Chain Binomial Model Research Articles

SARS-CoV-2 transmission in a highly vulnerable population of Brazil: a household cohort study

Household transmission studies seek to understand the transmission dynamics of a pathogen by estimating the risk of infection from household contacts and community exposures. We estimated within/extra-household SARS-CoV-2 infection risk and associated factors in a household cohort study in one of the most vulnerable neighbourhoods in Rio de Janeiro city. Individuals ≥1 years-old with suspected or confirmed COVID-19 in the past 30 days (index cases) and household members aged ≥1 year were enrolled and followed at 14 and 28 days (study period November/2020-December/2021). RT-PCR testing, COVID-19 symptoms, and SARS-CoV-2 serologies were ascertained in all visits. Chain binomial household transmission models were fitted using data from 2024 individuals (593 households). Extra-household infection risk was 74.2% (95% credible interval [CrI] 70.3-77.8), while within-household infection risk was 11.4% (95% CrI 5.7-17.2). Participants reporting having received two doses of a COVID-19 vaccine had lower extra-household (68.9%, 95% CrI 57.3-77.6) and within-household (4.1%, 95% CrI 0.4-16.6) infection risk. Within-household infection risk was higher among participants aged 10-19 years, from overcrowded households, and with low family income. Contrastingly, extra-household infection risk was higher among participants aged 20-29 years, unemployed, and public transportation users. Our study provides important insights into COVID-19 household/community transmission in a vulnerable population that resided in overcrowded households and who struggled to adhere to lockdown policies and social distancing measures. The high extra-household infection risk highlights the extreme social vulnerability of this population. Prioritising vaccination of the most socially vulnerable could protect these individuals and reduce widespread community transmission. Fundação Oswaldo Cruz, CNPq, FAPERJ, Royal Society, Instituto Serrapilheira, FAPESP.

Risk Factors for Community and Intrahousehold Transmission of SARS-CoV-2: Modeling in a Nationwide French Population-Based Cohort Study, the EpiCoV Study.

We assessed the risk of acquiring severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) from household and community exposure according to age, family ties, and socioeconomic and living conditions using serological data from a nationwide French population-based cohort study, the Epidémiologie et Conditions de Vie (EpiCoV) Study. A history of SARS-CoV-2 infection was defined by a positive anti-SARS-CoV-2 enzyme-linked immunosorbent assay immunoglobulin G result in November-December 2020. We applied stochastic chain binomial models fitted to the final distribution of household infections to data from 17,983 individuals aged ≥6 years from 8,165 households. Models estimated the competing risks of being infected from community and household exposure. The age group 18-24 years had the highest risk of extrahousehold infection (8.9%, 95% credible interval (CrI): 7.5, 10.4), whereas the oldest (≥75 years) and youngest (6-10 years) age groups had the lowest risk, at 2.6% (95% CrI: 1.8, 3.5) and 3.4% (95% CrI: 1.9, 5.2), respectively. Extrahousehold infection was also associated with socioeconomic conditions. Within households, the probability of person-to-person transmission increased with age, from 10.6% (95% CrI: 5.0, 17.9) among children aged 6-10 years to 43.1% (95% CrI: 32.6, 53.2) among adults aged 65-74 years. Transmission was higher between partners (29.9%, 95% CrI: 25.6, 34.3) and from mother to child (29.1%, 95% CrI: 21.4, 37.3) than between individuals related by other family ties. In 2020 in France, the main factors identified for extrahousehold SARS-CoV-2 infection were age and socioeconomic conditions. Intrahousehold infection mainly depended on age and family ties.

