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Theory versus data: how to calculate R0?

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 R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) 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 R(0)>1 the outbreak generates an epidemic, and if R(0)<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., R(0)). Surprisingly, we find that this value of R(0) 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 R(0) from empirical contact tracing data collected by epidemiologists and using this R(0) 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.

SUBMITTER: Breban R

PROVIDER: S-EPMC1804098 | biostudies-literature | 2007 Mar

REPOSITORIES: biostudies-literature

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Theory versus data: how to calculate R0?

Breban Romulus R Vardavas Raffaele R Blower Sally S

PloS one 20070314 3

To predict the potential severity of outbreaks of infectious diseases such as SARS, HIV, TB and smallpox, a summary parameter, the basic reproduction number R(0), is generally calculated from a population-level model. R(0) specifies the average number of secondary infections caused by one infected individual during his/her entire infectious period at the start of an outbreak. R(0) is used to assess the severity of the outbreak, as well as the strength of the medical and/or behavioral interventio ...[more]

PMID: 17356693

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Project description:The basic reproduction ratio, R0, is a fundamental concept in epidemiology. It is defined as the total number of secondary infections brought on by a single primary infection, in a totally susceptible population. The value of R0 indicates whether a starting epidemic reaches a considerable part of the population and causes a lot of damage, or whether it remains restricted to a relatively small number of individuals. To calculate R0 one has to evaluate an integral that ranges over the duration of the infection of the host. This duration is, of course, limited by remaining host longevity. So, R0 depends on remaining host longevity and in this paper we show that for long-lived hosts this aspect may not be ignored for long-lasting infections. We investigate in particular how this epidemiological measure of pathogen fitness depends on host longevity. For our analyses we adopt and combine a generic within- and between-host model from the literature. To find the optimal strategy for a pathogen from an evolutionary point of view, we focus on the indicator [Formula: see text], i.e., the optimum of R0 as a function of its replication and mutation rates. These are the within-host parameters that the pathogen has at its disposal to optimize its strategy. We show that [Formula: see text] is highly influenced by remaining host longevity in combination with the contact rate between hosts in a susceptible population. In addition, these two parameters determine whether a killer-like or a milker-like strategy is optimal for a given pathogen. In the killer-like strategy the pathogen has a high rate of reproduction within the host in a short time span causing a relatively short disease, whereas in the milker-like strategy the pathogen multiplies relatively slowly, producing a continuous small amount of offspring over time with a small effect on host health. The present research allows for the determination of a bifurcation line in the plane of host longevity versus contact rate that forms the boundary between the milker-like and killer-like regions. This plot shows that for short remaining host longevities the killer-like strategy is optimal, whereas for very long remaining host longevities the milker-like strategy is advantageous. For in-between values of host longevity, the contact rate determines which of both strategies is optimal.

Project description:The growth of COVID-19 pandemic throughout more than 213 countries around the world have put a lot of pressures on governments and health services to try to stop the rapid expansion of the pandemic. During 2009, H1N1 Influenza pandemic, statistical and mathematical methods were used to track how the virus spreads around countries. Most of these models that were developed at the beginning of the XXI century are based on the classical susceptible-infected-recovered (SIR) model developed almost a hundred years ago. The evolution of this model allows us to forecast and compute basic and effective reproduction numbers (R t and R 0 ), measures that quantify the epidemic potential of a pathogen and estimates different scenarios. In this study, we present a traditional estimation technique for R0 with statistical distributions by best fitting and a Bayesian approach based on continuous feed of prior distributions to obtain posterior distributions and computing real time Rt . We use data from COVID-19 officially reported cases in Ecuador since the first confirmed case on February 29th. Because of the lack of data, in the case of R0 we compare two methods for the estimation of these parameters below exponential growth and maximum likelihood estimation. We do not make any assumption about the evolution of cases due to limited information and we use previous methods to compare scenarios about R0 and in the case of Rt we used Bayesian inference to model uncertainty in contagious proposing a new modification to the well-known model of Bettencourt and Ribeiro based on a time window of m days to improve estimations. Ecuadorian R0 with exponential growth criteria was 3.45 and with the maximum likelihood estimation method was 2.93. The results show that Guayas, Pichincha and Manabí were the provinces with the highest number of cases due to COVID-19. Some reasons explain the increased transmissibility in these localities: massive events, population density, cities dispersion patterns, and the delayed time of public health actions to contain pandemic. In conclusion, this is a novel approach that allow us to measure infection dynamics and outbreak distribution when not enough detailed data is available. The use of this model can be used to predict pandemic distribution and to implement data-based effective measures.

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Theory versus data: how to calculate R0?

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Theory versus data: how to calculate R0?

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