Analysis of SDEs Applied to SEIR Epidemic Models by Extended Kalman Filter Method

Ndanguza, Denis; Mbalawata, Isambi Sailon; Nsabimana, J. P.

doi:10.4236/am.2016.717175

Cited by 8 publications

(5 citation statements)

References 27 publications

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“…In the present study, a novel EI-PF is introduced for the modeling of epidemic outbreaks. The presented approach incorporates time-varying transmissibility and mortality rates, which frequently characterize the prevalence of epidemics [19,20,25,50]. Furthermore, two extra parameters were integrated that improve the particle weight distribution and consequently the resampling procedure.…”

Section: Discussionmentioning

confidence: 99%

“…Sebbagh and Kechida [19], employed a SEIRD-extended Kalman filter (EKF), including the parameters of the model in the updating process of the EKF. Ndanguza et al [20] included in the EKF-SEIR model the estimation of the epidemic parameters, while Costa et al [21] combined also an EKF with a SEIR scheme to simulate an epidemic outbreak. Calvetti et al [22], mixed the susceptible-exposed-asymptomatic-infectious-recovered structure with the methodology of the particle filter for the estimation of the early-stages of the spread of COVID-19 in Ohio and Michigan.…”

Section: Introductionmentioning

confidence: 99%

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A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022

Papageorgiou,

Kolias

2024

Inverse Problems

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Contagious diseases are constantly affecting more and more people every day, resulting in widespread health crises especially in developing nations. Previous studies have developed deterministic and stochastic mathematical models to investigate the spread of epidemics. In the present study, a hybrid particle filtering epidemiological model is proposed, which combines the elements of a deterministic susceptible-exposed-infectious-recovered-deceased (SEIRD) model with the inclusion of stochastic and penalty factors, in order to efficiently evaluate the dynamics of the disease. The inclusion of penalty factors stands out as the main novelty of the proposed methodology, guaranteeing estimations that align with the unique aspects of the examined natural phenomenon. The model is applied to the monkeypox (mpox) data of the United States from June 25th to November 21th, 2022. Our approach is compared to four alternatives, corresponding to deterministic and stochastic approaches that are associated with either fixed or time-varying parameters. In all cases, the particle filtering models displayed better characteristics in terms of infectious cases and deaths compared to their deterministic counterpart. The final version of the proposed epidemiologically informed particle filtering (EI-PF) model exhibited significant potential and provided the best fitting/predictive performance compared to other examined methodologies. The predictive effectiveness of the proposed methodology has been thoroughly evaluated across various time intervals. Moreover, the inclusion of additional penalty factors in the weight computation procedure, assists in reducing fitting and prediction errors while simultaneously providing increased likelihood estimates. This modelling approach can be readily applied to other epidemics, both existing and emerging, where uncertainties in system dynamics and real-time observations hinder the accurate capture of the epidemic's progression. 

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022

Papageorgiou,

Kolias

2024

Inverse Problems

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“…The introduction of random effects into Equations (2) leads to a stochastic differential equation system. The deduced model is the stochastic equivalent of the modified SEIR model [24].…”

Section: Stochastic Equivalent Of the Deterministic Seir Modelmentioning

confidence: 99%

Probabilistic Modelling of COVID-19 Dynamic in the Context of Madagascar

Raherinirina¹,

Fandresena²,

Hajalalaina³

et al. 2021

OJMSi

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We propose a probabilistic approach to modelling the propagation of the coronavirus disease 2019 in Madagascar, with all its specificities. With the strategy of the Malagasy state, which consists of isolating all suspected cases and hospitalized confirmed case, we get an epidemic model with seven compartments: susceptible (S), Exposed (E), Infected (I), Asymptomatic (A), Hospitalized (H), Cured (C) and Death (D). In addition to the classical deterministic models used in epidemiology, the stochastic model offers a natural representation of the evolution of the COVID-19 epidemic. We inferred the models with the official data provided by the COVID-19 Command Center (CCO) of Madagascar, between March and August 2020. The basic reproduction number R 0 and the other parameters were estimated with a Bayesian approach. We developed an algorithm that allows having a temporal estimate of this number with confidence intervals. The estimated values are slightly lower than the international references. Generally, we were able to obtain a simple but effective model to describe the spread of the disease.

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“…Singh et al [15] utilize the standard Kalman Filter to estimate the evolution of the pandemic in India, but as they state, these estimations are only reliable over a short time period. Costa et al [16] combine a SEIR model with an extended Kalman filter (EKF) to simulate the outbreak of an epidemic, while Ndanguza et al [17] include in the SEIR-EKF combination the estimation of the epidemiological model's parameters. Sebbagh and Kechida [18] propose a SIRD-EKF model for the estimation of the evolution of COVID-19.…”

Section: Introductionmentioning

confidence: 99%

An improved epidemiological-unscented Kalman filter (hybrid SEIHCRDV-UKF) model for the prediction of COVID-19. Application on real-time data

Papageorgiou

Tsaklidis

2023

Chaos, Solitons & Fractals

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Analysis of SDEs Applied to SEIR Epidemic Models by Extended Kalman Filter Method

Cited by 8 publications

References 27 publications

A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022

A novel epidemiologically informed particle filter for assessing epidemic phenomena. Application to the monkeypox outbreak of 2022

Probabilistic Modelling of COVID-19 Dynamic in the Context of Madagascar

An improved epidemiological-unscented Kalman filter (hybrid SEIHCRDV-UKF) model for the prediction of COVID-19. Application on real-time data

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