Behavioral factors and SARS-CoV-2 transmission heterogeneity within a household cohort in Costa Rica

IntroductionVariability in household secondary attack rates and transmission risks factors of SARS-CoV-2 remain poorly understood.MethodsWe conducted a household transmission study of SARS-CoV-2 in Costa Rica, with SARS-CoV-2 index cases selected from a larger prospective cohort study and their household contacts were enrolled. A total of 719 household contacts of 304 household index cases were enrolled from November 21, 2020, through July 31, 2021. Blood specimens were collected from contacts within 30–60 days of index case diagnosis; and serum was tested for presence of spike and nucleocapsid SARS-CoV-2 IgG antibodies. Evidence of SARS-CoV-2 prior infections among household contacts was defined based on the presence of both spike and nucleocapsid antibodies. We fitted a chain binomial model to the serologic data, to account for exogenous community infection risk and potential multi-generational transmissions within the household.ResultsOverall seroprevalence was 53% (95% confidence interval (CI) 48–58%) among household contacts. The estimated household secondary attack rate is 34% (95% CI 5–75%). Mask wearing by the index case is associated with the household transmission risk reduction by 67% (adjusted odds ratio = 0.33 with 95% CI: 0.09–0.75) and not sharing bedroom with the index case is associated with the risk reduction of household transmission by 78% (adjusted odds ratio = 0.22 with 95% CI 0.10–0.41). The estimated distribution of household secondary attack rates is highly heterogeneous across index cases, with 30% of index cases being the source for 80% of secondary cases.ConclusionsModeling analysis suggests that behavioral factors are important drivers of the observed SARS-CoV-2 transmission heterogeneity within the household.

A novel complex social network rumor stochastic model: Convergence in distribution to a final rumor size

We introduce a chain-binomial model in a heterogeneous complex social network (HCSN) to investigate the spread of a rumor. A novel formulation of the state of the Markov chain (MC) for the SEIR (susceptible-exposed-infected-removed) rumor epidemic model is obtained, where two discrete time measures represent individuals in their disease states both instantaneously, and also the total time duration in each state. The general MC is characterized in the HCSN, for both the mean-field and global levels of the network rumor epidemic dynamics. The convergence in distribution of the MC to the final size of the rumor epidemic random variable is fully characterized. Moreover, the algorithm to obtain the expected final number of nodes that ever hear the rumor is given. An example to demonstrate the algorithm is presented.

Household Transmission Dynamics of Seasonal Human Coronaviruses.

Household transmission studies inform how viruses spread among close contacts, but few characterize household transmission of endemic coronaviruses. We used data collected from 223 households with school-age children participating in weekly disease surveillance over 2 respiratory virus seasons (December 2015 to May 2017), to describe clinical characteristics of endemic human coronaviruses (HCoV-229E, HcoV-HKU1, HcoV-NL63, HcoV-OC43) infections, and community and household transmission probabilities using a chain-binomial model correcting for missing data from untested households. Among 947 participants in 223 households, we observed 121 infections during the study, most commonly subtype HCoV-OC43. Higher proportions of infected children (<19 years) displayed influenza-like illness symptoms than infected adults (relative risk, 3.0; 95% credible interval [CrI], 1.5-6.9). The estimated weekly household transmission probability was 9% (95% CrI, 6-13) and weekly community acquisition probability was 7% (95% CrI, 5-10). We found no evidence for differences in community or household transmission probabilities by age or symptom status. Simulations suggest that our study was underpowered to detect such differences. Our study highlights the need for large household studies to inform household transmission, the challenges in estimating household transmission probabilities from asymptomatic individuals, and implications for controlling endemic CoVs.

Vaccination with BNT162b2 reduces transmission of SARS-CoV-2 to household contacts in Israel.

The individual-level effectiveness of vaccines against COVID-19 is well-established. However, few studies have examined vaccine effectiveness against transmission. We used a chain binomial model to estimate the effectiveness of vaccination with BNT162b2 (Pfizer-BioNTech mRNA-based vaccine) against household transmission of SARS-CoV-2 in Israel before and after the Delta variant emerged. Vaccination reduced susceptibility to infection by 89.4% (95% confidence interval (CI): 88.7%, 90.0%), while the vaccine effectiveness against infectiousness given infection was 23.0% (95% CI: −11.3%, 46.7%) during days 10–90 after the second dose prior to June 1, 2021. Total vaccine effectiveness was 91.8%, 95% CI: 88.1%, 94.3%). However, vaccine effectiveness is reduced over time due to the combined effect of waning of immunity and the emergence of the Delta variant.

