A Brief History of R0 and a Recipe for its Calculation

  title={A Brief History of R0 and a Recipe for its Calculation},
  author={J.A.P. Heesterbeek},
  journal={Acta Biotheoretica},
In this paper I present the genesis of R0 in demography, ecology and epidemiology, from embryo to its current adult form. I argue on why it has taken so long for the concept to mature in epidemiology when there were ample opportunities for cross-fertilisation from demography and ecology from where it reached adulthood fifty years earlier. Today, R0 is a more fully developed adult in epidemiology than in demography. In the final section I give an algorithm for its calculation in heterogeneous… 

The many guises of R0 (a didactic note).

The mathematics of the reproduction number R for Covid-19: A primer for demographers

The reproduction number R is a key indicator to monitor the dynamics of Covid-19 and to assess the effect of control strategies that frequently have high social and economic costs. Despite having an

Basic Reproduction Number \(R_0\)

This chapter forms a general definition for the basic reproduction number \(R_0\) of structured populations in time-heterogeneous environments, and shows that the basic reproduced number can be calculated as the spectral radius of the next-generation operator in a constant environment or in a periodic environment.

On a new perspective of the basic reproduction number in heterogeneous environments

  • H. Inaba
  • Mathematics
    Journal of mathematical biology
  • 2012
A new definition of R0 is introduced based on the generation evolution operator (GEO), which has intuitively clear biological meaning and can be applied to structured populations in any heterogeneous environment.

Reviewing the Reproduction Number R in Covid-19 Models

Most of the epidemiological models of the Covid-19 pandemic contain the reproduction number (R) as a parameter. In this article we focus on some shortcomings regarding its role in driving health

Perspectives on the basic reproductive ratio

An overview of common methods of formulating R0 and surrogate threshold parameters from deterministic, non-structured models and the recent use of R0 in assessing emerging diseases, such as severe acute respiratory syndrome and avian influenza, a number of recent livestock diseases, and vector-borne diseases malaria, dengue and West Nile virus are surveyed.

A new method for estimating the effort required to control an infectious disease

Using this methodology, the long–term effects of disease–control strategies for particular subgroups of the population, to estimate the level of control necessary when targeting control effort at a subset of host types, and to identify host types that constitute a reservoir of infection are identified.

On the reproduction number in epidemics

  • M. Batista
  • Mathematics
    Journal of biological dynamics
  • 2021
This note provides an elementary derivation of the basic reproduction number and the effective reproduction number from the discrete Kermack–McKendrick epidemic model. The derived formulae match

Commentary on the use of the reproduction number R during the COVID-19 pandemic

It is argued that careful definition of R, and the data and methods used to estimate it, can make R a more useful metric for future management of the epidemic.

Beyond R 0: Demographic Models for Variability of Lifetime Reproductive Output

A new approach is presented, using the theory of Markov chains with rewards, obtaining all the moments of the distribution of lifetime reproduction, which applies to age- or stage-classified models, to constant, periodic, or stochastic environments, and to any kind of reproductive schedule.



The concept of RO in epidemic theory

The historical development of Ro is reviewed, an exposition of the recently formalised theory to define and calculate R0 for structured populations is given, and the interaction of demography and epidemiology is returned to for an example of the use of the concept to study vaccination campaigns.

Contribution to the Analysis of Malaria Epidemiology. I. General Part

The author does not, in the work cited, give the general solution of the differential equations developed by him, but restricts his discussion to the final state of equilibrium to which they lead.

Modeling Nature: Episodes in the History of Population Biology

The rise of "the new natural history" is debated, the ecology's future as a large-scale scientific enterprize is examined and the field's theoretical, empirical and institutional development are examined.

On the definition and the computation of the basic reproduction ratio R0 in models for infectious diseases in heterogeneous populations

It is shown that in certain special cases one can easily compute or estimate the expected number of secondary cases produced by a typical infected individual during its entire period of infectiousness in a completely susceptible population.


summary A summary of P. D. En'ko's contributions to the theory of epidemics is presented. This work appeared 1889 in Russian in St. Petersburg. En'ko actually fitted his discrete time model to

Resolving a historical confusion in population analysis.

A lone pioneer throughout much of his career, with no cadre of graduate students and colleagues, Alfred J. Lotka could naturally be expected to be prickly over failures to recognize and acknowledge his important contributions to demography.

Ecology: Individuals, Populations and Communities

A revised and updated edition of this textbook. As before the study of plant and animal ecology is fully integrated and mathematical and laborotory studies are described where necessary. Examples

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Early work in the mathematical theory of epidemics was mainly concerned with the development of deterministic models for the spread of disease through a population. An excellent review of the

A contribution to the mathematical theory of epidemics

The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.

The estimation of the basic reproduction number for infectious diseases

  • K. Dietz
  • Medicine, Economics
    Statistical methods in medical research
  • 1993
The present paper gives a survey about the various estimation methods available for the basic reproduction number Ro, which may vary considerably for different infectious diseases but also for the same disease in different populations.