Estimates Of Epidemiological Parameters Research Articles

Estimation of epidemiological parameters and ascertainment rate from early transmission of COVID-19 across Africa.

Country reported case counts suggested a slow spread of SARS-CoV-2 in the initial phase of the COVID-19 pandemic in Africa. Owing to inadequate public awareness, unestablished monitoring practices, limited testing and stigmas, there might exist extensive under-ascertainment of the true number of cases, especially at the beginning of the novel epidemic. We developed a compartmentalized epidemiological model to track the early epidemics in 54 African countries. Data on the reported cumulative number of cases and daily confirmed cases were used to fit the model for the time period with no or little massive national interventions yet in each country. We estimated that the mean basic reproduction number is 2.02 (s.d. 0.7), with a range between 1.12 (Zambia) and 3.64 (Nigeria). The mean overall report rate was estimated to be 5.37% (s.d. 5.71%), with the highest 30.41% in Libya and the lowest 0.02% in São Tomé and Príncipe. An average of 5.46% (s.d. 6.4%) of all infected cases were severe cases and 66.74% (s.d. 17.28%) were asymptomatic ones. The estimated low reporting rates in Africa suggested a clear need for improved reporting and surveillance systems in these countries.

Association between pertussis vaccination coverage and other sociodemographic factors and pertussis incidence using surveillance data

Routine vaccination with pertussis vaccines has been successful in driving down pertussis mortality and morbidity globally. Despite high vaccination coverage, countries such as Australia, USA, and UK have experienced increase in pertussis activity over the last few decades. This may be due to local pockets of low vaccination coverage that result in persistence of pertussis in the population and occasionally lead to large outbreaks. The objective of this study was to characterize the association between pertussis vaccination coverage and sociodemographic factors and pertussis incidence at the school district level in King County, Washington, USA. We used monthly pertussis incidence data for all ages reported to the Public Health Seattle and King County between January 1, 2010 and December 31, 2017 to obtain school district level pertussis incidence. We obtained immunization data from the Washington State Immunization Information System to estimate school-district level vaccination coverage as proportion of 19–35 month old children fully vaccinated with ≥4 doses of the Diphtheria-Tetanus-acellular-Pertussis (DTaP) vaccine in a school district. We used two methods to quantify the effects of vaccination coverage on pertussis incidence: an ecological vaccine model and an endemic–epidemic model. Even though the effect of vaccination is modeled differently in the two approaches, both models can be used to estimate the association between vaccination coverage and pertussis incidence. Using the ecological vaccine model, we estimated the vaccine effectiveness of 4 doses of Diphtheria-Tetanus-acellular-Pertussis vaccine to be 83% (95% credible interval: 63%, 95%). In the endemic–epidemic model, under-vaccination was statistically significantly associated with epidemic risk of pertussis (adjusted Relative Risk, aRR: 2.76; 95% confidence interval: 1.44, 16.6). Household size and median income were statistically significantly associated with endemic pertussis risk. The endemic–epidemic model suffers from ecological bias, whereas the ecological vaccine model provides less biased and more interpretable estimates of epidemiological parameters, such as DTaP vaccine effectiveness, for each school district.

Deep learning from phylogenies to uncover the epidemiological dynamics of outbreaks

Widely applicable, accurate and fast inference methods in phylodynamics are needed to fully profit from the richness of genetic data in uncovering the dynamics of epidemics. Standard methods, including maximum-likelihood and Bayesian approaches, generally rely on complex mathematical formulae and approximations, and do not scale with dataset size. We develop a likelihood-free, simulation-based approach, which combines deep learning with (1) a large set of summary statistics measured on phylogenies or (2) a complete and compact representation of trees, which avoids potential limitations of summary statistics and applies to any phylodynamics model. Our method enables both model selection and estimation of epidemiological parameters from very large phylogenies. We demonstrate its speed and accuracy on simulated data, where it performs better than the state-of-the-art methods. To illustrate its applicability, we assess the dynamics induced by superspreading individuals in an HIV dataset of men-having-sex-with-men in Zurich. Our tool PhyloDeep is available on github.com/evolbioinfo/phylodeep.

A Novel Tool for Real-time Estimation of Epidemiological Parameters of Communicable Diseases Using Contact-Tracing Data: Development and Deployment.

