West Nile virus transfusion-transmission risk in Australia associated with a seasonal outbreak in the United States.

BACKGROUND: West Nile virus (WNV) is a potentially transfusion-transmissible virus endemic in the US. The aim of this study was to estimate the monthly WNV transfusion transmission (TT) risk in Australia associated with donors returning from the US in 2018 and consider the implications for mitigation strategies. STUDY DESIGN AND METHODS: We used a probabilistic risk model to estimate the monthly WNV TT risks for each outbreak state/district in the US for the 2018 transmission season and the cumulative monthly risk for all US states/districts. RESULTS: The highest monthly cumulative transfusion risk in Australia occurred in August 2018 when 746 West Nile neuroinvasive disease cases were reported in the US and the estimated mean WNV TT risk in Australia was 1 in 1.0 × 108 donations (95% confidence interval [CI]: 1.6 × 108 -7.0 × 107 ). The highest risk during August was associated with California, with a mean risk of 1 in 4.1 × 108 donations (95% CI: 2.9 × 108 -6.6 × 108 ), representing 24% of the total risk in Australia. The cumulative TT risk in Australia for the other 11 months varied from 1 in 1.5 × 108 donations (95% CI: 2.3 × 108 -1.0 × 108 ) in September to 1 in 3.9 × 1010 donations (95% CI: 6.1 × 1010 -2.7 × 1010 ) in February. DISCUSSION: Our modeling indicates that the WNV TT risk in Australia associated with seasonal outbreaks in the US is extremely small and may not warrant donation restrictions for donors returning from the US.

Review of Mathematical Models of Vaccination for Preventing Congenital Cytomegalovirus Infection.

BACKGROUND: Several cytomegalovirus (CMV) vaccine candidates are under development. To reduce the burden of congenital CMV infection, potential strategies under consideration include vaccination of adult women, adolescent girls, and/or young children (both sexes). METHODS: We reviewed 5 studies that used infectious disease modeling to assess the potential impact of vaccination for preventing congenital CMV infection. All models assumed CMV vaccination would prevent primary infection and 2 models also assumed prevention of reinfections and reactivations. RESULTS: Despite differences in structure, assumptions, and population data, infant vaccination (both sexes) was the optimal strategy in all models, but in 1 model vaccinating seronegative women at 19-21 years of age was also optimal (for duration of vaccine protection ≥8 years). In 3 models, infant vaccination increased average age at primary infection as a result of decreased secondary transmission (herd immunity) combined with waning vaccine-induced immunity. This effect could increase the risk of congenital CMV infections in populations where primary CMV infection occurs early in childhood but could be minimized by administering a second dose of vaccine during adolescence. CONCLUSIONS: Understanding vaccine efficacy and duration of immunity, and how these might vary depending on CMV serostatus and age at vaccination, will be key to defining CMV vaccination strategies.

Modeling the West Nile virus transfusion transmission risk in a nonoutbreak country associated with traveling donors.

BACKGROUND: West Nile virus (WNV) is a mosquito-borne virus and transfusion transmission (TT) has been demonstrated. The European Union and neighboring countries experience an annual transmission season. STUDY DESIGN AND METHODS: We developed a novel probabilistic model to estimate the WNV TT risk in Australia attributable to returned donors who had travelled to the European Union and neighboring countries during the 2018. We estimated weekly WNV TT risks in Australia for each outbreak country and the cumulative risk for all countries. RESULTS: Highest mean weekly TT risk in Australia attributable to donors returning from a specific outbreak country was 1 in 23.3 million (plausible range, 16.8-41.9 million) donations during Week 39 in Croatia. Highest mean weekly cumulative TT risk was 1 in 8.5 million donations (plausible range, 5.1-17.8 million) during Week 35. CONCLUSIONS: The estimated TT risk in Australia attributable to returning donors from the European Union and neighboring countries in 2018 was very small, and additional risk mitigation strategies were not indicated. In the context of such low TT risks, a simpler but effective approach would be to monitor the number of weekly reported West Nile fever cases and implement risk modeling only when the reported cases reached a predefined number or trigger point.

Forecasting the 2014 West African Ebola Outbreak.