Household transmission but without the community-acquired outbreak of COVID-19 in Taiwan

BackgroundHousehold transmission is responsible for the subsequent outbreak of community-acquired COVID-19. The aim of this study was to elucidate the household transmission mode and to further estimate effective and basic reproductive number with and without non-pharmaceutical interventions (NPIs).MethodsA total of 26 households with 39 family clusters between January, 2020 and February, 2021 in Taiwan were enrolled for analysis. The Becker's chain binomial model was used to analyze the probabilities of being infected and escaping from SARS-COV-2 before and after January 1st, 2021, which were further converted to estimating basic reproductive numbers in the absence of NPIs. The likelihood of leading to the subsequent community-acquired outbreak given NPIs was further assessed.ResultsThe secondary attack rate was 46.2%. Given the saturated Greenwood model selected as the best fitted model, the probability of being infected and escaping from COVID-19 within household was estimated as 44.4% (95% CI: 5.0%–53.7%) and 55.7% (95% CI: 46.3%–65.0%), respectively. In the second period of early 2021, the infected probability was increased to 58.3% (95% CI: 12.7%–90.0%) and the escape probability was lowered to 41.7% (95% CI: 0.0%–86.9%). The corresponding basic reproductive numbers (R0) increased from 4.29 in the first period to 6.73 in the second period without NPIs. However, none of subsequent community-acquired outbreak was noted in Taiwan given very effective NPIs in both periods.ConclusionThe proposed method and results are useful for designing household-specific containment measures and NPIs to stamp out a large-scale community-acquired outbreak as demonstrated in Taiwan.

Taking account of asymptomatic infections: A modeling study of the COVID-19 outbreak on the Diamond Princess cruise ship.

The COVID-19 outbreak on the Diamond Princess (DP) cruise ship has provided empirical data to study the transmission potential of COVID-19 with the presence of pre/asymptomatic cases. We studied the changes in R0 on DP from January 21 to February 19, 2020 based on chain binomial models under two scenarios: no quarantine assuming a random mixing condition, and quarantine of passengers in cabins—passengers may get infected either by an infectious case in a shared cabin or by pre/asymptomatic crew who continued to work. Estimates of R0 at the beginning of the epidemic were 3.27 (95% CI, 3.02–3.54) and 3.78 (95% CI, 3.49–4.09) respectively for serial intervals of 5 and 6 days; and when quarantine started, with the reported asymptomatic ratio 0.505, R0 rose to 4.18 (95%CI, 3.86–4.52) and 4.73 (95%CI, 4.37–5.12) respectively for passengers who might be exposed to the virus due to pre/asymptomatic crew. Results confirm that the higher the asymptomatic ratio is, the more infectious contacts would happen. We find evidence to support a US CDC report that “a high proportion of asymptomatic infections could partially explain the high attack rate among cruise ship passengers and crew.” Our study suggests that if the asymptomatic ratio is high, the conventional quarantine procedure may not be effective to stop the spread of virus.

Estimating and interpreting secondary attack risk: Binomial considered biased

The household secondary attack risk (SAR), often called the secondary attack rate or secondary infection risk, is the probability of infectious contact from an infectious household member A to a given household member B, where we define infectious contact to be a contact sufficient to infect B if he or she is susceptible. Estimation of the SAR is an important part of understanding and controlling the transmission of infectious diseases. In practice, it is most often estimated using binomial models such as logistic regression, which implicitly attribute all secondary infections in a household to the primary case. In the simplest case, the number of secondary infections in a household with m susceptibles and a single primary case is modeled as a binomial(m, p) random variable where p is the SAR. Although it has long been understood that transmission within households is not binomial, it is thought that multiple generations of transmission can be neglected safely when p is small. We use probability generating functions and simulations to show that this is a mistake. The proportion of susceptible household members infected can be substantially larger than the SAR even when p is small. As a result, binomial estimates of the SAR are biased upward and their confidence intervals have poor coverage probabilities even if adjusted for clustering. Accurate point and interval estimates of the SAR can be obtained using longitudinal chain binomial models or pairwise survival analysis, which account for multiple generations of transmission within households, the ongoing risk of infection from outside the household, and incomplete follow-up. We illustrate the practical implications of these results in an analysis of household surveillance data collected by the Los Angeles County Department of Public Health during the 2009 influenza A (H1N1) pandemic.

