Contagiousness

Basic reproduction number

The Basic reproduction number R0 summarizes all demographic, epidemiologic und clinical parameters which infltuence the transmission. Technically, R0 is the largest eigen value of the "Next generation matrix" which is calculated from the contact matrix, the different fractions of the course of disease and the accompanying durations und degrees of contagiousness. The Basic reproduction number always relates to a population, which is fully susceptible and in whcih no interventions take place (an analogous term which refers to transmission in a partly immune population where also interventions may take place, is the "effective reproduction number").

As the Basic reproduction number is supplied directly by the user, it cannot be calculated by InfluSim. Instead the entries of the contact matrix have to be multiplied with a calibration factor in order to be consistent with this entry. This constant (which is not shown on the user interface) may be regarded as the transmission probability, given a contact. An approximative interpretation of R0 is intended by the "Example SIR model".

Example SIR Model

In the simplified SIR Model without different courses of disease and with a contact matrix which only has identical entries, the Basic reproduction number R0 has the following properties: R0 is the average number of secondary cases produced by an index case during the whole course of the infectious period in a fully susceptible population in which no interventions take place. If a fraction 1-1/R0 of the population is immunised (e.g. by vaccination), an infected individual causes on average only one secondary case (i.e. an epidemic is no longer possible). An epidemic is at its peak when the susceptible fraction of the population is reduced to 1/R0. The fraction F of the populaiton which will be infected during the whole course of the epidemic can numerically be calculated from the implicit formula "-ln(1-F)=R0 F" if the population is initially fully susceptible and if no interventions take place.

The model used by InfluSim is much more complicated than this simplified SIR model, but the features described here may still hold approximately.

Cross-references

	The contact matrix and the underlying age distribution crucially influence the calculation of the Basic reproduction number.
	The different courses of disease and the accompanying durations and degrees of contagiousness influence the calculation of R0.
	As infected individuals can already be infected during the end of the latent period, the duration of latency and the early contagiousness also influence the calculation of R0.
	Severely sick children do not attend day care centers and do not go to school which changed their contact pattern. Because of this, child-child contacts at school [%] and the child health care contact factor influence the calculation of R0.
	Increasing the Basic reproduction number makes the infection spread quicker and leads to higher peaks in the epidemic curve. It reduces the effect of all interventions and leads to a quicker depletion of antiviral ressources. Finally, all this increases the total Costs of the epidemic.

Output

The Basic reproduction number mainly determines the speed at which the epidemic curves rise and also the total number of individuals who are infected.

Literature

Basic reproduction number: Various values have been proposed for the basic reproduction number of pandemic influenza. Some examples are given by: Longini IM Jr, Halloran ME, Nizam A, Yang Y. Containing pandemic influenza with antiviral agents. Am. J. Epidemiol. 2004; 159: 623-633. Fergusson NM, Cummings DA, Cauchemez S, Fraser C, Riley S, Meeyai A et al.: Strategies for containing an emerging influenza pandemic in Southeast Asia. Nature 2005; 437: 209-14. Chowell G, Nishiura H, Bettencourt LMA. Comparative estimation of the reproduction number for pandemic influenza from daily case notification data. Journal of the Royal Society Interface 2006; (in press)

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