In 2014-2015, a large Ebola outbreak afflicted Liberia, Guinea, and Sierra Leone. We performed a systematic review of 26 manuscripts, published between 2014 and April 2015, that forecasted the West African Ebola outbreak while it was occurring, and we derived implications for how results could be interpreted by policymakers. Forecasted case counts varied widely. An important determinant of forecast accuracy for case counts was how far into the future predictions were made. Generally, forecasts for less than 2 months into the future tended to be more accurate than those made for more than 10 weeks into the future. The exceptions were parsimonious statistical models in which the decay of the rate of spread of the pathogen among susceptible individuals was dealt with explicitly. The most important lessons for policymakers regarding future outbreaks, when using similar modeling results, are: 1) uncertainty of forecasts will be greater in the beginning of the outbreak; 2) when data are limited, forecasts produced by models designed to inform specific decisions should be used complementarily for robust decision-making (e.g., 2 statistical models produced the most reliable case-counts forecasts for the studied Ebola outbreak but did not enable understanding of interventions' impact, whereas several compartmental models could estimate interventions' impact but required unavailable data); and 3) timely collection of essential data is necessary for optimal model use.

The role of super-spreading events in Mycobacterium tuberculosis transmission: evidence from contact tracing.

BACKGROUND: In current epidemiology of tuberculosis (TB), heterogeneity in infectiousness among TB patients is a challenge, which is not well studied. We aimed to quantify this heterogeneity and the presence of "super-spreading" events that can assist in designing optimal public health interventions. METHODS: TB epidemiologic investigation data notified between 1 January 2005 and 31 December 2015 from Victoria, Australia were used to quantify TB patients' heterogeneity in infectiousness and super-spreading events. We fitted a negative binomial offspring distribution (NBD) for the number of secondary infections and secondary active TB disease each TB patient produced. The dispersion parameter, k, of the NBD measures the level of heterogeneity, where low values of k (e.g. k < 1) indicate over-dispersion. Super-spreading was defined as patients causing as many or more secondary infections as the 99th centile of an equivalent homogeneous distribution. Contact infection was determined based on a tuberculin skin test (TST) result of ≥10 mm. A NBD model was fitted to identify index characteristics that were associated with the number of contacts infected and risk ratios (RRs) were used to quantify the strength of this association. RESULTS: There were 4190 (2312 pulmonary and 1878 extrapulmonary) index TB patients and 18,030 contacts. A total of 15,522 contacts were tested with TST, of whom 3213 had a result of ≥10 mm. The dispersion parameter, k for secondary infections was estimated at 0.16 (95%CI 0.14-0.17) and there were 414 (9.9%) super-spreading events. From the 3213 secondary infections, 2415 (75.2%) were due to super-spreading events. There were 226 contacts who developed active TB disease and a higher level of heterogeneity was found for this outcome than for secondary infection, with k estimated at 0.036 (95%CI 0.025-0.046). In regression analyses, we found that infectiousness was greater among index patients found by clinical presentation and those with bacteriological confirmation. CONCLUSION: TB transmission is highly over dispersed and super-spreading events are responsible for a substantial majority of secondary infections. Heterogeneity of transmission and super-spreading are critical issues to consider in the design of interventions and models of TB transmission dynamics.

Agent-based models of malaria transmission: a systematic review.

BACKGROUND: Much of the extensive research regarding transmission of malaria is underpinned by mathematical modelling. Compartmental models, which focus on interactions and transitions between population strata, have been a mainstay of such modelling for more than a century. However, modellers are increasingly adopting agent-based approaches, which model hosts, vectors and/or their interactions on an individual level. One reason for the increasing popularity of such models is their potential to provide enhanced realism by allowing system-level behaviours to emerge as a consequence of accumulated individual-level interactions, as occurs in real populations. METHODS: A systematic review of 90 articles published between 1998 and May 2018 was performed, characterizing agent-based models (ABMs) relevant to malaria transmission. The review provides an overview of approaches used to date, determines the advantages of these approaches, and proposes ideas for progressing the field. RESULTS: The rationale for ABM use over other modelling approaches centres around three points: the need to accurately represent increased stochasticity in low-transmission settings; the benefits of high-resolution spatial simulations; and heterogeneities in drug and vaccine efficacies due to individual patient characteristics. The success of these approaches provides avenues for further exploration of agent-based techniques for modelling malaria transmission. Potential extensions include varying elimination strategies across spatial landscapes, extending the size of spatial models, incorporating human movement dynamics, and developing increasingly comprehensive parameter estimation and optimization techniques. CONCLUSION: Collectively, the literature covers an extensive array of topics, including the full spectrum of transmission and intervention regimes. Bringing these elements together under a common framework may enhance knowledge of, and guide policies towards, malaria elimination. However, because of the diversity of available models, endorsing a standardized approach to ABM implementation may not be possible. Instead it is recommended that model frameworks be contextually appropriate and sufficiently described. One key recommendation is to develop enhanced parameter estimation and optimization techniques. Extensions of current techniques will provide the robust results required to enhance current elimination efforts.

