Inferencing superspreading potential using zero-truncated negative binomial model: exemplification with COVID-19

Time series analysis and short-term forecasting of monkeypox outbreak trends in the 10 major affected countries

BACKGROUND

Considering the rapidly spreading monkeypox outbreak, WHO has declared a global health emergency. Still in the category of being endemic, the monkeypox disease shares numerous clinical characters with smallpox. This study focuses on determining the most effective combination of autoregressive integrated moving average model to encapsulate time dependent flow behaviour of the virus with short run prediction.

METHODS

This study includes the data of confirmed reported cases and cumulative cases from eight most burdened countries across the globe, over the span of May 18, 2022, to December 31, 2022. The data was assembled from the website of Our World in Data and it involves countries such as United States, Brazil, Spain, France, Colombia, Mexico, Peru, United Kingdom, Germany and Canada. The job of modelling and short-term forecasting is facilitated by the employment of autoregressive integrated moving average. The legitimacy of the estimated models is argued by offering numerous model performance indices such as, root mean square error, mean absolute error and mean absolute prediction error.

RESULTS

The best fit models were deduced for each country by using the data of confirmed reported cases of monkeypox infections. Based on diverse set of performance evaluation criteria, the best fit models were then employed to provide forecasting of next twenty days. Our results indicate that the USA is expected to be the hardest-hit country, with an average of 58 cases per day with 95% confidence interval of (00-400). The second most burdened country remained Brazil with expected average cases of 23 (00-130). The outlook is not much better for Spain and France, with average forecasts of 52 (00-241) and 24 (00-121), respectively.

CONCLUSION

This research provides profile of ten most severely hit countries by monkeypox transmission around the world and thus assists in epidemiological management. The prediction trends indicate that the confirmed cases in the USA may exceed than other contemporaries. Based on the findings of this study, it remains plausible to recommend that more robust health surveillance strategy is required to control the transmission flow of the virus especially in USA.

Superspreading, overdispersion and their implications in the SARS-CoV-2 (COVID-19) pandemic: a systematic review and meta-analysis of the literature

BACKGROUND

A recurrent feature of infectious diseases is the observation that different individuals show different levels of secondary transmission. This inter-individual variation in transmission potential is often quantified by the dispersion parameter k. Low values of k indicate a high degree of variability and a greater probability of superspreading events. Understanding k for COVID-19 across contexts can assist policy makers prepare for future pandemics.

METHODS

A literature search following a systematic approach was carried out in PubMed, Embase, Web of Science, Cochrane Library, medRxiv, bioRxiv and arXiv to identify publications containing epidemiological findings on superspreading in COVID-19. Study characteristics, epidemiological data, including estimates for k and R0, and public health recommendations were extracted from relevant records.

RESULTS

The literature search yielded 28 peer-reviewed studies. The mean k estimates ranged from 0.04 to 2.97. Among the 28 studies, 93% reported mean k estimates lower than one, which is considered as marked heterogeneity in inter-individual transmission potential. Recommended control measures were specifically aimed at preventing superspreading events. The combination of forward and backward contact tracing, timely confirmation of cases, rapid case isolation, vaccination and preventive measures were suggested as important components to suppress superspreading.

CONCLUSIONS

Superspreading events were a major feature in the pandemic of SARS-CoV-2. On the one hand, this made outbreaks potentially more explosive but on the other hand also more responsive to public health interventions. Going forward, understanding k is critical for tailoring public health measures to high-risk groups and settings where superspreading events occur.