BackgroundThe Surveillance Outbreak Response Management and Analysis System (SORMAS) contains a management module to support countries in their epidemic response. It consists of the documentation, linkage, and follow-up of cases, contacts, and events. To allow SORMAS users to visualize data, compute essential surveillance indicators, and estimate epidemiological parameters from such network data in real-time, we developed the SORMAS Statistics (SORMAS-Stats) application.ObjectiveThis study aims to describe the essential visualizations, surveillance indicators, and epidemiological parameters implemented in the SORMAS-Stats application and illustrate the application of SORMAS-Stats in response to the COVID-19 outbreak.MethodsBased on findings from a rapid review and SORMAS user requests, we included the following visualization and estimation of parameters in SORMAS-Stats: transmission network diagram, serial interval (SI), time-varying reproduction number R(t), dispersion parameter k, and additional surveillance indicators presented in graphs and tables. We estimated SI by fitting lognormal, gamma, and Weibull distributions to the observed distribution of the number of days between symptom onset dates of infector-infectee pairs. We estimated k by fitting a negative binomial distribution to the observed number of infectees per infector. Furthermore, we applied the Markov Chain Monte Carlo approach and estimated R(t) using the incidence data and the observed SI computed from the transmission network data.ResultsUsing COVID-19 contact-tracing data of confirmed cases reported between July 31 and October 29, 2021, in the Bourgogne-Franche-Comté region of France, we constructed a network diagram containing 63,570 nodes. The network comprises 1.75% (1115/63,570) events, 19.59% (12,452/63,570) case persons, and 78.66% (50,003/63,570) exposed persons, including 1238 infector-infectee pairs and 3860 transmission chains with 24.69% (953/3860) having events as the index infector. The distribution with the best fit to the observed SI data was a lognormal distribution with a mean of 4.30 (95% CI 4.09-4.51) days. We estimated a dispersion parameter k of 21.11 (95% CI 7.57-34.66) and an effective reproduction number R of 0.9 (95% CI 0.58-0.60). The weekly estimated R(t) values ranged from 0.80 to 1.61.ConclusionsWe provide an application for real-time estimation of epidemiological parameters, which is essential for informing outbreak response strategies. The estimates are commensurate with findings from previous studies. The SORMAS-Stats application could greatly assist public health authorities in the regions using SORMAS or similar tools by providing extensive visualizations and computation of surveillance indicators.

Estimation of Epidemiological Parameters and Ascertainment Rate from Early Transmission of COVID-19 across Africa

Estimation of Epidemiological Parameters and Ascertainment Rate from Early Transmission of COVID-19 across Africa

Estimation of Epidemiological Parameters and Ascertainment Rate from Early Transmission of COVID-19 Across Africa

Estimation of Epidemiological Parameters and Ascertainment Rate from Early Transmission of COVID-19 Across Africa

On some fundamental challenges in monitoring epidemics.

Epidemic models often reflect characteristic features of infectious spreading processes by coupled nonlinear differential equations considering different states of health (such as susceptible, infectious or recovered). This compartmental modelling approach, however, delivers an incomplete picture of the dynamics of epidemics, as it neglects stochastic and network effects, and the role of the measurement process, on which the estimation of epidemiological parameters and incidence values relies. In order to study the related issues, we combine established epidemiological spreading models with a measurement model of the testing process, considering the problems of false positives and false negatives as well as biased sampling. Studying a model-generated ground truth in conjunction with simulated observation processes (virtual measurements) allows one to gain insights into the fundamental limitations of purely data-driven methods when assessing the epidemic situation. We conclude that epidemic monitoring, simulation, and forecasting are wicked problems, as applying a conventional data-driven approach to a complex system with nonlinear dynamics, network effects and uncertainty can be misleading. Nevertheless, some of the errors can be corrected for, using scientific knowledge of the spreading dynamics and the measurement process. We conclude that such corrections should generally be part of epidemic monitoring, modelling and forecasting efforts.This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.

Data science approaches to confronting the COVID-19 pandemic: a narrative review.