Assessment of the Status of Measles Elimination in the United States, 2001-2014.

We assessed the status of measles elimination in the United States using outbreak notification data. Measles transmissibility was assessed by estimation of the reproduction number, R, the average number of secondary cases per infection, using 4 methods; elimination requires maintaining R at <1. Method 1 estimates R as 1 minus the proportion of cases that are imported. Methods 2 and 3 estimate R by fitting a model of the spread of infection to data on the sizes and generations of chains of transmission, respectively. Method 4 assesses transmissibility before public health interventions, by estimating R for the case with the earliest symptom onset in each cluster (Rindex). During 2001-2014, R and Rindex estimates obtained using methods 1-4 were 0.72 (95% confidence interval (CI): 0.68, 0.76), 0.66 (95% CI: 0.62, 0.70), 0.45 (95% CI: 0.40, 0.49), and 0.63 (95% CI: 0.57, 0.69), respectively. Year-to-year variability in the values of R and Rindex and an increase in transmissibility in recent years were noted with all methods. Elimination of endemic measles transmission is maintained in the United States. A suggested increase in measles transmissibility since elimination warrants continued monitoring and emphasizes the importance of high measles vaccination coverage throughout the population.

Estimating Direct and Indirect Protective Effect of Influenza Vaccination in the United States.

With influenza vaccination rates in the United States recently exceeding 45% of the population, it is important to understand the impact that vaccination is having on influenza transmission. In this study, we used a Bayesian modeling approach, combined with a simple dynamical model of influenza transmission, to estimate this impact. The combined framework synthesized evidence from a range of data sources relating to influenza transmission and vaccination in the United States. We found that, for seasonal epidemics, the number of infections averted ranged from 9.6 million in the 2006-2007 season (95% credible interval (CI): 8.7, 10.9) to 37.2 million (95% CI: 34.1, 39.6) in the 2012-2013 season. Expressed in relative terms, the proportion averted ranged from 20.8% (95% CI: 16.8, 24.3) of potential infections in the 2011-2012 season to 47.5% (95% CI: 43.7, 50.8) in the 2008-2009 season. The percentage averted was only 1.04% (95% CI: 0.15, 3.2) for the 2009 H1N1 pandemic, owing to the late timing of the vaccination program in relation to the pandemic in the Northern hemisphere. In the future, further vaccination coverage, as well as improved influenza vaccines (especially those offering better protection in the elderly), could have an even stronger effect on annual influenza epidemics.

Neisseria gonorrhoeae Transmission Among Men Who Have Sex With Men: An Anatomical Site-Specific Mathematical Model Evaluating the Potential Preventive Impact of Mouthwash.

BACKGROUND: Gonorrhoea notifications are rapidly rising in men who have sex with men (MSM). We developed a model to assess mouthwash as a novel intervention for gonorrhoea control. METHODS: We developed a model of Neisseria gonorrhoeae (NG) transmission to explain anatomic site-specific prevalence of gonorrhoea among MSM. The model was calibrated to available epidemiological and behavioral data. We estimated the contribution of various sexual acts to gonorrhoea incidence and evaluate the potential impacts of screening scale-up and utilization of mouthwash on the gonorrhoea epidemic. RESULTS: We calibrated the model to prevalence of oropharyngeal, anal, and urethral gonorrhoea of 8.6% (7.7-9.5%), 8.3% (7.4-9.1%), and 0.20% (0.04-0.35%), respectively, among MSM. Oropharynx to oropharynx transmission through kissing is estimated to account for nearly three quarters of all incident cases (71.6% [64.4-80.5%]) of gonorrhoea in MSM. Substantially increasing annual oropharynx screening for gonorrhoea from the current 40% to 100% may only halve the prevalence of gonorrhoea in MSM. In contrast, the use of mouthwash with moderate efficacy (additional 1% clearance per daily use) would further reduce the corresponding prevalence rates to 3.1% (2.2-4.4%), 3.8% (2.3-4.9%), and 0.10% (0.06-0.11%), and a high-efficacy mouthwash (additional 1.5% clearance per daily use) may further halve the gonorrhoea prevalence. Without oropharynx to oropharynx transmission, we could not replicate current prevalence data. CONCLUSIONS: Despite a dearth of empirical data, our model suggests that kissing could potentially play an important role in NG transmission among MSM. Control through sexually transmitted infection screening alone is unlikely to have a substantial impact on the gonorrhoea epidemic in MSM.