Region-specific air pollutants and meteorological parameters influence COVID-19: A study from mainland China

Coronavirus disease 2019 (COVID-19) was first detected in December 2019 in Wuhan, China, with 11,669,259 positive cases and 539,906 deaths globally as of July 8, 2020. The objective of the present study was to determine whether meteorological parameters and air quality affect the transmission of COVID-19, analogous to SARS. We captured data from 29 provinces, including numbers of COVID-19 cases, meteorological parameters, air quality and population flow data, between Jan 21, 2020 and Apr 3, 2020. To evaluate the transmissibility of COVID-19, the basic reproductive ratio (R0) was calculated with the maximum likelihood “removal” method, which is based on chain-binomial model, and the association between COVID-19 and air pollutants or meteorological parameters was estimated by correlation analyses. The mean estimated value of R0 was 1.79 ± 0.31 in 29 provinces, ranging from 1.08 to 2.45. The correlation between R0 and the mean relative humidity was positive, with coefficient of 0.370. In provinces with high flow, indicators such as carbon monoxide (CO) and 24-h average concentration of carbon monoxide (CO_24 h) were positively correlated with R0, while nitrogen dioxide (NO2), 24-h average concentration of nitrogen dioxide (NO2_24 h) and daily maximum temperature were inversely correlated to R0, with coefficients of 0.644, 0.661, −0.636, −0.657, −0.645, respectively. In provinces with medium flow, only the weather factors were correlated with R0, including mean/maximum/minimum air pressure and mean wind speed, with coefficients of −0.697, −0.697, −0.697 and −0.841, respectively. There was no correlation with R0 and meteorological parameters or air pollutants in provinces with low flow. Our findings suggest that higher ambient CO concentration is a risk factor for increased transmissibility of the novel coronavirus, while higher temperature and air pressure, and efficient ventilation reduce its transmissibility. The effect of meteorological parameters and air pollutants varies in different regions, and requires that these issues be considered in future modeling disease transmissibility.

Taking Account of Asymptomatic Infections in Modeling the Transmission Potential of the COVID-19 Outbreak on the Diamond Princess Cruise Ship

Background: The COVID-19 outbreak on the Diamond Princess (DP) cruise ship provided empirical data to study the transmission potential of COVID-19 under quarantine with the presence of asymptomatic cases. Methods: We studied the changes in R0 on the DP from January 21 to February 19, 2020 based on chain-binomial models under two scenarios: no quarantine assuming a random mixing condition, and quarantine of passengers in cabins — passengers may get infected either by an infectious case in a shared cabin or by asymptomatic crew who continued to work. Results: Estimates of R0 at the beginning of the epidemic were 3.27 (95% CI, 3.02-3.54) and 3.78 (95% CI, 3.49-4.09) respectively for serial intervals of 5 and 6 days; and when quarantine started, with the reported asymptomatic ratio 0.505, R0 rose to 4.18 (95%CI, 3.86-4.52) and 4.73 (95%CI, 4.37-5.12) respectively for passengers who might be exposed to the virus due to contacts with asymptomatic crew. The overall R0 for both crew and passengers was decreased to 2.55 (95%CI, 2.36-2.76) and 2.90 (95% CI, 2.67-3.13). Results show that the higher the asymptomatic ratio is, the more infectious contacts would happen. Conclusions: We find evidence to support a US CDC report that “a high proportion of asymptomatic infections could partially explain the high attack rate among cruise ship passengers and crew.” Our study suggests that the effects of quarantine may be limited if the asymptomatic ratio is high, implying that a combination of preventive measures is needed to stop the spread of virus. .