During the COVID-19 pandemic, more than ever, data science has become a powerful weapon in combating an infectious disease epidemic and arguably any future infectious disease epidemic. Computer scientists, data scientists, physicists and mathematicians have joined public health professionals and virologists to confront the largest pandemic in the century by capitalizing on the large-scale ‘big data’ generated and harnessed for combating the COVID-19 pandemic. In this paper, we review the newly born data science approaches to confronting COVID-19, including the estimation of epidemiological parameters, digital contact tracing, diagnosis, policy-making, resource allocation, risk assessment, mental health surveillance, social media analytics, drug repurposing and drug development. We compare the new approaches with conventional epidemiological studies, discuss lessons we learned from the COVID-19 pandemic, and highlight opportunities and challenges of data science approaches to confronting future infectious disease epidemics.This article is part of the theme issue ‘Data science approaches to infectious disease surveillance’.

Estimating effects of intervention measures on COVID-19 outbreak in Wuhan taking account of improving diagnostic capabilities using a modelling approach

BackgroundAlthough by late February 2020 the COVID-19 epidemic was effectively controlled in Wuhan, China, estimating the effects of interventions, such as transportation restrictions and quarantine measures, on the early COVID-19 transmission dynamics in Wuhan is critical for guiding future virus containment strategies. Since the exact number of infected cases is unknown, the number of documented cases was used by many disease transmission models to infer epidemiological parameters. This means that it was possible to produce biased estimates of epidemiological parameters and hence of the effects of intervention measures, because the percentage of all cases that were documented changed during the first 2 months of the epidemic, as a consequence of a gradually improving diagnostic capability.MethodsTo overcome these limitations, we constructed a stochastic susceptible-exposed-infected-quarantined-recovered (SEIQR) model, accounting for intervention measures and temporal changes in the proportion of new documented infections out of total new infections, to characterize the transmission dynamics of COVID-19 in Wuhan across different stages of the outbreak. Pre-symptomatic transmission was taken into account in our model, and all epidemiological parameters were estimated using the Particle Markov-chain Monte Carlo (PMCMC) method.ResultsOur model captured the local Wuhan epidemic pattern as two-peak transmission dynamics, with one peak on February 4 and the other on February 12, 2020. The impact of intervention measures determined the timing of the first peak, leading to an 86% drop in the Re from 3.23 (95% CI, 2.22 to 4.20) to 0.45 (95% CI, 0.20 to 0.69). The improved diagnostic capability led to the second peak and a higher proportion of documented infections. Our estimated proportion of new documented infections out of the total new infections increased from 11% (95% CI 1–43%) to 28% (95% CI 4–62%) after January 26 when more detection kits were released. After the introduction of a new diagnostic criterion (case definition) on February 12, a higher proportion of daily infected cases were documented (49% (95% CI 7–79%)).ConclusionsTransportation restrictions and quarantine measures together in Wuhan were able to contain local epidemic growth.

Effective epidemic model for COVID-19 using accumulated deaths.

The severe acute respiratory syndrome COVID-19 has been in the center of the ongoing global health crisis in 2020. The high prevalence of mild cases facilitates sub-notification outside hospital environments and the number of those who are or have been infected remains largely unknown, leading to poor estimates of the crude mortality rate of the disease. Here we use a simple model to describe the number of accumulated deaths caused by COVID-19. The close connection between the proposed model and an approximate solution of the SIR model provides estimates of epidemiological parameters. We find values for the crude mortality between and which are lower than estimated numbers obtained from laboratory-confirmed patients. We also calculate quantities of practical interest such as the basic reproduction number and subsequent increment after relaxation of lockdown and other control measures.

Dynamic estimation of epidemiological parameters of COVID-19 outbreak and effects of interventions on its spread.

