Outbreak analysis with a logistic growth model shows COVID-19 suppression dynamics in China

Chaos theory in the understanding of COVID-19 pandemic dynamics

The chaos theory, a field of study in mathematics and physics, offers a unique lens through which to understand the dynamics of the COVID-19 pandemic. This theory, which deals with complex systems whose behavior is highly sensitive to initial conditions, can provide insights into the unpredictable and seemingly random nature of the pandemic's spread. In this review, we will discuss some literature data with the aim of showing how chaos theory could provide valuable perspectives in understanding the complex and dynamic nature of the COVID-19 pandemic. In particular, we will emphasize how the chaos theory can help in dissecting the unpredictable, non- linear progression of the disease, the importance of initial conditions, and the complex interactions between various factors influencing its spread. These insights are crucial for developing effective strategies to manage and mitigate the impact of the pandemic.

Simple mathematical model for predicting COVID-19 outbreaks in Japan based on epidemic waves with a cyclical trend

BACKGROUND

Several models have been used to predict outbreaks during the COVID-19 pandemic, with limited success. We developed a simple mathematical model to accurately predict future epidemic waves.

METHODS

We used data from the Ministry of Health, Labour and Welfare of Japan for newly confirmed COVID-19 cases. COVID-19 case data were summarized as weekly data, and epidemic waves were visualized and identified. The periodicity of COVID-19 in each prefecture of Japan was confirmed using time-series analysis and the autocorrelation coefficient, which was used to investigate the longer-term pattern of COVID-19 cases. Outcomes using the autocorrelation coefficient were visualized via a correlogram to capture the periodicity of the data. An algorithm for a simple prediction model of the seventh COVID-19 wave in Japan comprised three steps. Step 1: machine learning techniques were used to depict the regression lines for each epidemic wave, denoting the "rising trend line"; Step 2: an exponential function with good fit was identified from data of rising straight lines up to the sixth wave, and the timing of the rise of the seventh wave and speed of its spread were calculated; Step 3: a logistic function was created using the values calculated in Step 2 as coefficients to predict the seventh wave. The accuracy of the model in predicting the seventh wave was confirmed using data up to the sixth wave.

RESULTS

Up to March 31, 2023, the correlation coefficient value was approximately 0.5, indicating significant periodicity. The spread of COVID-19 in Japan was repeated in a cycle of approximately 140 days. Although there was a slight lag in the starting and peak times in our predicted seventh wave compared with the actual epidemic, our developed prediction model had a fairly high degree of accuracy.

CONCLUSION

Our newly developed prediction model based on the rising trend line could predict COVID-19 outbreaks up to a few months in advance with high accuracy. The findings of the present study warrant further investigation regarding application to emerging infectious diseases other than COVID-19 in which the epidemic wave has high periodicity.

Threats of COVID-19 arouse public awareness of climate change risks

Public climate change awareness is indispensable to dealing with climate change threats. Understanding whether and how the COVID-19 pandemic impacts on individuals’ climate change risk perception would thus be critical to green economic recovery. We conducted a longitudinal survey study in China when the pandemic was at its height and when it was mitigated. The cross-lagged analysis confirmed our assumed “arousal” effect of perceived COVID-19 risks on climate change risk awareness. We further tested and verified the proposed “dual-pathway” mechanisms of affective generalization (i.e., negative affective states aroused by COVID-19 “spillover” to the assessment of climate change risk) and cognitive association (i.e., the outbreak of COVID-19 awakens people’s recognition of the human-nature-climate issues) via multiple mediation analyses. Our results implied that climate policies could be integrated into pandemic control, and that the public should be more awakened to confront multiple crises with proper guidance.