The effect of variation of individual infectiousness on SARS-CoV-2 transmission in households

Quantifying variation of individual infectiousness is critical to inform disease control. Previous studies reported substantial heterogeneity in transmission of many infectious diseases including SARS-CoV-2. However, those results are difficult to interpret since the number of contacts is rarely considered in such approaches. Here, we analyze data from 17 SARS-CoV-2 household transmission studies conducted in periods dominated by ancestral strains, in which the number of contacts was known. By fitting individual-based household transmission models to these data, accounting for number of contacts and baseline transmission probabilities, the pooled estimate suggests that the 20% most infectious cases have 3.1-fold (95% confidence interval: 2.2- to 4.2-fold) higher infectiousness than average cases, which is consistent with the observed heterogeneity in viral shedding. Household data can inform the estimation of transmission heterogeneity, which is important for epidemic management.

On Spatiotemporal Overdispersion and Macroparasite Accumulation in Hosts Leading to Aggregation: A Quantitative Framework

In many host-parasite systems, overdispersion in the distribution of macroparasites leads to parasite aggregation in the host population. This overdispersed distribution is often characterized by the negative binomial or by the power law. The aggregation is shown by a clustering of parasites in certain hosts, while other hosts have few or none. Here, I present a theory behind the overdispersion in complex spatiotemporal systems as well as a computational analysis for tracking the behavior of transmissible diseases with this kind of dynamics. I present a framework where heterogeneity and complexity in host-parasite systems are related to aggregation. I discuss the problem of focusing only on the average parasite burden without observing the risk posed by the associated variance; the consequences of under- or overestimation of disease transmission in a heterogenous system and environment; the advantage of including the network of social interaction in epidemiological modeling; and the implication of overdispersion in the management of health systems during outbreaks.

Basic reproduction number of the COVID-19 Delta variant: Estimation from multiple transmission datasets

The basic reproduction number, $ R_0 $, plays a central role in measuring the transmissibility of an infectious disease, and it thus acts as the fundamental index for planning control strategies. In the present study, we apply a branching process model to meticulously observed contact tracing data from Wakayama Prefecture, Japan, obtained in early 2020 and mid-2021. This allows us to efficiently estimate $ R_0 $ and the dispersion parameter $ k $ of the wild-type COVID-19, as well as the relative transmissibility of the Delta variant and relative transmissibility among fully vaccinated individuals, from a very limited data. $ R_0 $ for the wild type of COVID-19 is estimated to be 3.78 (95% confidence interval [CI]: 3.72-3.83), with $ k = 0.236 $ (95% CI: 0.233-0.240). For the Delta variant, the relative transmissibility to the wild type is estimated to be 1.42 (95% CI: 0.94-1.90), which gives $ R_0 = 5.37 $ (95% CI: 3.55-7.21). Vaccine effectiveness, determined by the reduction in the number of secondary transmissions among fully vaccinated individuals, is estimated to be 91% (95% CI: 85%-97%). The present study highlights that basic reproduction numbers can be accurately estimated from the distribution of minor outbreak data, and these data can provide further insightful epidemiological estimates including the dispersion parameter and vaccine effectiveness regarding the prevention of transmission.

The role of inter-regional mobility in forecasting SARS-CoV-2 transmission

In this paper, we present a method to forecast the spread of SARS-CoV-2 across regions with a focus on the role of mobility. Mobility has previously been shown to play a significant role in the spread of the virus, particularly between regions. Here, we investigate under which epidemiological circumstances incorporating mobility into transmission models yields improvements in the accuracy of forecasting, where we take the situation in The Netherlands during and after the first wave of transmission in 2020 as a case study. We assess the quality of forecasting on the detailed level of municipalities, instead of on a nationwide level. To model transmissions, we use a simple mobility-enhanced SEIR compartmental model with subpopulations corresponding to the Dutch municipalities. We use commuter information to quantify mobility, and develop a method based on maximum likelihood estimation to determine the other relevant parameters. We show that taking inter-regional mobility into account generally leads to an improvement in forecast quality. However, at times when policies are in place that aim to reduce contacts or travel, this improvement is very small. By contrast, the improvement becomes larger when municipalities have a relatively large amount of incoming mobility compared with the number of inhabitants.

