Inverse problem for coefficient identification in SIR epidemic models

Marinov, Tchavdar; Marinova, Rossitza S.; Omojola, Joe; Jackson, Michael L.

doi:10.1016/j.camwa.2014.02.002

Cited by 31 publications

(33 citation statements)

References 6 publications

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“…The present work extends the method proposed in [23] for finding optimum values for the infectivity and recovery rates. In [23], these values are assumed to be constant over the whole interval because we applied the method to a short outbreak of influenza instead of considering the long term evolution of a pandemic as with the case of COVID-19. Here, we assume the infectivity and recovery rates are functions of time, namely a = a(t) and b = b(t).…”

Section: Introductionmentioning

confidence: 72%

“…COVID-19. The problem for the estimation of the constants a and b is an inverse problem solved in [23]. A similar approach for identifying coefficients in an Euler-Bernoulli equation from over-posed data is used in [22] and [25].…”

Section: The Direct Problemmentioning

confidence: 99%

“…We are now ready to construct an algorithm for approximating the solution (S, I), (a, b) of the inverse problem (1), (2), (4), (5). For estimating the coefficients a and b of the SIR model, we use an approach that is very similar to the variational method used in [23]. This method is a generalization of the Least Squares Method.…”

Section: The Inverse Problemmentioning

confidence: 99%

“…3 Solving the inverse problem for the time dependent infectivity and recovery rates A method for solving the inverse problem in the case of constant coefficients a and b is given in [23], along with a discussion of some theoretical aspects. Here, we present the numerical algorithm for estimating the coefficients if they depend on time, i.e., a = a(t) and b = b(t).…”

Section: The Reproduction Rate and The Herd Immunitymentioning

confidence: 99%

See 3 more Smart Citations

Inverse Problem for Identification of Infectivity and Recovery Rates in SIR Epidemic Models as Functions of Time Illustrated with Corona Virus Dynamics up to July 09, 2020

Marinov

Marinova

2020

Preprint

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This work deals with the inverse problem in epidemiology based on a SIR model with time-dependent infectivity and recovery rates, allowing for a better prediction of the long term evolution of a pandemic. The method is used for investigating the COVID-19 spread by first solving an inverse problem for estimating the infectivity and recovery rates from real data. Then, the estimated rates are used to compute the evolution of the disease. The time-depended parameters are estimated for the World and several countries (The United States of America, Canada, Italy, France, Germany, Sweden, Russia, Brazil, Bulgaria, Japan, South Korea, New Zealand) and used for investigating the COVID-19 spread in these countries.

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Section: Introductionmentioning

confidence: 72%

Section: The Direct Problemmentioning

confidence: 99%

Section: The Inverse Problemmentioning

confidence: 99%

Section: The Reproduction Rate and The Herd Immunitymentioning

confidence: 99%

See 2 more Smart Citations

Inverse Problem for Identification of Infectivity and Recovery Rates in SIR Epidemic Models as Functions of Time Illustrated with Corona Virus Dynamics up to July 09, 2020

Marinov

Marinova

2020

Preprint

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“…Here, one aims to estimate different parameters appearing in our epidemiological models based on observed data. Different deterministic approaches by optimisation techniques 29,30 like least-squares methods 31,32 , variational imbedding 33 and Gaussian fitting 34 or stochastic models like time-series 35 or parameter identification by Bayesian methods 36 have been successfully used in inverse epidemiological problems. Evaluating the calculated constant or time-varying transfer rates on acquired data, we have reasonable foundations to make model assumptions plausible.…”

Section: Introductionmentioning

confidence: 99%

Time-Discrete Parameter Identification Algorithms for Two Deterministic Epidemiological Models applied to the Spread of COVID-19

Wacker

Schlüter

2020

Preprint

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The pandemic outbreak of COVID-19 threatens people worldwide. Politicians around the globe have to balance different interests. Accordingly, they make decisions which heavily impact our daily life or even curtail fundamental rights. They consequently base their judgements on advices from scientists. For these reasons, many epidemiological models have appeared and have been famous since the beginning of the twentieth century. However, scientists depend on rich data to evaluate them and their assumptions. As this pandemic outbreak has lead to large data collections by the John Hopkins University since its beginning, we take advantage of this situation and compare two deterministic epidemiological models heavily used - the Susceptible-Infectious-Recovered model (SIR model) and the Susceptible-Infectious-Recovered-Dead model (SIRD model). In contrast to other works which concentrate on future predictions, we aim to investigate the validity of assumptions with respect to available data. For that purpose, instead of using these models forward in time, we propose modified time-discrete versions of the continuous models with relaxing all transfer rates to be time-varying and develop algorithms to predict these coefficients based on the principle of “divide-and-conquer” for the inverse problems. Since Asia, Europe and North America are especially affected by this pandemic, we choose countries from these continents to illustrate our results. In the main part of this article, we escepially discuss our results for Hubei (China). As supplementary material, we illustrate our findings for the aforementioned choice of countries. We finally draw some conclusions for future applications of these models and data acquisition.

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