Range of reproduction number estimates for COVID-19 spread

Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany

The effective reproductive number Rt has taken a central role in the scientific, political, and public discussion during the COVID-19 pandemic, with numerous real-time estimates of this quantity routinely published. Disagreement between estimates can be substantial and may lead to confusion among decision-makers and the general public. In this work, we compare different estimates of the national-level effective reproductive number of COVID-19 in Germany in 2020 and 2021. We consider the agreement between estimates from the same method but published at different time points (within-method agreement) as well as retrospective agreement across eight different approaches (between-method agreement). Concerning the former, estimates from some methods are very stable over time and hardly subject to revisions, while others display considerable fluctuations. To evaluate between-method agreement, we reproduce the estimates generated by different groups using a variety of statistical approaches, standardizing analytical choices to assess how they contribute to the observed disagreement. These analytical choices include the data source, data pre-processing, assumed generation time distribution, statistical tuning parameters, and various delay distributions. We find that in practice, these auxiliary choices in the estimation of Rt may affect results at least as strongly as the selection of the statistical approach. They should thus be communicated transparently along with the estimates.

Markov modeling and performance analysis of infectious diseases with asymptomatic patients

After over three years of COVID-19, it has become clear that infectious diseases are difficult to eradicate, and humans remain vulnerable under their influence in a long period. The presence of presymptomatic and asymptomatic patients is a significant obstacle to preventing and eliminating infectious diseases. However, the long-term transmission of infectious diseases involving asymptomatic patients still remains unclear. To address this issue, this paper develops a novel Markov process for infectious diseases with asymptomatic patients by means of a continuous-time level-dependent quasi-birth-and-death (QBD) process. The model accurately captures the transmission of infectious diseases by specifying several key parameters (or factors). To analyze the role of asymptomatic and symptomatic patients in the infectious disease transmission process, a simple sufficient condition for the stability of the Markov process of infectious diseases is derived using the mean drift technique. Then, the stationary probability vector of the QBD process is obtained by using RG-factorizations. A method of using the stationary probability vector is provided to obtain important performance measures of the model. Finally, some numerical experiments are presented to demonstrate the model's feasibility through analyzing COVID-19 as an example. The impact of key parameters on the system performance evaluation and the infectious disease transmission process are analyzed. The methodology and results of this paper can provide theoretical and technical support for the scientific control of the long-term transmission of infectious diseases, and we believe that they can serve as a foundation for developing more general models of infectious disease transmission.

Trajectories of COVID-19: A longitudinal analysis of many nations and subnational regions

The COVID-19 pandemic is the first to be rapidly and sequentially measured by nation-wide PCR community testing for the presence of the viral RNA at a global scale. We take advantage of the novel "natural experiment" where diverse nations and major subnational regions implemented various policies including social distancing and vaccination at different times with different levels of stringency and adherence. Initially, case numbers expand exponentially with doubling times of ~1-2 weeks. In the nations where interventions were not implemented or perhaps lees effectual, case numbers increased exponentially but then stabilized around 102-to-103 new infections (per km2 built-up area per day). Dynamics under effective interventions were perturbed and infections decayed to low levels. They rebounded concomitantly with the lifting of social distancing policies or pharmaceutical efficacy decline, converging on a stable equilibrium setpoint. Here we deploy a mathematical model which captures this V-shape behavior, incorporating a direct measure of intervention efficacy. Importantly, it allows the derivation of a maximal estimate for the basic reproductive number Ro (mean 1.6-1.8). We were able to test this approach by comparing the approximated "herd immunity" to the vaccination coverage observed that corresponded to rapid declines in community infections during 2021. The estimates reported here agree with the observed phenomena. Moreover, the decay (0.4-0.5) and rebound rates (0.2-0.3) were similar throughout the pandemic and among all the nations and regions studied. Finally, a longitudinal analysis comparing multiple national and regional results provides insights on the underlying epidemiology of SARS-CoV-2 and intervention efficacy, as well as evidence for the existence of an endemic steady state of COVID-19.

