Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation

Lykou, Rodi; Tsaklidis, George

doi:10.3390/math9121445

Cited by 4 publications

(4 citation statements)

References 35 publications

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“…As this quantity cannot be calculated directly [48], we employ the estimation

{\overset{N}{true}}_{eff} (normalt) = \frac{1}{\sum_{i = 1}^{N_{p}} {((), {normalw}_{normalt}^{normali})}^{2}} .

…”

Section: Methodsmentioning

confidence: 99%

A stochastic particle extended SEIRS model with repeated vaccination: Application to real data of COVID‐19 in Italy

Papageorgiou,

Tsaklidis

2024

Math Methods in App Sciences

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The prediction of the evolution of epidemics plays an important role in limiting the transmissibility and the burdensome consequences of infectious diseases, which leads to the employment of mathematical modeling. In this paper, we propose a stochastic particle filtering extended SEIRS model with repeated vaccination and time‐dependent parameters, aiming to efficiently describe the demanding dynamics of time‐varying epidemics. The validity of our model is examined using daily records of COVID‐19 in Italy for a period of 525 days, revealing a notable capacity to uncover the hidden dynamics of the pandemic. The main findings include the estimation of asymptomatic cases, which is a well‐known feature of the current pandemic. Unlike other proposed models that employ extra compartments for asymptomatic cases, which force the estimation of this proportion and significantly increase the model's complexity, our approach leads to the evaluation of the hidden dynamics of COVID‐19 without additional computational burden. Other findings that confirm the model's appropriateness and robustness are its parameter evolution and the estimation of more ICU‐admitted cases compared to the official records during the most prevalent infection wave of January 2022, attributed to the intensified increase in admissions that may have led to full occupancy in ICUs. As the vast majority of datasets contain time series of total recovered and vaccinated cases, we propose a statistical algorithm to estimate the currently recovered and protected through vaccination cases. This necessity arises from the attenuation of antibodies after vaccination/infection and is necessary for long‐time interval predictions. Finally, we not only present a novel stochastic epidemiological model and test its efficiency but also investigate its mathematical properties, such as the existence and stability of epidemic equilibria, giving new insights to the literature. The latter provides additional details concerning the system's long‐term behavior, while the conclusions drawn from the index provide perspectives on the severity and future of the COVID‐19 pandemic.

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“…As this quantity cannot be calculated directly [48], we employ the estimation

{\overset{N}{true}}_{eff} (normalt) = \frac{1}{\sum_{i = 1}^{N_{p}} {((), {normalw}_{normalt}^{normali})}^{2}} .

…”

Section: Methodsmentioning

confidence: 99%

A stochastic particle extended SEIRS model with repeated vaccination: Application to real data of COVID‐19 in Italy

Papageorgiou,

Tsaklidis

2024

Math Methods in App Sciences

Self Cite

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“…, which is also the most frequently utilized selection in the literature [22,[30][31][32][33][34][35][36][37][38]. It is important to mention that when the variance of the process model noise is very low, the samples will have minor variations, and over multiple iterations, the particles may converge to a single point in the state space.…”

Section: An Epidemiologically Informed Sequential Importance Resampli...mentioning

confidence: 99%

“…Algorithm 1 summarizes the implementation of the epidemiologically informed sequential importance resampling particle filter, with penalty factors regarding the evolution of cumulative recovered and deceased cases (EI-PF). We denote by M the number of particles, while the decision on whether the existing particles should be resampled, is based on the effective sample size measure of degeneracy [35]…”

Section: An Epidemiologically Informed Sequential Importance Resampli...mentioning

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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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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“…(iii2) Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation, by Lykou, R. and Tsaklidis, G. [25] This is the first of two papers related to observational errors of Particle Filtering. Particle Filter (PF) methodology that deals with the estimation of latent variables of stochastic processes taking into consideration noisy observations generated by the latent variables.…”

mentioning

confidence: 99%

Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields

Vassiliou

Georgiou

2021

Mathematics

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Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation

Cited by 4 publications

References 35 publications

A stochastic particle extended SEIRS model with repeated vaccination: Application to real data of COVID‐19 in Italy

A stochastic particle extended SEIRS model with repeated vaccination: Application to real data of COVID‐19 in Italy

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

Markov and Semi-Markov Chains, Processes, Systems, and Emerging Related Fields

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