Solvable delay model for epidemic spreading: the case of Covid-19 in Italy

Dell’Anna, Luca

doi:10.1038/s41598-020-72529-y

Cited by 61 publications

(49 citation statements)

References 7 publications

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“…An elegant analytical solution to a linear DDE has been given in Ref. [17], which does not focus too much on the modeling aspects.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to the Dynamic Modeling of an Infectious Disease

Shayak

Sharma

2020

Preprint

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In this work we propose a delay differential equation as a lumped parameter or compartmental infectious disease model featuring high descriptive and predictive capability, extremely high adaptability and low computational requirement. Whereas the model has been developed in the context of COVID-19, it is general enough to be applicable mutatis mutandis to other diseases as well. Our fundamental modeling philosophy consists of a decoupling of public health intervention effects, immune response effects and intrinsic infection properties into separate terms. All parameters in the model are directly related to the disease and its management; we can measure or calculate their values a priori basis our knowledge of the phenomena involved, instead of having to extrapolate them from solution curves. Our model can accurately predict the effects of applying or withdrawing interventions, individually or in combination, and can quickly accommodate any newly released information regarding, for example, the infection properties and the immune response to an emerging infectious disease. After demonstrating that the baseline model can successfully explain the COVID-19 case trajectories observed all over the world, we systematically show how the model can be expanded to account for heterogeneous transmissibility, detailed contact tracing drives, mass testing endeavours and immune responses featuring different combinations of limited-time sterilizing immunity, severity-reducing immunity and antibody dependent enhancement.

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“…An elegant analytical solution to a linear DDE has been given in Ref. [17], which does not focus too much on the modeling aspects.…”

Section: Introductionmentioning

confidence: 99%

A New Approach to the Dynamic Modeling of an Infectious Disease

Shayak

Sharma

2020

Preprint

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“…In fact, eq. (15) is identical to the functional retarded differential equation (11) in [10], with the averaging weights g i set to the constant value g i = 1 /T r .…”

Section: The Modelmentioning

confidence: 99%

“…To our knowledge, there are only a few approaches that are equally simple and effective. In [10] a delay model is presented with a single prognostic equation that has even an analytic solution. Arguments and results are comparable to ours, though our integral formulation is more general and more robust when extracting parameters from available data to feed the prognostic model.…”

Section: Introductionmentioning

confidence: 99%

A novel deterministic forecast model for COVID-19 epidemic based on a single ordinary integro-differential equation

Köhler-Rieper

Röhl

Micheli

2020

Preprint

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In this paper we present a new approach to deterministic modelling of COVID-19 epidemic. Our model dynamics is expressed by a single prognostic variable which satisfies an integro-differential equation. All unknown parameters are described with a single, time-dependent variable R(t). We show that our model has similarities to classic compartmental models, such as SIR, and that the variable R(t) can be interpreted as a generalized effective reproduction number. The advantages of our approach are the simplicity of having only one equation, the numerical stability due to an integral formulation and the reliability since the model is formulated in terms of the most trustable statistical data variable: the number of cumulative diagnosed positive cases of Covid-19. Once this dynamic variable is calculated, other non-dynamic variables, such as the number of heavy cases (hospital beds), the number of intensive-care cases (ICUs) and the fatalities, can be derived from it using a similarly stable, integral approach. The formulation with a single equation allows us to calculate from real data the values of the sample effective reproduction number, which can then be fitted. Extrapolated values of R(t) can be used in the model to make reliable forecasts, though under the assumption that measures for reducing infections are maintained. We have applied our model to more than 20 countries and the ongoing results are available on a web-based platform [1]. In this paper, we focus on the data for two exemplary countries, Italy and Germany, and show that the model is capable of reproducing the course of the epidemic in the past and forecasting its course for a period of four to five weeks with a reasonable numerical stability.

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“…There are several statistical studies ( 3, 4, 9, 11–15, 17, 23, 28 ), using a single measure ( 17 ), estimating the incubation period of the current pandemic. In addition to those statistical approaches, there are numerous analytical and computational studies based on mathematical models, involving Ordinary Differential Equations (ODE) ( 5, 8, 10, 19, 21 ) as well as Delay Differential Equations (DDE) ( 6, 7, 18, 22, 26, 27 ), to calculate the basic reproduction number R 0 and understand the underlying dynamics of the epidemic. Researchers usually consider a single delay models, occasionally two delays.…”

Section: Introductionmentioning

confidence: 99%

Distribution of Incubation Period of COVID-19 in the Canadian Context: Modeling and Computational Study

Paul

Lorin

2020

Preprint

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We propose an original model based on a set of coupled delay differential equations with fourteen delays in order to accurately estimate the incubation period of COVID-19, employing publicly available data of confirmed corona cases. In this goal, we separate the total cases into fourteen groups for the corresponding fourteen incubation periods. The estimated mean incubation period we obtain is 6.74 days (95% Confidence Interval(CI): 6.35 to 7.13), and the 90th percentile is 11.64 days (95% CI: 11.22 to 12.17), corresponding to a good agreement with statistical supported studies. This model provides an almost zero-cost approach to estimate the incubation period.

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Solvable delay model for epidemic spreading: the case of Covid-19 in Italy

Cited by 61 publications

References 7 publications

A New Approach to the Dynamic Modeling of an Infectious Disease

A New Approach to the Dynamic Modeling of an Infectious Disease

A novel deterministic forecast model for COVID-19 epidemic based on a single ordinary integro-differential equation

Distribution of Incubation Period of COVID-19 in the Canadian Context: Modeling and Computational Study

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