Background: A key challenge in estimating epidemiological parameters for a pandemic such as the initial COVID-19 outbreak in Wuhan is the discrepancy between the officially reported number of infections and the true number of infections. A common approach to tackling the challenge is to use the number of infections exported from the originating city to infer the true number. This approach can only provide a static estimate of the epidemiological parameters before city lockdown because there are almost no exported cases thereafter.Methods: We propose a Bayesian estimation method that dynamically estimates the epidemiological parameters by recovering true numbers of infections from day-to-day official numbers. To illustrate the use of this method, we provide a comprehensive retrospection on how the COVID-19 had progressed in Wuhan from January 19 to March 5, 2020. Particularly, we estimate that the outbreak sizes by January 23 and March 5 were 11,239 [95% CI 4,794–22,372] and 124,506 [95% CI 69,526–265,113], respectively.Results: The effective reproduction number attained its maximum on January 24 (3.42 [95% CI 3.34–3.50]) and became less than 1 from February 7 (0.76 [95% CI 0.65–0.92]). We also estimate the effects of two major government interventions on the spread of COVID-19 in Wuhan.Conclusions: This case study by our proposed method affirms the believed importance and effectiveness of imposing tight nonessential travel restrictions and affirm the importance and effectiveness of government interventions (e.g., transportation suspension and large scale hospitalization) for effective mitigation of COVID-19 community spread.Significance for public healthIn fighting global pandemic such as COVID-19, an important early task for understanding the spread is to closely monitor the infection size and assess the disease epidemiological parameters. The in- sights gained from the epidemiological parameter estimation enable public health practitioners to dynamically monitor the temporal spread trend and to quantitatively analyze the effectiveness of new public health policies. In this paper, we aim to address a key technical challenge potentially arising from the under-reporting issues in pandemic early periods, and critically re-examine the COVID-19 situation at the initial epicenter Wuhan city as a practically relevant case study. Methodological development for modeling dynamic evolution involving parameter estimation therefore has important public health applications and is expected to have significant impact on modeling practice for understanding future epidemic events well beyond COVID-19.

The collective wisdom in the COVID-19 research: Comparison and synthesis of epidemiological parameter estimates in preprints and peer-reviewed articles

ObjectivesWe aimed to explore the collective wisdom of preprints related to COVID-19 by comparing and synthesizing them with results of peer-reviewed publications. MethodsPubMed, Google Scholar, medRxiv, bioRxiv, arXiv, and SSRN were searched for papers regarding the estimation of four epidemiological parameters of COVID-19: the basic reproduction number, incubation period, infectious period, and case-fatality-rate. Distributions of parameters and timeliness of preprints and peer-reviewed papers were compared. Four parameters in two groups were synthesized by bootstrapping, and their validities were evaluated by simulated cumulative cases of the susceptible-exposed-infectious-recovered-dead-cumulative (SEIRDC) model. ResultsA total of 106 papers were included for analysis. The distributions of four parameters in two literature groups were close, and the timeliness of preprints was better. Synthesized estimates of the basic reproduction number (3.18, 95% CI 2.85–3.53), incubation period (5.44 days, 95% CI 4.98–5.99), infectious period (6.25 days, 95% CI 5.09–7.51), and case-fatality-rate (4.51%, 95% CI 3.41%–6.29%) were obtained. Simulated cumulative cases of the SEIRDC model matched well with the onset cases in China. ConclusionsThe validity of the COVID-19 parameter estimations of the preprints was on par with that of peer-reviewed publications, and synthesized results of literatures could reduce the uncertainty and be used for epidemic decision-making.

Serial interval of SARS-CoV-2 was shortened over time by nonpharmaceutical interventions.

Studies of novel coronavirus disease 2019 (COVID-19), which is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), have reported varying estimates of epidemiological parameters, including serial interval distributions-i.e., the time between illness onset in successive cases in a transmission chain-and reproduction numbers. By compiling a line-list database of transmission pairs in mainland China, we show that mean serial intervals of COVID-19 shortened substantially from 7.8 to 2.6 days within a month (9 January to 13 February 2020). This change was driven by enhanced nonpharmaceutical interventions, particularly case isolation. We also show that using real-time estimation of serial intervals allowing for variation over time provides more accurate estimates of reproduction numbers than using conventionally fixed serial interval distributions. These findings could improve our ability to assess transmission dynamics, forecast future incidence, and estimate the impact of control measures.