Emerging infectious disease agents and blood safety in Australia: spotlight on Zika virus.

Emerging infectious diseases (EIDs) are infectious diseases whose incidence has increased in humans in the past 20 years or could increase in the near future. EID agents may represent a threat to blood safety if they infect humans, cause a clinically significant illness, include an asymptomatic blood phase in the course of infection, and are transmissible by transfusion. EID agents are typically not well characterised, but there is a consensus that we can expect ongoing outbreaks. Strategies to manage the risk to blood safety from EIDs include ongoing surveillance, regular risk assessments, modelling transfusion transmission risk, and deferral of donors with a recent travel history to outbreak areas. The 2015-16 Zika virus (ZIKV) outbreak in the Americas is the largest reported ZIKV outbreak to date, and it highlights the unpredictable nature of EID outbreaks and how quickly they can become a major public health problem. This ZIKV outbreak has provided evidence of a causal link between the virus and microcephaly in newborns. In assessing the potential risk of ZIKV to blood safety in Australia, it should be noted that a relatively small number of imported ZIKV infections have been reported in Australia, there have been no reported cases of local ZIKV transmission, and the geographical distribution of the potential ZIKV mosquito vector in Australia (Aedes aegypti) is limited to northern Queensland. Moreover, reported transfusion-transmitted ZIKV cases worldwide are rare. At present, ZIKV represents a low risk to blood safety in Australia.

Exportations of Symptomatic Cases of MERS-CoV Infection to Countries outside the Middle East.

In 2012, an outbreak of infection with Middle East respiratory syndrome coronavirus (MERS-CoV), was detected in the Arabian Peninsula. Modeling can produce estimates of the expected annual number of symptomatic cases of MERS-CoV infection exported and the likelihood of exportation from source countries in the Middle East to countries outside the region.

Estimation of Severe Middle East Respiratory Syndrome Cases in the Middle East, 2012-2016.

Using data from travelers to 4 countries in the Middle East, we estimated 3,250 (95% CI 1,300-6,600) severe cases of Middle East respiratory syndrome occurred in this region during September 2012-January 2016. This number is 2.3-fold higher than the number of laboratory-confirmed cases recorded in these countries.

Enhanced antibiotic distribution strategies and the potential impact of facial cleanliness and environmental improvements for the sustained control of trachoma: a modelling study.

BACKGROUND: Despite some success in controlling trachoma with repeated mass drug administration (MDA), some hyperendemic regions are not responding as fast as anticipated. Available data suggests that individuals with higher bacterial infection loads are less likely to resolve infection following a single dose of treatment, and thus remain a source of re-emergent infection following treatment. We assessed the potential impact of a new double-dose antibiotic distribution strategy in addition to enhanced facial cleanliness (F) and environmental improvements (E). METHODS: Using a within-community mathematical model of trachoma transmission we assessed the impact of a new double-dose antibiotic distribution strategy given 2 weeks apart, with and without enhanced F&E. We compared the annual double-dose strategy to single-dose annual MDA treatment in hyper-, meso- and hypoendemic settings, and to biannual MDA at 6-monthly intervals in hyperendemic communities. RESULTS: The findings from our mathematical model suggest that implementing the new double-dose strategy for 5 years or less was predicted to control infection more successfully than annual or 6-monthly treatment. Infection was controlled more readily if treatment was combined with enhanced F&E. The results appeared robust to variation in a number of key epidemiological parameters. To have long-term impact on transmission, enhanced F&E is essential for high transmission settings. CONCLUSION: Our current findings are based on simualtion modelling only, due to lack of epidemilogical data, however they do suggest that the  annual double-dose treatment strategy is encouraging for trachoma control. In high transmission settings, both MDA and enhanced F&E are needed for sustained control.