Systematic review and meta-analyses of superspreading of SARS-CoV-2 infections

Superspreading, or overdispersion in transmission, is a feature of SARS-CoV-2 transmission which results in surging epidemics and large clusters of infection. The dispersion parameter is a statistical parameter used to characterize and quantify heterogeneity. In the context of measuring transmissibility, it is analogous to measures of superspreading potential among populations by assuming that collective offspring distribution follows a negative-binomial distribution. We conducted a systematic review and meta-analysis on globally reported dispersion parameters of SARS-CoV-2 infection. All searches were carried out on 10 September 2021 in PubMed for articles published from 1 January 2020 to 10 September 2021. Multiple estimates of the dispersion parameter have been published for 17 studies, which could be related to where and when the data was obtained, in 8 countries (e.g., China, USA, India, Indonesia, Israel, Japan, New Zealand, and Singapore). High heterogeneity was reported among the included studies. The mean estimates of dispersion parameters range from 0.06 to 2.97 over eight countries, the pooled estimate was 0.55 (95% CI: 0.30, 0.79), with changing means over countries and decreasing slightly with the increasing reproduction number. The expected proportion of cases accounting for 80% of all transmissions is 19% (95% CrI: 7, 34) globally. The study location and method were found to be important drivers for diversity in estimates of dispersion parameters. While under high potential of superspreading, larger outbreaks could still occur with the import of the COVID-19 virus by traveling even when an epidemic seems to be under control. This article is protected by copyright. All rights reserved.

Characterizing superspreading potential of infectious disease: Decomposition of individual transmissibility

In the context of infectious disease transmission, high heterogeneity in individual infectiousness indicates that a few index cases can generate large numbers of secondary cases, a phenomenon commonly known as superspreading. The potential of disease superspreading can be characterized by describing the distribution of secondary cases (of each seed case) as a negative binomial (NB) distribution with the dispersion parameter, k. Based on the feature of NB distribution, there must be a proportion of individuals with individual reproduction number of almost 0, which appears restricted and unrealistic. To overcome this limitation, we generalized the compound structure of a Poisson rate and included an additional parameter, and divided the reproduction number into independent and additive fixed and variable components. Then, the secondary cases followed a Delaporte distribution. We demonstrated that the Delaporte distribution was important for understanding the characteristics of disease transmission, which generated new insights distinct from the NB model. By using real-world dataset, the Delaporte distribution provides improvements in describing the distributions of COVID-19 and SARS cases compared to the NB distribution. The model selection yielded increasing statistical power with larger sample sizes as well as conservative type I error in detecting the improvement in fitting with the likelihood ratio (LR) test. Numerical simulation revealed that the control strategy-making process may benefit from monitoring the transmission characteristics under the Delaporte framework. Our findings highlighted that for the COVID-19 pandemic, population-wide interventions may control disease transmission on a general scale before recommending the high-risk-specific control strategies.

Superspreading is one of the key transmission features of many infectious diseases and is considered a consequence of the heterogeneity in infectiousness of individual cases. To characterize the superspreading potential, we divided individual infectiousness into two independent and additive components, including a fixed baseline and a variable part. Such decomposition produced an improvement in the fit of the model explaining the distribution of real-world datasets of COVID-19 and SARS that can be captured by the classic statistical tests. Disease control strategies may be developed by monitoring the characteristics of superspreading. For the COVID-19 pandemic, population-wide interventions are suggested first to limit the transmission at a scale of general population, and then high-risk-specific control strategies are recommended subsequently to lower the risk of superspreading.

Modelling COVID-19 outbreak on the Diamond Princess ship using the public surveillance data

The novel coronavirus disease 2019 (COVID-19) outbreak on the Diamond Princess (DP) ship has caused over 634 cases as of February 20, 2020. We model the transmission process on DP ship as a stochastic branching process, and estimate the reproduction number at the innitial phase of 2.9 (95%CrI: 1.7–7.7). The epidemic doubling time is 3.4 days, and thus timely actions on COVID-19 control were crucial. We estimate the COVID-19 transmissibility reduced 34% after the quarantine program on the DP ship which was implemented on February 5. According to the model simulation, relocating the population at risk may sustainably decrease the epidemic size, postpone the timing of epidemic peak, and thus relieve the tensive demands in the healthcare. The lesson learnt on the ship should be considered in other similar settings.

