An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it

  title={An attempt at a new analysis of the mortality caused by smallpox and of the advantages of inoculation to prevent it},
  author={Daniel Bernoulli and Sally M. Blower},
  journal={Reviews in Medical Virology},
‘I simply wish that, in a matter which so closelyconcerns the wellbeing of the human race, no deci-sion shall be made without all the knowledge whicha little analysis and calculation can provide’Daniel Bernoulli 1760.INTRODUCTIONShould the general population be vaccinatedagainst smallpox (Variola Major)? Would the bene-fits of mass vaccination outweigh the risks? Howmany deaths would occur as the result of a massvaccination campaign against smallpox? Canmathematical models of smallpox… 

The prevention and eradication of smallpox: a commentary on Sloane (1755) ‘An account of inoculation’

  • R. WeissJ. Esparza
  • Medicine
    Philosophical Transactions of the Royal Society B: Biological Sciences
  • 2015
The significance of variolation and vaccination with respect to scientific, public health and ethical controversies concerning these ‘weapons of mass protection’ are discussed.

Mathematical model and COVID-19

These models used for COVID-19 have supported and will continue to provide information for the selection and implementation of programs and public policies that prevent associated complications, reduce the speed of the virus spread and minimize the occurrence of severe cases of the disease that may collapse health systems.

Extracting key information from historical data to quantify the transmission dynamics of smallpox

Basic methods and findings in mathematical and statistical studies of smallpox which estimate key transmission parameters from historical data are reviewed and needs to analyze previous smallpox outbreaks systematically are pointed out.

Patterns of smallpox mortality in London, England, over three centuries

A spectral analysis reveals how periodicities in smallpox dynamics changed over decades and centuries, and how these changes were related to control interventions and public health policy changes.

Estimation of the infection rate in epidemic models with multiple populations

A new estimation method is introduced for this crucial parameter, the socalled infection rate, that is able to accurately infer it from the arrival times of the first infective individual in each population in meta-population models.

Human-Human interaction: epidemiology

It is shown in this work how that human relations are important in transmitting diseases and there is example, where it is possible to conduct experiments of significant policy relevance (vaccinating), such as investigating the initial growth of an epidemic on a real-world network.

Modeling the transmission dynamics of brucellosis

Five epidemiological models that seek to evaluate the role of intervention strategies on the transmission dynamics of brucellosis in animal population have been studied and all the proposed models incorporate relevant biological and ecological factors as well as possible disease intervention strategies.

Seventy-five years of estimating the force of infection from current status data

An historical overview is presented, discussing the relevance of Muench's work, and the wide array of newer methods with illustrations on pre-vaccination serological survey data of two airborne infections: rubella and parvovirus B19 are explained.

How mathematical epidemiology became a field of biology: a commentary on Anderson and May (1981) ‘The population dynamics of microparasites and their invertebrate hosts’

It is argued that their 1981 paper fits seamlessly in the systematic study of infectious disease dynamics that was initiated by the authors in 1978, combining effective use of simple mathematical models, firmly rooted in biology, with observable or empirically measurable ingredients and quantities, and promoting extensive capacity building.



A model for a smallpox-vaccination policy.

The analysis favors prior vaccination of health care workers unless the likelihood of any attack is very low, but it favors vaccination of the public only if the likelihoodof a national attack or of multiple attacks is high.

Transmission potential of smallpox in contemporary populations

Despite eradication, smallpox still presents a risk to public health whilst laboratory stocks of virus remain. One factor crucial to any assessment of this risk is R0, the average number of secondary

Daniel Bernoulli's epidemiological model revisited.

Oscillatory dynamics of smallpox and the impact of vaccination.

The evolution of smallpox epidemics in London, 1647-1893, was studied by time series analysis of deaths from the disease in the Bills of Mortality and the dynamics of the disease can now be described by an SEIR model: severe outbreaks ofSmallpox are followed by decaying epidemics.

Containing Bioterrorist Smallpox

Results suggest that increasing herd immunity, perhaps with a combination of preemptive voluntary vaccination and vaccination of first responders, could enhance the effectiveness of postattack intervention and help targeted vaccination be more competitive with mass vaccination at both preventing and containing a deliberate introduction of smallpox.

Emergency response to a smallpox attack: The case for mass vaccination

Estimating the number of cases and deaths that would result from an attack in a large urban area of the United States and comparing the results to mass vaccination from the moment an attack is recognized finds that mass vaccination results in both far fewer deaths and much faster epidemic eradication.

Modeling potential responses to smallpox as a bioterrorist weapon.

A mathematical model is constructed to describe the spread of smallpox after a deliberate release of the virus and indicates that a stockpile of 40 million doses should be adequate to stop outbreaks.

An hypothesis for the periodicity of smallpox epidemics as revealed by time series analysis.

Parish registers have been studied by time series analysis to detect smallpox epidemics in England during 1600-1800 and it is concluded that, in the towns studied, the disease was not endemic but that the oscillations were established by 5-year cycles of periods of famine associated with high wheat prices.

Infant mortality and famine: a study in historical epidemiology in northern England.

The lags between neonatal and post-neonatal mortalities and wheat prices, together with the analysis of the famine of 1623, support the hypothesis that neonatal mortality was related to malnutrition in pregnancy whereas post-nursing mortality was primarily directly dependent on exogenous causes in the first year of life.

A History of Epidemics in Britain

The historian is further confronted with the difficulty of identifying, under the confused nomenclature of by-gone days, the various pestilences described, and of assigning to them their proper place in modern nosology.