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Public COVID-19 risk perception arouses their climate change awareness

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A longitudinal survey in China was conducted to verify this arousal effect

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Generalized negative affect states explain the effect

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Cognitive association also explains the effect

Mathematical Models Supporting Control of COVID-19

Mathematical models have played an important role in the management of the coronavirus disease 2019 (COVID-19) pandemic. The aim of this review is to describe the use of COVID-19 mathematical models, their classification, and the advantages and disadvantages of different types of models. We conducted subject heading searches of PubMed and China National Knowledge Infrastructure with the terms "COVID-19," "Mathematical Statistical Model," "Model," "Modeling," "Agent-based Model," and "Ordinary Differential Equation Model" and classified and analyzed the scientific literature retrieved in the search. We categorized the models as data-driven or mechanism-driven. Data-driven models are mainly used for predicting epidemics, and have the advantage of rapid assessment of disease instances. However, their ability to determine transmission mechanisms is limited. Mechanism-driven models include ordinary differential equation (ODE) and agent-based models. ODE models are used to estimate transmissibility and evaluate impact of interventions. Although ODE models are good at determining pathogen transmission characteristics, they are less suitable for simulation of early epidemic stages and rely heavily on availability of first-hand field data. Agent-based models consider influences of individual differences, but they require large amounts of data and can take a long time to develop fully. Many COVID-19 mathematical modeling studies have been conducted, and these have been used for predicting trends, evaluating interventions, and calculating pathogen transmissibility. Successful infectious disease modeling requires comprehensive considerations of data, applications, and purposes.

Prediction of COVID-19 Data Using Hybrid Modeling Approaches

A major emphasis is the dissemination of COVID-19 across the country's many regions and provinces. Using the present COVID-19 pandemic as a guide, the researchers suggest a hybrid model architecture for analyzing and optimizing COVID-19 data during the complete country. The analysis of COVID-19's exploration and death rate uses an ARIMA model with susceptible-infectious-removed and susceptible-exposed-infectious-removed (SEIR) models. The logistic model's failure to forecast the number of confirmed diagnoses and the snags of the SEIR model's too many tuning parameters are both addressed by a hybrid model method. Logistic regression (LR), Autoregressive Integrated Moving Average Model (ARIMA), support vector regression (SVR), multilayer perceptron (MLP), Recurrent Neural Networks (RNN), Gate Recurrent Unit (GRU), and long short-term memory (LSTM) are utilized for the same purpose. Root mean square error, mean absolute error, and mean absolute percentage error are used to show these models. New COVID-19 cases, the number of quarantines, mortality rates, and the deployment of public self-protection measures to reduce the epidemic are all outlined in the study's findings. Government officials can use the findings to guide future illness prevention and control choices.

Modeling and Preliminary Analysis of the Impact of Meteorological Conditions on the COVID-19 Epidemic

Since the COVID-19 epidemic outbreak at the end of 2019, many studies regarding the impact of meteorological factors on the attack have been carried out, and inconsistent conclusions have been reached, indicating the issue's complexity. To more accurately identify the effects and patterns of meteorological factors on the epidemic, we used a combination of logistic regression (LgR) and partial least squares regression (PLSR) modeling to investigate the possible effects of common meteorological factors, including air temperature, relative humidity, wind speed, and surface pressure, on the transmission of the COVID-19 epidemic. Our analysis shows that: (1) Different countries and regions show spatial heterogeneity in the number of diagnosed patients of the epidemic, but this can be roughly classified into three types: "continuous growth", "staged shock", and "finished"; (2) Air temperature is the most significant meteorological factor influencing the transmission of the COVID-19 epidemic. Except for a few areas, regional air temperature changes and the transmission of the epidemic show a significant positive correlation, i.e., an increase in air temperature is conducive to the spread of the epidemic; (3) In different countries and regions studied, wind speed, relative humidity, and surface pressure show inconsistent correlation (and significance) with the number of diagnosed cases but show some regularity.

