An Epidemic Model with Time Delay Determined by the Disease Duration

Ghosh, Samiran; Volpert, Vitaly; Banerjee, Malay

doi:10.3390/math10152561

Cited by 15 publications

(10 citation statements)

References 46 publications

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“…This conclusion allows the simplification of modelling approach since we do not need to determine distributed rate functions, and the point-wise delay model is simpler than the model with distributed delay (Ghosh et al. 2022a ).…”

Section: Discussionmentioning

confidence: 99%

An age-dependent immuno-epidemiological model with distributed recovery and death rates

2023

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The work is devoted to a new immuno-epidemiological model with distributed recovery and death rates considered as functions of time after the infection onset. Disease transmission rate depends on the intra-subject viral load determined from the immunological submodel. The age-dependent model includes the viral load, recovery and death rates as functions of age considered as a continuous variable. Equations for susceptible, infected, recovered and dead compartments are expressed in terms of the number of newly infected cases. The analysis of the model includes the proof of the existence and uniqueness of solution. Furthermore, it is shown how the model can be reduced to age-dependent SIR or delay model under certain assumptions on recovery and death distributions. Basic reproduction number and final size of epidemic are determined for the reduced models. The model is validated with a COVID-19 case data. Modelling results show that proportion of young age groups can influence the epidemic progression since disease transmission rate for them is higher than for other age groups.

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Section: Discussionmentioning

confidence: 99%

An age-dependent immuno-epidemiological model with distributed recovery and death rates

2023

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“…Finally, our current work relies on generalizing the model developed by (5), which has common elements with some cited works here. Indeed, in (5), we introduced the same time delay that models the average time to recover or die, as in (3). At the same time, we could interpret our previous model (5) as one incorporating a long memory effect in the sense that it allows the reproduction of multi-wave peaks depending on the parameter values, as we showed.…”

Section: Introductionmentioning

confidence: 86%

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile

Cumsille

Rojas-Díaz

Conca

2023

Front. Public Health

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BackgroundOne of the main lessons of the COVID-19 pandemic is that we must prepare to face another pandemic like it. Consequently, this article aims to develop a general framework consisting of epidemiological modeling and a practical identifiability approach to assess combined vaccination and non-pharmaceutical intervention (NPI) strategies for the dynamics of any transmissible disease.Materials and methodsEpidemiological modeling of the present work relies on delay differential equations describing time variation and transitions between suitable compartments. The practical identifiability approach relies on parameter optimization, a parametric bootstrap technique, and data processing. We implemented a careful parameter optimization algorithm by searching for suitable initialization according to each processed dataset. In addition, we implemented a parametric bootstrap technique to accurately predict the ICU curve trend in the medium term and assess vaccination.ResultsWe show the framework's calibration capabilities for several processed COVID-19 datasets of different regions of Chile. We found a unique range of parameters that works well for every dataset and provides overall numerical stability and convergence for parameter optimization. Consequently, the framework produces outstanding results concerning quantitative tracking of COVID-19 dynamics. In addition, it allows us to accurately predict the ICU curve trend in the medium term and assess vaccination. Finally, it is reproducible since we provide open-source codes that consider parameter initialization standardized for every dataset.ConclusionThis work attempts to implement a holistic and general modeling framework for quantitative tracking of the dynamics of any transmissible disease, focusing on accurately predicting the ICU curve trend in the medium term and assessing vaccination. The scientific community could adapt it to evaluate the impact of combined vaccination and NPIs strategies for COVID-19 or any transmissible disease in any country and help visualize the potential effects of implemented plans by policymakers. In future work, we want to improve the computational cost of the parametric bootstrap technique or use another more efficient technique. The aim would be to reconstruct epidemiological curves to predict the combined NPIs and vaccination policies' impact on the ICU curve trend in real-time, providing scientific evidence to help anticipate policymakers' decisions.

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“…In this regard, it is worth noting that the COVID-19 pandemic has received a great deal of attention since its appearance. From a mathematical point of view, various theoretical models have been proposed to investigate this still current problem (for more recent examples, see [47][48][49][50][51][52][53]). To that end, here we explore some additional possibilities in modeling the dynamics of COVID data.…”

Section: Application Of the Modelmentioning

confidence: 99%

Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

Stojanović¹,

Bakouch

Ljajko³

et al. 2023

Mathematics

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Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probability-generating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.

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An Epidemic Model with Time Delay Determined by the Disease Duration

Cited by 15 publications

References 46 publications

An age-dependent immuno-epidemiological model with distributed recovery and death rates

An age-dependent immuno-epidemiological model with distributed recovery and death rates

A general modeling framework for quantitative tracking, accurate prediction of ICU, and assessing vaccination for COVID-19 in Chile

Zero-and-One Integer-Valued AR(1) Time Series with Power Series Innovations and Probability Generating Function Estimation Approach

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