Discrete-Time vs. Continuous-Time Epidemic Models in Networks

Chen, Zesheng

doi:10.1109/access.2019.2940132

Cited by 12 publications

(14 citation statements)

References 26 publications

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“…Finally, it is to be noticed that, as an alternative to (1) - (3) , the discrete-time version of the SIR can be straightforwardly formulated (since a comparison between the two variants is out of the scope of this contribution, we refer the interested reader to the work in Chen (2019) for details). Independently from the choice of the time domain, the SIR model is able to characterize in broad terms the spread of a pandemic, thus disregarding the multiple and complex facets of a real pandemic.…”

Section: Model Of the Covid-19 Dynamicsmentioning

confidence: 99%

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

Carli

Cavone

Epicoco

et al. 2020

Annual Reviews in Control

100

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The COVID-19 outbreak is deeply influencing the global social and economic framework, due to restrictive measures adopted worldwide by governments to counteract the pandemic contagion. In multi-region areas such as Italy, where the contagion peak has been reached, it is crucial to find targeted and coordinated optimal exit and restarting strategies on a regional basis to effectively cope with possible onset of further epidemic waves, while efficiently returning the economic activities to their standard level of intensity. Differently from the related literature, where modeling and controlling the pandemic contagion is typically addressed on a national basis, this paper proposes an optimal control approach that supports governments in defining the most effective strategies to be adopted during post-lockdown mitigation phases in a multi-region scenario. Based on the joint use of a non-linear Model Predictive Control scheme and a modified Susceptible-Infected-Recovered (SIR)-based epidemiological model, the approach is aimed at minimizing the cost of the so-called non-pharmaceutical interventions (that is, mitigation strategies), while ensuring that the capacity of the network of regional healthcare systems is not violated. In addition, the proposed approach supports policy makers in taking targeted intervention decisions on different regions by an integrated and structured model, thus both respecting the specific regional health systems characteristics and improving the system-wide performance by avoiding uncoordinated actions of the regions. The methodology is tested on the COVID-19 outbreak data related to the network of Italian regions, showing its effectiveness in properly supporting the definition of effective regional strategies for managing the COVID-19 diffusion.

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Section: Model Of the Covid-19 Dynamicsmentioning

confidence: 99%

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

Carli

Cavone

Epicoco

et al. 2020

Annual Reviews in Control

100

View full text Add to dashboard Cite

show abstract

“…Finally, it is to be noticed that, as an alternative to (1)-( 3), the discrete-time version of the SIR can be straightforwardly formulated (since a comparison between the two variants is out of the scope of this contribution, we refer the interested reader to the work in [30] for details). Independently from the choice of the time domain, the SIR model is able to characterize in broad terms the spread of a pandemic, thus disregarding the multiple and complex facets of a real pandemic.…”

Section: Basics On Sir-based Epidemiological Modelsmentioning

confidence: 99%

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

Scarabaggio¹,

Carli²,

Dotoli³

et al. 2020

Preprint

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The COVID-19 outbreak is deeply influencing the global social and economic framework, due to restrictive measures adopted worldwide by governments to counteract the pandemic contagion. In multi-region areas such as Italy, where the contagion peak has been reached, it is crucial to find targeted and coordinated optimal exit and restarting strategies on a regional basis to effectively cope with possible onset of further epidemic waves, while efficiently returning the economic activities to their standard level of intensity. Differently from the related literature, where modeling and controlling the pandemic contagion is typically addressed on a national basis, this paper proposes an optimal control approach that supports governments in defining the most effective strategies to be adopted during post-lockdown mitigation phases in a multi-region scenario. Based on the joint use of a non-linear Model Predictive Control scheme and a modified Susceptible-Infected-Recovered (SIR)-based epidemiological model, the approach is aimed at minimizing the cost of the so-called non-pharmaceutical interventions (that is, mitigation strategies), while ensuring that the capacity of the network of regional healthcare systems is not violated. In addition, the proposed approach supports policy makers in taking targeted intervention decisions on different regions by an integrated and structured model, thus both respecting the specific regional health systems characteristics and improving the system-wide performance by avoiding uncoordinated actions of the regions. The methodology is tested on the COVID-19 outbreak data related to the network of Italian regions, showing its effectiveness in properly supporting the definition of effective regional strategies for managing the COVID-19 diffusion.

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“…It can be pointed out that continuous-time models are widely used since they are more tractable mathematically than the discrete models while having a direct physical interpretation [25]. In particular, the positivity of the solution under nonnegative initial conditions can be proved from the differential system describing the model without the use of extradiscretization adjusting parameters.…”

Section: Introductionmentioning

confidence: 99%

On an Sir Epidemic Model for the COVID-19 Pandemic and the Logistic Equation

Sen

Ibeas

2020

Discrete Dynamics in Nature and Society

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The main objective of this paper is to describe and interpret an SIR (Susceptible-Infectious-Recovered) epidemic model though a logistic equation, which is parameterized by a Malthusian parameter and a carrying capacity parameter, both being time-varying, in general, and then to apply the model to the COVID-19 pandemic by using some recorded data. In particular, the Malthusian parameter is related to the growth rate of the infection solution while the carrying capacity is related to its maximum reachable value. The quotient of the absolute value of the Malthusian parameter and the carrying capacity fixes the transmission rate of the disease in the simplest version of the epidemic model. Therefore, the logistic version of the epidemics’ description is attractive since it offers an easy interpretation of the data evolution especially when the pandemic outbreaks. The SIR model includes recruitment, demography, and mortality parameters, and the total population minus the recovered population is not constant though time. This makes the current logistic equation to be time-varying. An estimation algorithm, which estimates the transmission rate through time from the discrete-time estimation of the parameters of the logistic equation, is proposed. The data are picked up at a set of samples which are either selected by the adaptive sampling law or allocated at constant intervals between consecutive samples. Numerical simulated examples are also discussed.

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Discrete-Time vs. Continuous-Time Epidemic Models in Networks

Cited by 12 publications

References 26 publications

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

Model predictive control to mitigate the COVID-19 outbreak in a multi-region scenario

On an Sir Epidemic Model for the COVID-19 Pandemic and the Logistic Equation

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