Analyzing COVID-19's impact on the travel mobility of various social groups in China's Greater Bay Area via mobile phone big data

The COVID-19 outbreak has significantly impacted people's mobility in terms of travel, which is directly related to regional economic vitality and individuals' well-being. This study conducted research on the COVID-19 epidemic's impact on travel mobility in China's Greater Bay Area, utilizing mobile phone big data. The overall influence of COVID-19 was measured by investigating the impact between different income and migration groups in three core cities: Shenzhen, Guangzhou, and Foshan. Individuals' weekly travel frequency and activity space area between December 2019 and May 2020 were calculated, and the average values between the different cities and various social groups were compared. The results showed that travel mobility declined during the epidemic's peak, followed by a recovery based on the overall trend. The start and end of strict law enforcement had a significant impact on the initial decline and subsequent recovery of travel mobility in the core cities. COVID-19 had a larger impact on core cities than peripheral areas, and on non-commute travel frequency, compared to commute travel frequency. Compared to advantaged groups, socially disadvantaged groups experienced a steeper decline in travel mobility during the epidemic's peak, but a more significant recovery afterwards. These findings indicate that discretionary activities have not yet recovered and remain below the pre-epidemic level, and that disadvantaged social groups had limited access to superior precautionary measures for avoiding infection. Based on the findings, we provide several policy suggestions regarding the recovery of travel mobility.

An Easy-to-Use Public Health-Driven Method (the Generalized Logistic Differential Equation Model) Accurately Simulated COVID-19 Epidemic in Wuhan and Correctly Determined the Early Warning Time

Introduction

Modeling on infectious diseases is significant to facilitate public health policymaking. There are two main mathematical methods that can be used for the simulation of the epidemic and prediction of optimal early warning timing: the logistic differential equation (LDE) model and the more complex generalized logistic differential equation (GLDE) model. This study aimed to compare and analyze these two models.

Methods

We collected data on (coronavirus disease 2019) COVID-19 and four other infectious diseases and classified the data into four categories: different transmission routes, different epidemic intensities, different time scales, and different regions, using R2 to compare and analyze the goodness-of-fit of LDE and GLDE models.

Results

Both models fitted the epidemic curves well, and all results were statistically significant. The R2 test value of COVID-19 was 0.924 (p < 0.001) fitted by the GLDE model and 0.916 (p < 0.001) fitted by the LDE model. The R2 test value varied between 0.793 and 0.966 fitted by the GLDE model and varied between 0.594 and 0.922 fitted by the LDE model for diseases with different transmission routes. The R2 test values varied between 0.853 and 0.939 fitted by the GLDE model and varied from 0.687 to 0.769 fitted by the LDE model for diseases with different prevalence intensities. The R2 test value varied between 0.706 and 0.917 fitted by the GLDE model and varied between 0.410 and 0.898 fitted by the LDE model for diseases with different time scales. The GLDE model also performed better with nation-level data with the R2 test values between 0.897 and 0.970 vs. 0.731 and 0.953 that fitted by the LDE model. Both models could characterize the patterns of the epidemics well and calculate the acceleration weeks.

Conclusion

The GLDE model provides more accurate goodness-of-fit to the data than the LDE model. The GLDE model is able to handle asymmetric data by introducing shape parameters that allow it to fit data with various distributions. The LDE model provides an earlier epidemic acceleration week than the GLDE model. We conclude that the GLDE model is more advantageous in asymmetric infectious disease data simulation.

Undergraduates' perceptions on emergency remote learning in ecology in the post‐pandemic era

The COVID‐19 pandemic has strongly disrupted academic activities, particularly in disciplines with a strong empirical component among other reasons by limiting our mobility. It is thus essential to assess emergency remote teaching plans by surveying learners’ opinions and perceptions during these unusual circumstances. To achieve this aim, we conducted a survey during the spring semester of 2021 in an environmental science program to ascertain learners’ perceptions on online and onsite learning activities in ecology‐based modules. We were particularly interested not only in comparing the performance of these two types of activities but also in understanding the role played by learners’ perceptions about nature in shaping this pattern. Environmental science programs are rather heterogeneous from a conceptual point of view and, thus, learners may also be more diverse than in traditional ecology programs, which may affect their interest for ecology‐based modules. We assessed connectedness to nature by computing the reduced version of the Nature Relatedness Scale. Here, we found that online activities systematically obtained significantly lower scores than onsite activities regardless of the wording employed, and that altruistic behaviors were prevalent among learners. Interestingly, scores for both onsite and online activities were strongly influenced by learners’ connectedness to nature, as learners with a stronger connection to nature gave higher scores to both types of activities. Our results suggest that an effort to improve the efficacy of remote learning activities should be the focus of research about teaching methodologies in predominantly empirical scientific disciplines.