Comparisons of statistical distributions for cluster sizes in a developing pandemic

BACKGROUND

We consider cluster size data of SARS-CoV-2 transmissions for a number of different settings from recently published data. The statistical characteristics of superspreading events are commonly described by fitting a negative binomial distribution to secondary infection and cluster size data as an alternative to the Poisson distribution as it is a longer tailed distribution, with emphasis given to the value of the extra parameter which allows the variance to be greater than the mean. Here we investigate whether other long tailed distributions from more general extended Poisson process modelling can better describe the distribution of cluster sizes for SARS-CoV-2 transmissions.

METHODS

We use the extended Poisson process modelling (EPPM) approach with nested sets of models that include the Poisson and negative binomial distributions to assess the adequacy of models based on these standard distributions for the data considered.

RESULTS

We confirm the inadequacy of the Poisson distribution in most cases, and demonstrate the inadequacy of the negative binomial distribution in some cases.

CONCLUSIONS

The probability of a superspreading event may be underestimated by use of the negative binomial distribution as much larger tail probabilities are indicated by EPPM distributions than negative binomial alternatives. We show that the large shared accommodation, meal and work settings, of the settings considered, have the potential for more severe superspreading events than would be predicted by a negative binomial distribution. Therefore public health efforts to prevent transmission in such settings should be prioritised.

System dynamics analysis of COVID-19 prevention and control strategies

The COVID-19 pandemic now affects the entire world and has many major effects on the global economy, environment, health, and society. Focusing on the harm COVID-19 poses for human health and society, this study used system dynamics to establish a prevention and control model that combines material supply, public opinion dissemination, public awareness, scientific and technological research, staggered work shifts, and the warning effect (of law/policy). Causal loop analysis was used to identify interactions between subsystems and explore the key factors affecting social benefit. Further, different scenarios were dynamically simulated to explore optimal combination modes. The main findings were as follows: (1) The low supervision mode will produce a lag effect and superimposed effect on material supply and impede social benefit. (2) The strong supervision mode has multiple performances; it can reduce online public opinion dissemination and the rate of concealment and false declaration and improve government credibility and social benefit. However, a fading effect will appear in the middle and late periods, and over time, the effect of strong supervision will gradually weaken (but occasionally rebound) and thus require adjustment. These findings can provide a theoretical basis for improving epidemic prevention and control measures.

The co-circulating transmission dynamics of SARS-CoV-2 Alpha and Eta variants in Nigeria: A retrospective modeling study of COVID-19

BACKGROUND

The COVID-19 pandemic poses serious threats to public health globally, and the emerging mutations in SARS-CoV-2 genomes has become one of the major challenges of disease control. In the second epidemic wave in Nigeria, the roles of co-circulating SARS-CoV-2 Alpha (ie, B.1.1.7) and Eta (ie, B.1.525) variants in contributing to the epidemiological outcomes were of public health concerns for investigation.

METHODS

We developed a mathematical model to capture the transmission dynamics of different types of strains in Nigeria. By fitting to the national-wide COVID-19 surveillance data, the transmission advantages of SARS-CoV-2 variants were estimated by likelihood-based inference framework.

RESULTS

The reproduction numbers were estimated to decrease steadily from 1.5 to 0.8 in the second epidemic wave. In December 2020, when both Alpha and Eta variants were at low prevalent levels, their transmission advantages (against the wild type) were estimated at 1.51 (95% credible intervals (CrI) = 1.48, 1.54), and 1.56 (95% CrI = 1.54, 1.59), respectively. In January 2021, when the original variants almost vanished, we estimated a weak but significant transmission advantage of Eta against Alpha variants with 1.14 (95% CrI = 1.11, 1.16).