A change in vaccine efficacy and duration of protection explains recent rises in pertussis incidence in the United States.

Over the past ten years the incidence of pertussis in the United States (U.S.) has risen steadily, with 2012 seeing the highest case number since 1955. There has also been a shift over the same time period in the age group reporting the largest number of cases (aside from infants), from adolescents to 7-11 year olds. We use epidemiological modelling and a large case incidence dataset to explain the upsurge. We investigate several hypotheses for the upsurge in pertussis cases by fitting a suite of dynamic epidemiological models to incidence data from the National Notifiable Disease Surveillance System (NNDSS) between 1990-2009, as well as incidence data from a variety of sources from 1950-1989. We find that: the best-fitting model is one in which vaccine efficacy and duration of protection of the acellular pertussis (aP) vaccine is lower than that of the whole-cell (wP) vaccine, (efficacy of the first three doses 80% [95% CI: 78%, 82%] versus 90% [95% CI: 87%, 94%]), increasing the rate at which disease is reported to NNDSS is not sufficient to explain the upsurge and 3) 2010-2012 disease incidence is predicted well. In this study, we use all available U.S. surveillance data to: 1) fit a set of mathematical models and determine which best explains these data and 2) determine the epidemiological and vaccine-related parameter values of this model. We find evidence of a difference in efficacy and duration of protection between the two vaccine types, wP and aP (aP efficacy and duration lower than wP). Future refinement of the model presented here will allow for an exploration of alternative vaccination strategies such as different age-spacings, further booster doses, and cocooning.

Improvements in life expectancy among Australians due to reductions in smoking: Results from a risk percentiles approach.

BACKGROUND: Tobacco smoking is a major burden on the Australian population in terms of health, social and economic costs. Because of this, in 2008, all Australian Governments agreed to set targets to reduce prevalence of smoking to 10 % by 2018 and subsequently introduced several very strong anti-smoking measures. On this backdrop, we estimated in 2012-13 the impact of several scenarios related to reduction of smoking prevalence to 10 % across the entire Australian population and for below specific ages, on improving life expectancy. METHODS: Using the risk percentiles method the Australian Diabetes, Obesity and Lifestyle (AUSDIAB) baseline survey and the Australian Bureau of Statistics (ABS) age-sex specific death counts were analyzed. RESULTS: Amongst men the gains in life expectancy associated with 10 % smoking prevalence are generally greater than those of women with average life expectancy for men increasing by 0.11 to 0.41 years, and for women by 0.12 to 0.29 years. These are at best 54 % and 49 % for men and women of the gains achieved by complete smoking cessation. The gains plateau for interventions targeting those <70 and <80 years. Amongst smokers the potential gains are much greater, with an increase in average life expectancy amongst men smokers of 0.43 to 2.08 years, and 0.73 to 2.05 years amongst women smokers. These are at best 46 % and 38 % for men and women smokers of the gains achieved by complete smoking cessation. CONCLUSION: The estimated optimum gain in life expectancy is consistent with potentially moderate gains which occur when both men and women below 60 years are targeted to reduce smoking prevalence to 10 %.

Infectious disease modeling methods as tools for informing response to novel influenza viruses of unknown pandemic potential.

The rising importance of infectious disease modeling makes this an appropriate time for a guide for public health practitioners tasked with preparing for, and responding to, an influenza pandemic. We list several questions that public health practitioners commonly ask about pandemic influenza and match these with analytical methods, giving details on when during a pandemic the methods can be used, how long it might take to implement them, and what data are required. Although software to perform these tasks is available, care needs to be taken to understand: (1) the type of data needed, (2) the implementation of the methods, and (3) the interpretation of results in terms of model uncertainty and sensitivity. Public health leaders can use this article to evaluate the modeling literature, determine which methods can provide appropriate evidence for decision-making, and to help them request modeling work from in-house teams or academic groups.

Estimating the potential effects of a vaccine program against an emerging influenza pandemic--United States.