Evaluating prediction of COVID-19 at provincial level of South Africa: a statistical perspective

What is the impact of COVID-19 on South Africa? This paper envisages to assist researchers in battling of the COVID-19 pandemic focusing on South Africa. This paper focuses on the spread of the disease by applying heatmap retrieval of hotspot areas, and spatial analysis is carried out using the Moran index. For capturing spatial autocorrelation between the provinces of South Africa, the adjacent as well as the geographical distance measures are used as weight matrix for both absolute and relative counts. Furthermore, generalized logistic growth curve modelling is used for prediction of the COVID-19 spread. We expect this data-driven modelling to provide some insights into hotspot identification and timeous action controlling the spread of the virus.

The starting dates of COVID-19 multiple waves

The severe acute respiratory syndrome of coronavirus 2 spread globally very quickly, causing great concern at the international level due to the severity of the associated respiratory disease, the so-called COVID-19. Considering Rio de Janeiro city (Brazil) as an example, the first diagnosis of this disease occurred in March 2020, but the exact moment when the local spread of the virus started is uncertain as the Brazilian epidemiological surveillance system was not widely prepared to detect suspected cases of COVID-19 at that time. Improvements in this surveillance system occurred over the pandemic, but due to the complex nature of the disease transmission process, specifying the exact moment of emergence of new community contagion outbreaks is a complicated task. This work aims to propose a general methodology to determine possible start dates for the multiple community outbreaks of COVID-19, using for this purpose a parametric statistical approach that combines surveillance data, nonlinear regression, and information criteria to obtain a statistical model capable of describing the multiple waves of contagion observed. The dynamics of COVID-19 in the city of Rio de Janeiro is taken as a case study, and the results suggest that the original strain of the virus was already circulating in Rio de Janeiro city as early as late February 2020, probably being massively disseminated in the population during the carnival festivities.

What can we learn from COVID-19 data by using epidemic models with unidentified infectious cases?

The COVID-19 outbreak, which started in late December 2019 and rapidly spread around the world, has been accompanied by an unprecedented release of data on reported cases. Our objective is to offer a fresh look at these data by coupling a phenomenological description to the epidemiological dynamics. We use a phenomenological model to describe and regularize the reported cases data. This phenomenological model is combined with an epidemic model having a time-dependent transmission rate. The time-dependent rate of transmission involves changes in social interactions between people as well as changes in host-pathogen interactions. Our method is applied to cumulative data of reported cases for eight different geographic areas. In the eight geographic areas considered, successive epidemic waves are matched with a phenomenological model and are connected to each other. We find a single epidemic model that coincides with the best fit to the data of the phenomenological model. By reconstructing the transmission rate from the data, we can understand the contributions of the changes in social interactions (contacts between individuals) on the one hand and the contributions of the epidemiological dynamics on the other hand. Our study provides a new method to compute the instantaneous reproduction number that turns out to stay below 3.5 from the early beginning of the epidemic. We deduce from the comparison of several instantaneous reproduction numbers that the social effects are the most important factor in understanding the epidemic wave dynamics for COVID-19. The instantaneous reproduction number stays below 3.5, which implies that it is sufficient to vaccinate 71% of the population in each state or country considered in our study. Therefore, assuming the vaccines will remain efficient against the new variants and adjusting for higher confidence, it is sufficient to vaccinate 75-80% to eliminate COVID-19 in each state or country.

