Abstract
To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R0, is generally calculated from a population-level model. R0 specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R0 is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventions necessary for control. Conventionally, it is assumed that if R0>1 the outbreak generates an epidemic, and if R0<1 the outbreak becomes extinct. Here, we use computational and analytical methods to calculate the average number of secondary infections and to show that it does not necessarily represent an epidemic threshold parameter (as it has been generally assumed). Previously we have constructed a new type of individual-level model (ILM) and linked it with a population-level model. Our ILM generates the same temporal incidence and prevalence patterns as the population-level model; we use our ILM to directly calculate the average number of secondary infections (i.e., R0). Surprisingly, we find that this value of R0 calculated from the ILM is very different from the epidemic threshold calculated from the population-level model. This occurs because many different individual-level processes can generate the same incidence and prevalence patterns. We show that obtaining R0 from empirical contact tracing data collected by epidemiologists and using this R0 as a threshold parameter for a population-level model could produce extremely misleading estimates of the infectiousness of the pathogen, the severity of an outbreak, and the strength of the medical and/or behavioral interventions necessary for control.
Highlights
In Epidemiology, it is essential to quantify the severity of actual outbreaks of infectious diseases such as SARS [1,2], HIV [3], TB [4], and smallpox [5]
We explicitly show that certain population-level dynamics, theoretically specified by an Ordinary Differential Equations (ODEs) model, can be the result of many distinct individual-level model (ILM)
We further demonstrate that the R0 obtained from the ILM, by applying the definition of Anderson and May [6], may be different from the epidemic threshold parameter provided by the ODE model
Summary
In Epidemiology, it is essential to quantify the severity of actual (or potential) outbreaks of infectious diseases such as SARS [1,2], HIV [3], TB [4], and smallpox [5]. The established definition of R0, as phrased by Anderson and May [6], is ‘‘the average number of secondary infections produced when one infected individual is introduced into a host population where everyone is susceptible’’. They have stated that ‘‘If R0 is greater than one the outbreak will lead to an epidemic, and if R0 is less than one the outbreak will become extinct’’ [6]; they have assumed that R0 is a threshold parameter that establishes whether an outbreak yields an epidemic or not. We establish that the average number of secondary infections (i.e., R0) is not always an epidemic threshold parameter
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