A modified chain binomial model to analyse the ongoing measles epidemic in Greece, July 2017 to February 2018.

Greece is currently experiencing a large measles outbreak, in the context of multiple similar outbreaks across Europe. We devised and applied a modified chain-binomial epidemic model, requiring very simple data, to estimate the transmission parameters of this outbreak. Model results indicate sustained measles transmission among the Greek Roma population, necessitating a targeted mass vaccination campaign to halt further spread of the epidemic. Our model may be useful for other countries facing similar measles outbreaks.

A Modified Epidemic Chain Binomial Model (MECBM) and Its 2,3-Introductory Probabilities

Through the ages, human life and happiness are affected much by wide spread diseases, an unpredictable phenomenon. And infectious disease spread is one of the most unsolvable problems. How infection evolves, how it spreads from person to person and mainly which pattern it follows are some questions which are always unanswerable. Out of many techniques, discrete epidemic models like the chain binomial model are ones which are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infection from the same household with closed population. This paper emphasized mainly on developing the probabilities of all possible epidemic chains with two introductory cases for three-, four- and five-member household and three introductory cases for four- and five-member household. The key phenomenon towards developing this paper was to provide an extension of the modified chain binomial model and its possible probabilities.

On extinction time of a generalized endemic chain-binomial model

We considered a chain-binomial epidemic model not conferring immunity after infection. Mean field dynamics of the model has been analyzed and conditions for the existence of a stable endemic equilibrium are determined. The behavior of the chain-binomial process is probabilistically linked to the mean field equation. As a result of this link, we were able to show that the mean extinction time of the epidemic increases at least exponentially as the population size grows. We also present simulation results for the process to validate our analytical findings.

A Modified Epidemic Chain Binomial Model

Discrete epidemic models are applied to describe the physical phenomena of spreading infectious diseases in a household. In this paper, an attempt has been made to develop a modified epidemic chain model by assuming a beta distribution of third kind for the probability of being infected by contact with a given infective from the same household with closed population. This paper emphasizes mainly on developing the probabilities of all possible epidemic chains with one introductory case for three, four and five member household. The key phenomenon towards developing this paper is to provide an alternative model of chain binomial model.

Transmissibility of tuberculosis among school contacts: An outbreak investigation in a boarding middle school, China

Tuberculosis (TB) outbreak occurred in a boarding middle school of China. We explored its probable sources and quantified the transmissibility and pathogenicity of TB. Clinical evaluation, tuberculin skin testing and chest radiography were conducted to identify TB cases. Mycobacterium tuberculosis isolates underwent genotyping analysis to identify the outbreak source. A chain-binomial transmission model was used to evaluate transmissibility and pathogenicity of TB. A total of 46 active cases were ascertained among 258 students and 15 teachers/staff, an attack rate of 16.8%. Genetic analyses revealed two groups of M. tuberculosis cocirculating during the outbreak and possible importation from local communities. Secondary attack rates among students were 4.1% (2.9%, 5.3%) within grade and 7.9% (4.9%, 11%) within class. An active TB case was estimated to infect 8.4 (7.2, 9.6) susceptible people on average. The smear-positive cases were 28 (8, 101) times as infective as smear-negative cases. Previous BCG vaccination could reduce the probability of developing symptoms after infection by 70% (1.4%, 91%). The integration of clinical evaluation, genetic sequencing, and statistical modeling greatly enhanced our understanding of TB transmission dynamics. Timely diagnosis of smear-positive cases, especially in the early phase of the outbreak, is the key to preventing further spread among close contacts.