Forecasting COVID19 Reliability of the Countries by Using Non-Homogeneous Poisson Process Models

Reliability is the probability that a system or a product fulfills its intended function without failure over a period of time and it is generally used to determine the reliability, release and testing stop time of the system. The primary objective of this study is to predict and forecast COVID19 reliabilities of the countries by utilizing this definition of the reliability. To our knowledge, this study is the first carried out in the direction of this objective. The major contribution of this study is to model the COVID19 data by considering the intensity functions with different types of functional shapes, including geometric, exponential, Weibull, gamma and identifying best fit (BF) model for each country, separately. To achieve the objective determined, cumulative number of confirmed cases are modelled by eight Non-Homogenous Poisson Process (NHPP) models. BF models are selected based on three comparison criteria, including Root Mean Square Error (RMSE), Normalized Root Mean Square Error (NRMSE), and Theil Statistics (TS). The results can be summarized as follows: S-shaped models provide better fit for 56 of 70 countries. Current outbreak may continue in 43 countries and a new outbreak may occur in 27 countries. 50 countries have the reliability smaller than 75%, 9 countries between 75% and 90%, and 11 countries a 90% or higher on 11 August 2021.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s00354-022-00183-1.

Emergence of universality in the transmission dynamics of COVID-19

The complexities involved in modelling the transmission dynamics of COVID-19 has been a roadblock in achieving predictability in the spread and containment of the disease. In addition to understanding the modes of transmission, the effectiveness of the mitigation methods also needs to be built into any effective model for making such predictions. We show that such complexities can be circumvented by appealing to scaling principles which lead to the emergence of universality in the transmission dynamics of the disease. The ensuing data collapse renders the transmission dynamics largely independent of geopolitical variations, the effectiveness of various mitigation strategies, population demographics, etc. We propose a simple two-parameter model-the Blue Sky model-and show that one class of transmission dynamics can be explained by a solution that lives at the edge of a blue sky bifurcation. In addition, the data collapse leads to an enhanced degree of predictability in the disease spread for several geographical scales which can also be realized in a model-independent manner as we show using a deep neural network. The methodology adopted in this work can potentially be applied to the transmission of other infectious diseases and new universality classes may be found. The predictability in transmission dynamics and the simplicity of our methodology can help in building policies for exit strategies and mitigation methods during a pandemic.

Assessing the consequences of quarantines during a pandemic

This paper analyzes the epidemiological and economic effects of quarantines. We use a basic epidemiological model, a SEIR-model, that is calibrated to roughly resemble the COVID-19 pandemic, and we assume that individuals that become infected or are isolated on average lose a share of their productivity. An early quarantine postpones but does not alter the course of the pandemic at a cost that increases in the duration and the extent of the quarantine. For quarantines at later stages of the pandemic there is a trade-off between lowering the peak level of infectious people on the one hand and minimizing fatalities and economic losses on the other hand. A longer quarantine dampens the peak level of infectious people and also reduces the total number of infected persons but increases economic losses. Both the peak level of infectious individuals and the total share of the population that will have been infected are U-shaped in relation to the share of the population in quarantine, while economic costs increase in this share. In particular, a quarantine covering a moderate share of the population leads to a lower peak, fewer deaths and lower economic costs, but it implies that the peak of the pandemic occurs earlier.

Simple discrete-time self-exciting models can describe complex dynamic processes: A case study of COVID-19

Hawkes processes are a form of self-exciting process that has been used in numerous applications, including neuroscience, seismology, and terrorism. While these self-exciting processes have a simple formulation, they can model incredibly complex phenomena. Traditionally Hawkes processes are a continuous-time process, however we enable these models to be applied to a wider range of problems by considering a discrete-time variant of Hawkes processes. We illustrate this through the novel coronavirus disease (COVID-19) as a substantive case study. While alternative models, such as compartmental and growth curve models, have been widely applied to the COVID-19 epidemic, the use of discrete-time Hawkes processes allows us to gain alternative insights. This paper evaluates the capability of discrete-time Hawkes processes by modelling daily mortality counts as distinct phases in the COVID-19 outbreak. We first consider the initial stage of exponential growth and the subsequent decline as preventative measures become effective. We then explore subsequent phases with more recent data. Various countries that have been adversely affected by the epidemic are considered, namely, Brazil, China, France, Germany, India, Italy, Spain, Sweden, the United Kingdom and the United States. These countries are all unique concerning the spread of the virus and their corresponding response measures. However, we find that this simple model is useful in accurately capturing the dynamics of the process, despite hidden interactions that are not directly modelled due to their complexity, and differences both within and between countries. The utility of this model is not confined to the current COVID-19 epidemic, rather this model could explain many other complex phenomena. It is of interest to have simple models that adequately describe these complex processes with unknown dynamics. As models become more complex, a simpler representation of the process can be desirable for the sake of parsimony.