CONCLUSIONS

Our findings suggested evidence of the transmission advantages for both Alpha and Eta variants, of which Eta appeared slightly more infectious than Alpha. We highlighted the critical importance of COVID-19 control measures in mitigating the outbreak size and relaxing the burdens to health care systems in Nigeria.

Characterization of Unlinked Cases of COVID-19 and Implications for Contact Tracing Measures: Retrospective Analysis of Surveillance Data

BACKGROUND

Contact tracing and intensive testing programs are essential for controlling the spread of COVID-19. However, conventional contact tracing is resource intensive and may not result in the tracing of all cases due to recall bias and cases not knowing the identity of some close contacts. Few studies have reported the epidemiological features of cases not identified by contact tracing ("unlinked cases") or described their potential roles in seeding community outbreaks.

OBJECTIVE

For this study, we characterized the role of unlinked cases in the epidemic by comparing their epidemiological profile with the linked cases; we also estimated their transmission potential across different settings.

METHODS

We obtained rapid surveillance data from the government, which contained the line listing of COVID-19 confirmed cases during the first three waves in Hong Kong. We compared the demographics, history of chronic illnesses, epidemiological characteristics, clinical characteristics, and outcomes of linked and unlinked cases. Transmission potentials in different settings were assessed by fitting a negative binomial distribution to the observed offspring distribution.

RESULTS

Time interval from illness onset to hospital admission was longer among unlinked cases than linked cases (median 5.00 days versus 3.78 days; P<.001), with a higher proportion of cases whose condition was critical or serious (13.0% versus 8.2%; P<.001). The proportion of unlinked cases was associated with an increase in the weekly number of local cases (P=.049). Cluster transmissions from the unlinked cases were most frequently identified in household settings, followed by eateries and workplaces, with the estimated probability of cluster transmissions being around 0.4 for households and 0.1-0.3 for the latter two settings.

CONCLUSIONS

The unlinked cases were positively associated with time to hospital admission, severity of infection, and epidemic size-implying a need to design and implement digital tracing methods to complement current conventional testing and tracing. To minimize the risk of cluster transmissions from unlinked cases, digital tracing approaches should be effectively applied in high-risk socioeconomic settings, and risk assessments should be conducted to review and adjust the policies.

Exploring the Interaction between E484K and N501Y Substitutions of SARS-CoV-2 in Shaping the Transmission Advantage of COVID-19 in Brazil: A Modeling Study

The COVID-19 pandemic poses serious threats to global health, and the emerging mutation in SARS-CoV-2 genomes is one of the major challenges of disease control. Considering the growth of epidemic curve and the circulating SARS-CoV-2 variants in Brazil, the role of locally prevalent E484K and N501Y substitutions in contributing to the epidemiological outcomes is of public health interest for investigation. We developed a likelihood-based statistical framework to reconstruct reproduction numbers, estimate transmission advantage associated with different SARS-CoV-2 variants regarding the marking (identifying) 484K and 501Y substitutions (including Alpha, Zeta, and Gamma variants) in Brazil, and explored the interactive effects of genetic activities on transmission advantage marked by these two mutations. We found a significant transmission advantage associated with the 484K/501Y variants (including P.1 or Gamma variants), which increased the infectivity significantly by 23%. In contrast and by comparison to Gamma variants, E484K or N501Y (including Alpha or Zeta variants) substitution alone appeared less likely to secure a concrete transmission advantage in Brazil. Our finding indicates that the combined impact of genetic activities on transmission advantage marked by 484K/501Y outperforms their independent contributions in Brazil, which implies an interactive effect in shaping the increase in the infectivity of COVID-19. Future studies are needed to investigate the mechanisms of how E484K and N501Y mutations and the complex genetic mutation activities marked by them in SARS-CoV-2 affect the transmissibility of COVID-19.

