infected obtained by the controlled model in the presence of initial random data (29) and uncertain contact frequency (30). The value µ = 10 have been chosen accordingly to the WHO suggestions that around 80% are asymptomatic 1 .…”

Section: Test 2: Impact Of Uncertain Data On the Epidemic Outbreakmentioning

confidence: 99%

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Control with uncertain data of socially structured compartmental epidemic models

Albi

Pareschi

Zanella

2020

Preprint

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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 optimal control formulation of the epidemiological model in presence of uncertain data. After the introduction of the optimal control problem, we formulate an instantaneous approximation of the control that allows us to derive new feedback controlled compartmental models capable of describing the epidemic peak reduction. The need for long-term interventions shows that alternative actions based on the social structure of the system can be as effective as the more expensive global strategy. The importance of the timing and intensity of interventions is particularly relevant in the case of uncertain parameters on the actual number of infected people. Simulations related to data from the recent COVID-19 outbreak in Italy are presented and discussed.

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Section: Test 2: Impact Of Uncertain Data On the Epidemic Outbreakmentioning

confidence: 99%

“…Test 2. Evolution of expected number of infected and their confidence bands for the calibrated control model with ψ(I) = I q /q, q = 1, 2 with uncertain initial data(29) with µ = 10 and uncertain reproduction number (30) with α = 1 in the case of COVID-19 outbreak in Italy.…”

mentioning

confidence: 99%

Control with uncertain data of socially structured compartmental epidemic models

Albi

Pareschi

Zanella

2020

Preprint

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“…Novel insights on the optimal allocation of economic resources were also obtained from approaches embedding compartmental models into optimization frameworks such as optimal control theory or dynamic programming [39,45,[68][69][70][71]. For instance Lee et al [40], using optimal control theory, identified the optimal way to dynamically allocate control measures such as antiviral allocation and isolation, subject to the dynamics of the pandemic and the effects of the control measures on those dynamics.…”

Section: Economic Aspectsmentioning

confidence: 99%

Trends in parameterization, economics and host behaviour in influenza pandemic modelling: a review and reporting protocol

Carrasco

Jit²,

Chen

et al. 2013

Emerg Themes Epidemiol

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BackgroundThe volume of influenza pandemic modelling studies has increased dramatically in the last decade. Many models incorporate now sophisticated parameterization and validation techniques, economic analyses and the behaviour of individuals.MethodsWe reviewed trends in these aspects in models for influenza pandemic preparedness that aimed to generate policy insights for epidemic management and were published from 2000 to September 2011, i.e. before and after the 2009 pandemic.ResultsWe find that many influenza pandemics models rely on parameters from previous modelling studies, models are rarely validated using observed data and are seldom applied to low-income countries. Mechanisms for international data sharing would be necessary to facilitate a wider adoption of model validation. The variety of modelling decisions makes it difficult to compare and evaluate models systematically.ConclusionsWe propose a model Characteristics, Construction, Parameterization and Validation aspects protocol (CCPV protocol) to contribute to the systematisation of the reporting of models with an emphasis on the incorporation of economic aspects and host behaviour. Model reporting, as already exists in many other fields of modelling, would increase confidence in model results, and transparency in their assessment and comparison.

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“…The natural framework to study epidemic problems is the optimal control, aiming at determining the best action with respect to conflicting requirements, such as using as less resources as possible while maximising the effects, that is minimizing the number of infected patients, Refs. [15,[17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of Virus Spread under Different Conditions of Resources Limitations

Giamberardino¹,

Iacoviello²

2019

Information

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The paper addresses the problem of human virus spread reduction when the resources for the control actions are somehow limited. This kind of problem can be successfully solved in the framework of the optimal control theory, where the best solution, which minimizes a cost function while satisfying input constraints, can be provided. The problem is formulated in this contest for the case of the HIV/AIDS virus, making use of a model that considers two classes of susceptible subjects, the wise people and the people with incautious behaviours, and three classes of infected, the ones still not aware of their status, the pre-AIDS patients and the AIDS ones; the control actions are represented by an information campaign, to reduce the category of subjects with unwise behaviour, a test campaign, to reduce the number of subjects not aware of having the virus, and the medication on patients with a positive diagnosis. The cost function considered aims at reducing patients with positive diagnosis using as less resources as possible. Four different types of resources bounds are considered, divided into two classes: limitations on the instantaneous control and fixed total budgets. The optimal solutions are numerically computed, and the results of simulations performed are illustrated and compared to put in evidence the different behaviours of the control actions.

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An optimal control theory approach to non-pharmaceutical interventions

Cited by 75 publications

References 41 publications

Control with uncertain data of socially structured compartmental epidemic models

Control with uncertain data of socially structured compartmental epidemic models

Trends in parameterization, economics and host behaviour in influenza pandemic modelling: a review and reporting protocol

Optimal Control of Virus Spread under Different Conditions of Resources Limitations

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