Estimating the epidemiology of emerging Xylella fastidiosa outbreaks in olives

AbstractXylella fastidiosa is an important insect‐vectored bacterial plant pathogen with a wide host range, causing significant economic impact in the agricultural and horticultural industries. Once restricted to the Americas, severe European outbreaks have been discovered recently in Italy, Spain, France, and Portugal. The Italian outbreak, detected in Puglia in 2013, has spread over 100 km, killing millions of olive trees, and is still expanding. To date, quantified assessment of important epidemiological parameters useful for risk assessment and management, such as transmission rates, symptomless periods, and time to death in field populations, has been lacking. This is due to the emergent and novel nature of the outbreak and length of time needed to monitor the course of disease progression. To address this, we developed a Bayesian method to infer epidemiological parameters by fitting and comparing compartmental epidemiological models to short snapshots of disease progression observed in multiple field plots. We estimated that each infected tree with symptoms is able to infect around 19 trees per year (95% credible range 14–26). The symptomless stage was estimated to have low to negligible infectivity and to last an average of approximately 1.2 years (95% credible range 1.0–1.3 years). Tree desiccation was estimated to occur approximately 4.3 years (95% credible range 4.0–4.6 years) after symptom appearance. However, we were unable to estimate the infectiousness of desiccated trees from the data. Our method could be used to make early estimates of epidemiological parameters in other emerging disease outbreaks where symptom expression is slow.

Dynamic Estimation of Epidemiological Parameters of COVID-19 Outbreak and Effects of Interventions on Its Spread

A key challenge for estimating the epidemiological parameters of the COVID-19 outbreak in Wuhan is the discrepancy between the officially reported number of infections and the true number of infections. A common approach to tackling the challenge is to use the number of infections exported from Wuhan to infer the true number in the city. This approach can only provide a static estimate of the epidemiological parameters before Wuhan lockdown on January 23, 2020, because there are almost no exported cases thereafter. Here, we propose a method to dynamically estimate the epidemiological parameters of the COVID-19 outbreak in Wuhan by recovering true numbers of infections from day-to-day official numbers. Using the method, we provide a comprehensive retrospection on how the disease had progressed in Wuhan from January 19 to March 5, 2020. Particularly, we estimate that the outbreak sizes by January 23 and March 5 were 11,239 [95% CI 4,794--22,372] and 124,506 [95% CI 69,526--265,113], respectively. The effective reproduction number attained its maximum on January 24 (3.42 [95% CI 3.34--3.50]) and became less than 1 from February 7 (0.76 [95% CI 0.65--0.92]). We also estimate the effects of two major government interventions on the spread of COVID-19 in Wuhan. In particular, transportation suspension and large scale hospitalization respectively prevented 33,719 and 90,072 people from getting infected in the nine-day time period right after its implementation.

Early in the epidemic: impact of preprints on global discourse about COVID-19 transmissibility

Early in the epidemic: impact of preprints on global discourse about COVID-19 transmissibility

Estimating epidemiological parameters from experiments in vector access to host plants, the method of matching gradients.

Estimation of pathogenic life-history values, for instance the duration a pathogen is retained in an insect vector (i.e., retention period) is of particular importance for understanding plant disease epidemiology. How can we extract values for these epidemiological parameters from conventional small-scale laboratory experiments in which transmission success is measured in relation to durations of vector access to host plants? We provide a solution to this problem by deriving formulae for the empirical curves that these experiments produce, called access period response curves (i.e., transmission success vs access period). We do this by writing simple equations for the fundamental life-cycle components of insect vectors in the laboratory. We then infer values of epidemiological parameters by matching the theoretical and empirical gradients of access period response curves. Using the example of Cassava brown streak virus (CBSV), which has emerged in sub-Saharan Africa and now threatens regional food security, we illustrate the method of matching gradients. We show how applying the method to published data produces a new understanding of CBSV through the inference of retention period, acquisition period and inoculation period parameters. We found that CBSV is retained for a far shorter duration in its insect vector (Bemisia tabaci whitefly) than had previously been assumed. Our results shed light on a number of critical factors that may be responsible for the transition of CBSV from sub- to super-threshold R0 in sub-Saharan Africa. The method is applicable to plant pathogens in general, to supply epidemiological parameter estimates that are crucial for practical management of epidemics and prediction of pandemic risk.

