State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

Theodosiadou, Ourania; Tsaklidis, George

doi:10.3390/math9161908

Cited by 5 publications

(4 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As part of future work, we believe it would be intriguing to explore the application of a Kalman Filter with nonnegativity constraints [64], Tobit-Kalman filtering [65], or neural networks [66], as they may offer advantages specific to epidemic modeling. Additionally, investigating disease dynamics using alternative stochastic approaches, such as discrete or continuous-time Markov chains, holds great promise [67][68][69].…”

Section: Discussionmentioning

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

View full text Add to dashboard Cite

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.

show abstract

Section: Discussionmentioning

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

View full text Add to dashboard Cite

show abstract

“…At this point, we should emphasize that despite the aforementioned issues, the statistical methodology proposed in [1], has an important role in the field of mathematical modelling in epidemiology. Kalman filtering provides the best linear unbiased estimate of a system's states in the presence of noise and uncertainty, while it optimally combines measurements and a priori system predictions [12,27,28]. It can adapt to changing system dynamics by adjusting the filter's parameters.…”

Section: Discussionmentioning

confidence: 99%

Analyzing the Asymptotic Behavior of an Extended SEIR Model with Vaccination for COVID-19

Papageorgiou,

Vasiliadis,

Tsaklidis

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

Several research papers have attempted to describe the dynamics of COVID-19 based on systems of differential equations. These systems have taken into account quarantined or isolated cases, vaccinations, control measures, and demographic parameters, presenting propositions regarding theoretical results that often investigate the asymptotic behavior of the system. In this paper, we discuss issues that concern the theoretical results proposed in the paper “An Extended SEIR Model with Vaccination for Forecasting the COVID-19 Pandemic in Saudi Arabia Using an Ensemble Kalman Filter”. We propose detailed explanations regarding the resolution of these issues. Additionally, this paper focuses on extending the local stability analysis of the disease-free equilibrium, as presented in the aforementioned paper, while emphasizing the derivation of theorems that validate the global stability of both epidemic equilibria. Emphasis is placed on the basic reproduction number R0, which determines the asymptotic behavior of the system. This index represents the expected number of secondary infections that are generated from an already infected case in a population where almost all individuals are susceptible. The derived propositions can inform health authorities about the long-term behavior of the phenomenon, potentially leading to more precise and efficient public measures. Finally, it is worth noting that the examined paper still presents an interesting epidemiological scheme, and the utilization of the Kalman filtering approach remains one of the state-of-the-art methods for modeling epidemic phenomena.

show abstract

“…At present, several types of constraints have been utilized, including non-negative constraints [1][2][3][4], monotonicity constraints [5][6][7][8], smoothing constraints [9][10][11], etc. Powell et al [12] proposed a Bayesian hierarchical model for estimating constraints conditional random fields to analyze the relationship between air pollution and health.…”

Section: Introductionmentioning

confidence: 99%

Kernel-Free Quadratic Surface Support Vector Regression with Non-Negative Constraints

Wang

Yang

et al. 2023

Entropy

View full text Add to dashboard Cite

In this paper, a kernel-free quadratic surface support vector regression with non-negative constraints (NQSSVR) is proposed for the regression problem. The task of the NQSSVR is to find a quadratic function as a regression function. By utilizing the quadratic surface kernel-free technique, the model avoids the difficulty of choosing the kernel function and corresponding parameters, and has interpretability to a certain extent. In fact, data may have a priori information that the value of the response variable will increase as the explanatory variable grows in a non-negative interval. Moreover, in order to ensure that the regression function is monotonically increasing on the non-negative interval, the non-negative constraints with respect to the regression coefficients are introduced to construct the optimization problem of NQSSVR. And the regression function obtained by NQSSVR matches this a priori information, which has been proven in the theoretical analysis. In addition, the existence and uniqueness of the solution to the primal problem and dual problem of NQSSVR, and the relationship between them are addressed. Experimental results on two artificial datasets and seven benchmark datasets validate the feasibility and effectiveness of our approach. Finally, the effectiveness of our method is verified by real examples in air quality.

show abstract

State Space Modeling with Non-Negativity Constraints Using Quadratic Forms

Cited by 5 publications

References 16 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

Analyzing the Asymptotic Behavior of an Extended SEIR Model with Vaccination for COVID-19

Kernel-Free Quadratic Surface Support Vector Regression with Non-Negative Constraints

Contact Info

Product

Resources

About