Importation, Local Transmission, and Model Selection in Estimating the Transmissibility of COVID-19: The Outbreak in Shaanxi Province of China as a Case Study

Background: Since the emergence of the COVID-19 pandemic, many models have been applied to understand its epidemiological characteristics. However, the ways in which outbreak data were used in some models are problematic, for example, importation was mixed up with local transmission. Methods: In this study, five models were proposed for the early Shaanxi outbreak in China. We demonstrated how to select a reasonable model and correctly use the outbreak data. Bayesian inference was used to obtain parameter estimates. Results: Model comparison showed that the renewal equation model generates the best model fitting and the Susceptible-Exposed-Diseased-Asymptomatic-Recovered (SEDAR) model is the worst; the performance of the SEEDAR model, which divides the exposure into two stages and includes the pre-symptomatic transmission, and SEEDDAAR model, which further divides infectious classes into two equally, lies in between. The Richards growth model is invalidated by its continuously increasing prediction. By separating continuous importation from local transmission, the basic reproduction number of COVID-19 in Shaanxi province ranges from 0.45 to 0.61, well below the unit, implying that timely interventions greatly limited contact between people and effectively contained the spread of COVID-19 in Shaanxi. Conclusions: The renewal equation model provides the best modelling; mixing continuous importation with local transmission significantly increases the estimate of transmissibility.

The fluctuation analysis of public opinion energy: Modeling social group opinion base on the event of social networks

In the period of Corona Virus Disease 2019 (COVID-19), millions of people participate in the discussion of COVID-19 on the Internet, which can easily trigger public opinion and threaten social stability. To find out the relationship between the intergroup variability in numbers and perspectives and the dynamic change of the number of infected people, this paper defines the public focus level to quantify the level of attention of people to the information related to an epidemic situation, and the POF model based on the level of epidemic focus is proposed. In this paper, we have carried out simulation experiments in small-world networks and scale-free networks, respectively, to explore the relationship between the model parameters and the spreading range and speed of each population. Furthermore, the paper also analyzed all the original microblog posts published by the People's Daily from January 14, 2020, to February 12, 2020, and compared the data simulated by the POF model with the real data from the People's Daily, the simulation data and the real data can be well fitted to prove the reliability of the model.

Flatten the curve: Empirical evidence on how non-pharmaceutical interventions substituted pharmaceutical treatments during COVID-19 pandemic

During the outbreak of the COVID-19 pandemic, Non-Pharmaceutical and Pharmaceutical treatments were alternative strategies for governments to intervene. Though many of these intervention methods proved to be effective to stop the spread of COVID-19, i.e., lockdown and curfew, they also posed risk to the economy; in such a scenario, an analysis on how to strike a balance becomes urgent. Our research leverages the mobility big data from the University of Maryland COVID-19 Impact Analysis Platform and employs the Generalized Additive Model (GAM), to understand how the social demographic variables, NPTs (Non-Pharmaceutical Treatments) and PTs (Pharmaceutical Treatments) affect the New Death Rate (NDR) at county-level. We also portray the mutual and interactive effects of NPTs and PTs on NDR. Our results show that there exists a specific usage rate of PTs where its marginal effect starts to suppress the NDR growth, and this specific rate can be reduced through implementing the NPTs.

How Transportation Restriction Shapes the Relationship Between Ambient Nitrogen Dioxide and COVID-19 Transmissibility: An Exploratory Analysis

Background: Several recent studies reported a positive (statistical) association between ambient nitrogen dioxide (NO₂) and COVID-19 transmissibility. However, considering the intensive transportation restriction due to lockdown measures that would lead to declines in both ambient NO₂ concentration and COVID-19 spread, the crude or insufficiently adjusted associations between NO₂ and COVID-19 transmissibility might be confounded. This study aimed to investigate whether transportation restriction confounded, mediated, or modified the association between ambient NO₂ and COVID-19 transmissibility.

Methods: The time-varying reproduction number (R_t) was calculated to quantify the instantaneous COVID-19 transmissibility in 31 Chinese cities from January 1, 2020, to February 29, 2020. For each city, we evaluated the relationships between ambient NO₂, transportation restriction, and COVID-19 transmission under three scenarios, including simple linear regression, mediation analysis, and adjusting transportation restriction as a confounder. The statistical significance (p-value < 0.05) of the three scenarios in 31 cities was summarized.

Results: We repeated the crude correlational analysis, and also found the significantly positive association between NO₂ and COVID-19 transmissibility. We found that little evidence supported NO₂ as a mediator between transportation restriction and COVID-19 transmissibility. The association between NO₂ and COVID-19 transmissibility appears less likely after adjusting the effects of transportation restriction.

Conclusions: Our findings suggest that the crude association between NO₂ and COVID-19 transmissibility is likely confounded by the transportation restriction in the early COVID-19 outbreak. After adjusting the confounders, the association between NO₂ and COVID-19 transmissibility appears unlikely. Further studies are warranted to validate the findings in other regions.