Surveillance of influenza from household to community in Taiwan

We propose a chain binomial model to elucidate the transmission modes of influenza within households and with which to further evaluate the spread of influenza in a community. Data on the surveillance of influenza in Taiwan were collected from July 2001 to March 2002. A series of chain binomial models were fitted to estimate the escape probability. This parameter together with accumulated cases of the first episode were further applied to derive the transmission probability, the contact rate and the recovery rate, yielding an estimate of the basic reproductive number and providing a simulation approach with which to assess the spread of influenza in the community. Of the 6 391 614 cases identified during the study period, 4 451 046 were from 3 654 320 households consisting of two to five people, with at least one case used to estimate the escape probabilities within households. The escape probability within households was 92.4%, which, in turn, led to a contact rate estimate of 7.7 per day. The transmission probability was estimated as 8.3%. These three parameters yielded 2.56 as the basic reproductive number. The proposed method provides a means for using household data to evaluate the transmissibility of influenza within a community.

Household transmission of influenza A and B in a school-based study of non-pharmaceutical interventions

The effect of school-based non-pharmaceutical interventions (NPIs) on influenza A and B transmission in children's households has not been estimated in published literature. We use data from a large school-based cluster randomized trial of improved hand and respiratory hygiene measures to explore the secondary transmission of influenza A and B in households of laboratory confirmed influenza cases. Data were taken from the Pittsburgh Influenza Prevention Project, a cluster-randomized trial of NPIs conducted in ten Pittsburgh, PA elementary schools during the 2007–2008 influenza season. We estimated two measures of influenza transmissibility in households; the susceptible infectious transmission probability, using variants of the Reed–Frost chain binomial model, and the secondary attack rate. We identified predictors of ILI using a logistic generalized estimating equation model. We estimate the secondary attack rates in intervention households to be 0.26 (95% confidence interval (CI) 0.19–0.34) compared to 0.30 (95% CI 0.23–0.38) in control households. Race and age were significant risk factors for secondary ILI acquisition in this study. We found no significant differences between the transmission probabilities for infectious individuals in intervention (0.19, 95% CI 0.14–0.25), and control households (0.22, 95% CI 0.16–0.29). Similarly, estimates for secondary attack rates and transmission probabilities for households with confirmed influenza A (0.31 and 0.22) were not significantly different from estimates from households with confirmed influenza B (0.25 and 0.20). While influenza A and B are thought to have different transmission characteristics, we find no significant differences in their transmissibility within households. Though our results suggest a potential effect, we found no statistically significant effect of school-based non-pharmaceutical interventions on transmission in symptomatic children's homes.

On the Markov Chain Binomial Model

Rudolfer [1] studied properties and estimation of a state Markov chain binomial (MCB) model of extra-binomial variation. The variance expression in Lemma 4 is stated without proof but is incorrect, resulting in both Lemma 5 and Theorem 2 also being incorrect. These errors were corrected in Rudolfer [2]. In Sections 2 and 3 of this paper, a new derivation of the variance expression in a setting involving the natural parameters is presented and the relation of the MCB model to Edwards’ [3] probability generating function (pgf) approach is discussed. Section 4 deals with estimation of the model parameters. Estimation by the maximum likelihood method is difficult for a larger number n of Markov trials due to the complexity of the calculation of probabilities using Equation (3.2) of Rudolfer [1]. In this section, the exact maximum likelihood estimation of model parameters is obtained utilizing a sequence of Markov trials each involving n observations from a {0,1}- state MCB model and may be used for any value of n. Two examples in Section 5 illustrate the usefulness of the MCB model. The first example gives corrected results for Skellam’s Brassica data while the second applies the “sequence approach” to data from Crouchley and Pickles [4].

A Generalized Chain Binomial Model with Aggregated Data

In large cohort studies it can be impractical to report individual data that only summary or aggregated data are available. Using aggregated data from Bernoulli trials is expected to result in overdispersion so that a quasi-binomial approach would seem feasible. We show that when applied to aggregated data arising from cohorts of individuals according to a chain binomial model, the quasi-binomial model results in biased estimates. We propose an alternate calibration estimator and demonstrate its improved performance by simulations. The calibration method is then applied to model the probability of leaving a personal emergency link service in Hong Kong.