BACKGROUND: Human illness from influenza A(H7N9) was identified in March 2013, and candidate vaccine viruses were soon developed. To understand factors that may impact influenza vaccination programs, we developed a model to evaluate hospitalizations and deaths averted considering various scenarios. METHODS: We utilized a model incorporating epidemic curves with clinical attack rates of 20% or 30% in a single wave of illness, case hospitalization ratios of 0.5% or 4.2%, and case fatality ratios of 0.08% or 0.53%. We considered scenarios that achieved 80% vaccination coverage, various starts of vaccination programs (16 or 8 weeks before, the same week of, or 8 or 16 weeks after start of pandemic), an administration rate of 10 or 30 million doses per week (the latter rate is an untested assumption), and 2 levels of vaccine effectiveness (2 doses of vaccine required; either 62% or 80% effective for persons aged <60 years, and either 43% or 60% effective for persons aged ≥ 60 years). RESULTS: The start date of vaccination campaigns most influenced impact; 141,000-2,200,000 hospitalizations and 11,000-281,000 deaths were averted when campaigns started before a pandemic, and <100-1 300,000 hospitalizations and 0-165,000 deaths were averted for programs beginning the same time as or after the introduction of the pandemic virus. The rate of vaccine administration and vaccine effectiveness did not influence campaign impact as much as timing of the start of campaign. CONCLUSIONS: Our findings suggest that efforts to improve the timeliness of vaccine production will provide the greatest impacts for future pandemic vaccination programs.

Modeling the effect of school closures in a pandemic scenario: exploring two different contact matrices.

BACKGROUND: School closures may delay the epidemic peak of the next influenza pandemic, but whether school closure can delay the peak until pandemic vaccine is ready to be deployed is uncertain. METHODS: To study the effect of school closures on the timing of epidemic peaks, we built a deterministic susceptible-infected-recovered model of influenza transmission. We stratified the U.S. population into 4 age groups (0-4, 5-19, 20-64, and ≥ 65 years), and used contact matrices to model the average number of potentially disease transmitting, nonphysical contacts. RESULTS: For every week of school closure at day 5 of introduction and a 30% clinical attack rate scenario, epidemic peak would be delayed by approximately 5 days. For a 15% clinical attack rate scenario, 1 week closure would delay the peak by 9 days. Closing schools for less than 84 days (12 weeks) would not, however, reduce the estimated total number of cases. CONCLUSIONS: Unless vaccine is available early, school closure alone may not be able to delay the peak until vaccine is ready to be deployed. Conversely, if vaccination begins quickly, school closure may be helpful in providing the time to vaccinate school-aged children before the pandemic peaks.

Transmission Models of Historical Ebola Outbreaks.

To guide the collection of data under emergent epidemic conditions, we reviewed compartmental models of historical Ebola outbreaks to determine their implications and limitations. We identified future modeling directions and propose that the minimal epidemiologic dataset for Ebola model construction comprises duration of incubation period and symptomatic period, distribution of secondary cases by infection setting, and compliance with intervention recommendations.

Can oral vitamin D prevent the cardiovascular diseases among migrants in Australia? Provider perspective using Markov modelling.

The study was designed to model the effectiveness and cost effectiveness of oral Vitamin D supplementation as a primary prevention strategy for cardiovascular disease among a migrant population in Australia. It was carried out in the Community Health Service, Kensington, Melbourne. Best-case scenario analysis using a Markov model was employed to look at the health care providers' perspective. Adult migrants who were vitamin D deficient and free from cardiovascular disease visiting the medical centre at least once during the period from 1 January 2010 to 31 December 2012 were included in the study. The blood pressure-lowering effect of vitamin D was taken from a published meta-analysis and applied in the Framingham 10 year cardiovascular risk algorithm (with and without oral vitamin D supplements) to generate the probabilities of cardiovascular events. A Markov decision model was used to estimate the provider costs associated with the events and treatments. Uncertainties were derived by Monte Carlo simulation. Vitamin D oral supplementation (1000 IU/day) for 10 years could potentially prevent 31 (interquartile range (IQR) 26 to 37) non-fatal and 11 (IQR 10 to 15) fatal cardiovascular events in a migrant population of 10,000 assuming 100% compliance. The provider perspective incremental cost effectiveness per year of life saved was AU$3,992 (IQR 583 to 8558). This study suggests subsidised supplementation of oral vitamin D may be a cost effective intervention to reduce non-fatal and fatal cardiovascular outcomes in high-risk migrant populations.