A differential equations model-fitting analysis of COVID-19 epidemiological data to explain multi-wave dynamics

Beira, Maria Jardim; Sebastião, Pedro J.

doi:10.1038/s41598-021-95494-6

Cited by 23 publications

(20 citation statements)

References 18 publications

(19 reference statements)

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“…Our investigations of the Delta and Omicron epidemics in the California/Mexico region illustrate the complex interplay and the multiplicity of viral and structural factors that need to be considered to limit viral spread, even as vaccination is reducing disease burden. While our phylodynamic analysis provided insight into patterns of viral introductions into the region and migration across the border, future analysis using compartmental ordinary differential equation models could provide additional insight on how changes in transmission rates, vaccination rates and flow across the border could impact these and future SARS-CoV-2 variant epidemics in the border region [ 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 ]. Given the rapid observed diffusion of Delta, and then Omicron, as the infectiousness of successive variants increases, containment strategies would need to be increasingly extreme to reduce spread.…”

Section: Discussionmentioning

confidence: 99%

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Mehta

Smith

Boukadida

et al. 2022

Viruses

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Evolutionary analysis using viral sequence data can elucidate the epidemiology of transmission. Using publicly available SARS-CoV-2 sequence and epidemiological data, we developed discrete phylogeographic models to interrogate the emergence and dispersal of the Delta and Omicron variants in 2021 between and across California and Mexico. External introductions of Delta and Omicron in the region peaked in early July (2021-07-10 [95% CI: 2021-04-20, 2021-11-01]) and mid-December (2021-12-15 [95% CI: 2021-11-14, 2022-01-09]), respectively, 3 months and 2 weeks after first detection. These repeated introductions coincided with domestic migration events with no evidence of a unique transmission hub. The spread of Omicron was most consistent with gravity centric patterns within Mexico. While cross-border events accounted for only 5.1% [95% CI: 4.3–6] of all Delta migration events, they accounted for 20.6% [95% CI: 12.4–29] of Omicron movements, paralleling the increase in international travel observed in late 2021. Our investigations of the Delta and Omicron epidemics in the California/Mexico region illustrate the complex interplay and the multiplicity of viral and structural factors that need to be considered to limit viral spread, even as vaccination is reducing disease burden. Understanding viral transmission patterns may help intra-governmental responses to viral epidemics.

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Section: Discussionmentioning

confidence: 99%

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Mehta

Smith

Boukadida

et al. 2022

Viruses

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“…Compared to the related studies with similar aim, our model presents both simplicity and functionality. Among them, the PSEIRD(S) model given by Beira and Sebastião [32] revealed its capability to explain the capricious epidemic wave. The model fitting was based on the data sets of daily infected, daily deceased, hospitalized and ICU patients in Portugal.…”

Section: Discussionmentioning

confidence: 99%

“…The optimal parameters were calculated for each Italian region separately. Beira and Sebastião [32] conceived a comprehensive PSEIRD(S) model to fit the data sets related to the infected, deceased and hospitalized cases reported for the severe post-Christmas outbreak in Portugal. Some of the model parameters fitted vary discretely with time, which indicates different scenarios of various epidemic waves.…”

Section: Introductionmentioning

confidence: 99%

Bayesian Framework for Multi-Wave COVID-19 Epidemic Analysis Using Empirical Vaccination Data

Tang

2021

Mathematics

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The COVID-19 pandemic has highlighted the necessity of advanced modeling inference using the limited data of daily cases. Tracking a long-term epidemic trajectory requires explanatory modeling with more complexities than the one with short-time forecasts, especially for the highly vaccinated scenario in the latest phase. With this work, we propose a novel modeling framework that combines an epidemiological model with Bayesian inference to perform an explanatory analysis on the spreading of COVID-19 in Israel. The Bayesian inference is implemented on a modified SEIR compartmental model supplemented by real-time vaccination data and piecewise transmission and infectious rates determined by change points. We illustrate the fitted multi-wave trajectory in Israel with the checkpoints of major changes in publicly announced interventions or critical social events. The result of our modeling framework partly reflects the impact of different stages of mitigation strategies as well as the vaccination effectiveness, and provides forecasts of near future scenarios.

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“…Most of the model revisions are concentrated on defining a time-dependent transmission coefficient. The attempts can achieve good fitting results, especially when handling the fluctuated epidemic situation [ 26 , 27 , 28 , 29 , 30 , 31 ]. Nevertheless, there are two major limitations of these approaches.…”

Section: Introductionmentioning

confidence: 99%

A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics

Zhang

Huang

2022

Biology

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To address the urgent need to accurately predict the spreading trend of the COVID-19 epidemic, a continuous Markov-chain model was, for the first time, developed in this work to predict the spread of COVID-19 infection. A probability matrix of infection was first developed in this model based upon the contact frequency of individuals within the population, the individual’s characteristics, and other factors that can effectively reflect the epidemic’s temporal and spatial variation characteristics. The Markov-chain model was then extended to incorporate both the mutation effect of COVID-19 and the decaying effect of antibodies. The developed comprehensive Markov-chain model that integrates the aforementioned factors was finally tested by real data to predict the trend of the COVID-19 epidemic. The result shows that our model can effectively avoid the prediction dilemma that may exist with traditional ordinary differential equations model, such as the susceptible–infectious–recovered (SIR) model. Meanwhile, it can forecast the epidemic distribution and predict the epidemic hotspots geographically at different times. It is also demonstrated in our result that the influence of the population’s spatial and geographic distribution in a herd infection event is needed in the model for a better prediction of the epidemic trend. At the same time, our result indicates that no simple derivative relationship exists between the threshold of herd immunity and the virus basic reproduction number R0. The threshold of herd immunity achieved through natural immunity is significantly higher than 1 − 1/R0. These not only explain the theoretical misconceptions of herd immunity thresholds in herd immunity theory but also provide a guidance for predicting the optimal vaccination coverage. In addition, our model can predict the temporal and spatial distribution of infections in different epidemic waves. It is implied from our model that it is challenging to eradicate COVID-19 in the short term for a large population size and a wide spatial distribution. It is predicted that COVID-19 is likely to coexist with humans for a long time and that it will exhibit multipoint epidemic effects at a later stage. The statistical evidence is consistent with our prediction and strongly supports our modeling results.

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A differential equations model-fitting analysis of COVID-19 epidemiological data to explain multi-wave dynamics

Cited by 23 publications

References 18 publications

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Comparative Dynamics of Delta and Omicron SARS-CoV-2 Variants across and between California and Mexico

Bayesian Framework for Multi-Wave COVID-19 Epidemic Analysis Using Empirical Vaccination Data

A Continuous Markov-Chain Model for the Simulation of COVID-19 Epidemic Dynamics

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