The performance of phenomenological models in providing near-term Canadian case projections in the midst of the COVID-19 pandemic: March - April, 2020

BACKGROUND

The COVID-19 pandemic has had an unprecedented impact on citizens and health care systems globally. Valid near-term projections of cases are required to inform the escalation, maintenance and de-escalation of public health measures, and for short-term health care resource planning.

METHODS

Near-term case and epidemic growth rate projections for Canada were estimated using three phenomenological models: the logistic model, Generalized Richard's model (GRM) and a modified Incidence Decay and Exponential Adjustment (m-IDEA) model. Throughout the COVID-19 epidemic in Canada, these models have been validated against official national epidemiological data on an ongoing basis.

RESULTS

The best-fit models estimated that the number of COVID-19 cases predicted to be reported in Canada as of April 1, 2020 and May 1, 2020 would be 11,156 (90 % prediction interval: 9,156-13,905) and 54,745 (90 % prediction interval: 54,252-55,239). The three models varied in their projections and their performance over the first seven weeks of their implementation. Both the logistic model and GRM under-predicted cases reported a week following the projection date in nearly all instances. The logistic model performed best at the early stages, the m-IDEA model performed best at the later stages, and the GRM performed most consistently during the full period assessed.

CONCLUSIONS

All three models have yielded qualitatively comparable near-term forecasts of cases and epidemic growth for Canada. Under or over-estimation of projected cases and epidemic growth by these models could be associated with changes in testing policies and/or public health measures. Simple forecasting models can be invaluable in projecting the changes in trajectory of subsequent waves of cases to provide timely information to support the pandemic response.

A Synergetic R-Shiny Portal for Modeling and Tracking of COVID-19 Data

The purpose of this paper is to introduce a useful online interactive dashboard (https://mahdisalehi.shinyapps.io/Covid19Dashboard/) that visualize and follow confirmed cases of COVID-19 in real-time. The dashboard was made publicly available on 6 April 2020 to illustrate the counts of confirmed cases, deaths, and recoveries of COVID-19 at the level of country or continent. This dashboard is intended as a user-friendly dashboard for researchers as well as the general public to track the COVID-19 pandemic, and is generated from trusted data sources and built in open-source R software (Shiny in particular); ensuring a high sense of transparency and reproducibility. The R Shiny framework serves as a platform for visualization and analysis of the data, as well as an advance to capitalize on existing data curation to support and enable open science. Coded analysis here includes logistic and Gompertz growth models, as two mathematical tools for predicting the future of the COVID-19 pandemic, as well as the Moran's index metric, which gives a spatial perspective via heat maps that may assist in the identification of latent responses and behavioral patterns. This analysis provides real-time statistical application aiming to make sense to academic- and public consumers of the large amount of data that is being accumulated due to the COVID-19 pandemic.

Estimation of SIR model's parameters of COVID-19 in Algeria

BACKGROUND

The coronavirus disease 2019 (COVID-19) is reported in Algeria on February 25th, 2020. Since then, the number is still increasing leading to a total number of 36,699 cases and 1333 deaths on August 12th, 2020. Thus, comprehension of the epidemic curve is very important to predict its evolution and subsequently adapt the best prevention strategies. In this way, the current study was conducted to estimate the parameters of the classical SIR model and to predict the peak of the COVID-19 epidemic in Algeria using data from February 25th, 2020 to August 12th, 2020.

RESULTS

Results showed that the peak of the epidemic will be reached on September 8th, 2021 and the total infected persons will exceed 800,000 cases at the end of the epidemic. Also, more than 15 million persons will be susceptible. The reproduction number (R ₀) is estimated at 1.23254.

CONCLUSION

These results may be helpful for the Algerian authorities to adapt their strategies and may be taken into consideration in the future phase of discontainment.