Superspreading and heterogeneity in transmission of SARS, MERS, and COVID-19: A systematic review

BACKGROUND

Severe acute respiratory syndrome (SARS), Middle East respiratory syndrome (MERS), and coronavirus disease 2019 (COVID-19) have caused substantial public health burdens and global health threats. Understanding the superspreading potentials of these viruses are important for characterizing transmission patterns and informing strategic decision-making in disease control. This systematic review aimed to summarize the existing evidence on superspreading features and to compare the heterogeneity in transmission within and among various betacoronavirus epidemics of SARS, MERS and COVID-19.

METHODS

PubMed, MEDLINE, and Embase databases were extensively searched for original studies on the transmission heterogeneity of SARS, MERS, and COVID-19 published in English between January 1, 2003, and February 10, 2021. After screening the articles, we extracted data pertaining to the estimated dispersion parameter (k) which has been a commonly-used measurement for superspreading potential.

FINDINGS

We included a total of 60 estimates of transmission heterogeneity from 26 studies on outbreaks in 22 regions. The majority (90%) of the k estimates were small, with values less than 1, indicating an over-dispersed transmission pattern. The point estimates of k for SARS and MERS ranged from 0.12 to 0.20 and from 0.06 to 2.94, respectively. Among 45 estimates of individual-level transmission heterogeneity for COVID-19 from 17 articles, 91% were derived from Asian regions. The point estimates of k for COVID-19 ranged between 0.1 and 5.0.

CONCLUSIONS

We detected a substantial over-dispersed transmission pattern in all three coronaviruses, while the k estimates varied by differences in study design and public health capacity. Our findings suggested that even with a reduced R value, the epidemic still has a high resurgence potential due to transmission heterogeneity.

A particle swarm optimization approach for predicting the number of COVID-19 deaths

The rapid spread of the COVID-19 pandemic has raised huge concerns about the prospect of a major health disaster that would result in a huge number of deaths. This anxiety was largely fueled by the fact that the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), responsible for the disease, was so far unknown, and therefore an accurate prediction of the number of deaths was particularly difficult. However, this prediction is of the utmost importance for public health authorities to make the most reliable decisions and establish the necessary precautions to protect people's lives. In this paper, we present an approach for predicting the number of deaths from COVID-19. This approach requires modeling the number of infected cases using a generalized logistic function and using this function for inferring the number of deaths. An estimate of the parameters of the proposed model is obtained using a Particle Swarm Optimization algorithm (PSO) that requires iteratively solving a quadratic programming problem. In addition to the total number of deaths and number of infected cases, the model enables the estimation of the infection fatality rate (IFR). Furthermore, using some mild assumptions, we derive estimates of the number of active cases. The proposed approach was empirically assessed on official data provided by the State of Qatar. The results of our computational study show a good accuracy of the predicted number of deaths.

Shrinkage in serial intervals across transmission generations of COVID-19

One of the key epidemiological characteristics that shape the transmission of coronavirus disease 2019 (COVID-19) is the serial interval (SI). Although SI is commonly considered following a probability distribution at a population scale, recent studies reported a slight shrinkage (or contraction) of the mean of effective SI across transmission generations or over time. Here, we develop a likelihood-based statistical inference framework with truncation to explore the change in SI across transmission generations after adjusting the impacts of case isolation. The COVID-19 contact tracing surveillance data in Hong Kong are used for exemplification. We find that for COVID-19, the mean of individual SI is likely to shrink with a factor at 0.72 per generation (95%CI: 0.54, 0.96) as the transmission generation increases, where a threshold may exist as the lower boundary of this shrinking process. We speculate that one of the probable explanations for the shrinkage in SI might be an outcome due to the competition among multiple candidate infectors within the same case cluster. Thus, the nonpharmaceutical interventive strategies are crucially important to block the transmission chains, and mitigate the COVID-19 epidemic.