Tuberculosis outbreak investigation using phylodynamic analysis

The fast evolution of pathogenic viruses has allowed for the development of phylodynamic approaches that extract information about the epidemiological characteristics of viral genomes. Thanks to advances in whole genome sequencing, they can be applied to slowly evolving bacterial pathogens like Mycobacterium tuberculosis. In this study, we investigate and compare the epidemiological dynamics underlying two M. tuberculosis outbreaks using phylodynamic methods. Specifically, we (i) test if the outbreak data sets contain enough genetic variation to estimate short-term evolutionary rates and (ii) reconstruct epidemiological parameters such as the effective reproduction number.The first outbreak occurred in the Swiss city of Bern (1987–2012) and was caused by a drug-susceptible strain belonging to the phylogenetic M. tuberculosis Lineage 4. The second outbreak was caused by a multidrug-resistant (MDR) strain of Lineage 2, imported from the Wat Tham Krabok (WTK) refugee camp in Thailand into California.There is little temporal signal in the Bern data set and moderate temporal signal in the WTK data set. Thanks to its high sampling proportion (90%) the Bern outbreak allows robust estimation of epidemiological parameters despite the poor temporal signal. Conversely, there is much uncertainty in the epidemiological estimates concerning the sparsely sampled (9%) WTK outbreak. Our results suggest that both outbreaks peaked around 1990, although they were only recognized as outbreaks in 1993 (Bern) and 2004 (WTK). Furthermore, individuals were infected for a significantly longer period (around 9 years) in the WTK outbreak than in the Bern outbreak (4–5 years).Our work highlights both the limitations and opportunities of phylodynamic analysis of outbreaks involving slowly evolving pathogens: (i) estimation of the evolutionary rate is difficult on outbreak time scales and (ii) a high sampling proportion allows quantification of the age of the outbreak based on the sampling times, and thus allows for robust estimation of epidemiological parameters.

Capturing individual‐level parameters of influenza A virus dynamics in wild ducks using multistate models

SummaryDisease prevalence in wildlife is governed by epidemiological parameters (infection and recovery rates) and response to infection, both of which vary within and among individual hosts. Studies quantifying these individual‐scale parameters and documenting their source of variation in wild hosts are fundamental for predicting disease dynamics. Such studies do not exist for the influenza A virus (IAV), despite its strong impact on the global economy and public health.Using capture–recaptures of 3500 individual mallardsAnas platyrhynchosduring seven migration seasons at a stopover site in southern Sweden, we provide the first empirical description of the individual‐based mechanisms ofIAVdynamics in a wild reservoir host.For most years, prevalence and risk ofIAVinfection peaked at a single time during the autumn migration season, but the timing, shape and intensity of the infection curve showed strong annual heterogeneity. In contrast, the seasonal pattern of recovery rate only varied in intensity across years.Adults and juveniles displayed similar seasonal patterns of infection and recovery each year. However, compared to adults, juveniles experienced twice the risk of becoming infected, whereas recovery rates were similar across age categories. Finally, we did not find evidence that infection influenced the timing of emigration.Synthesis and applications. Our study provides robust empirical estimates of epidemiological parameters for predicting influenza A virus (IAV) dynamics. However, the strong annual variation in infection curves makes forecasting difficult. Prevalence data can provide reliable surveillance indicators as long as they catch the variation in infection risk. However, individual‐based monitoring of infection is required to verify this assumption in areas where surveillance occurs. In this context, monitoring of captive sentinel birds kept in close contact with wild birds is useful. The fact that infection does not impact the timing of migration underpins the potential for mallards to spread viruses rapidly over large geographical scales. Hence, we strongly encourageIAVsurveillance with a multistate capture–recapture approach along the entire migratory flyway of mallards.

Simultaneous reconstruction of evolutionary history and epidemiological dynamics from viral sequences with the birth–death SIR model

The evolution of RNA viruses, such as human immunodeficiency virus (HIV), hepatitis C virus and influenza virus, occurs so rapidly that the viruses' genomes contain information on past ecological dynamics. Hence, we develop a phylodynamic method that enables the joint estimation of epidemiological parameters and phylogenetic history. Based on a compartmental susceptible–infected–removed (SIR) model, this method provides separate information on incidence and prevalence of infections. Detailed information on the interaction of host population dynamics and evolutionary history can inform decisions on how to contain or entirely avoid disease outbreaks. We apply our birth–death SIR method to two viral datasets. First, five HIV type 1 clusters sampled in the UK between 1999 and 2003 are analysed. The estimated basic reproduction ratios range from 1.9 to 3.2 among the clusters. All clusters show a decline in the growth rate of the local epidemic in the middle or end of the 1990s. The analysis of a hepatitis C virus genotype 2c dataset shows that the local epidemic in the Córdoban city Cruz del Eje originated around 1906 (median), coinciding with an immigration wave from Europe to central Argentina that dates from 1880 to 1920. The estimated time of epidemic peak is around 1970.