How the Efficacy of Interventions That Limit Transmission Depends on the Basic Reproduction Number, <i>R</i>₀

<p>The final proportion infected in a pandemic for a general class of models with homogeneous population mixing is plotted as a function of <i>R</i>₀ [<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0040228#pmed-0040228-b022" target="_blank">22</a>,<a href="http://www.plosmedicine.org/article/info:doi/10.1371/journal.pmed.0040228#pmed-0040228-b023" target="_blank">23</a>]. The arrows highlight the effect of an intervention that reduces transmission by 20% for three different baseline values of <i>R</i>₀. This curve can be used, for example, to predict the effect of a vaccine that directly protects 20% of individuals on those who are not directly protected. In scenario I, <i>R</i>₀ is 5 and the intervention reduces the attack rate by 1.3%. In scenario II, <i>R</i>₀ is 3 and the reduction is 6.2%. In scenario III, <i>R</i>₀ is 1.5 and the reduction is 26.9%</p

Single-step and iterative tracing on an epidemic tree, developing from left to right.

<div><p>Nodes are infecteds, lines are contacts, contactees that were not infected are not represented on the tree. Grey infecteds are asymptomatic, white infecteds are symptomatic, infecteds with a thick border are isolated or quarantined.</p> <p>Solid lines are traceable contacts, dotted lines are untraceable contacts.</p> <p>A. Single-step tracing.</p> <p>In A1a-c, a symptomatic infected is isolated and his traceable contactees are quarantined.</p> <p>In A2a-b (some time later), one of the quarantined infecteds got symptomatic and his traceable contactees are quarantined.</p> <p>B. Iterative tracing.</p> <p>In B1a-c, a symptomatic infected is isolated and all infecteds directly or indirectly linked to this infected by traceable contacts are quarantined.</p> <p>All quarantined infecteds form a traceable cluster.</p></div

Supplementary Text, Figures and Tables from An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to <i>Streptococcus pneumoniae</i>

The frequency of resistance to antibiotics in <i>Streptococcus pneumoniae</i> has been stable over recent decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance in two communities in Israel over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates <i>in phase</i> with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance

all.J.csv from An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to <i>Streptococcus pneumoniae</i>

The frequency of resistance to antibiotics in <i>Streptococcus pneumoniae</i> has been stable over recent decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance in two communities in Israel over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates <i>in phase</i> with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance

The effectiveness of single-step contact tracing without tracing delays.

<div><p>Effectiveness is expressed as the minimum proportion of contacts that need to be traced for effective control (critical tracing probability <i>p_c</i>*).</p> <p>The plots show <i>p_c</i>* as a function of the latent period relative to the mean time to detection (τ_lat).</p> <p>There are four special cases: A. Short infectious period and variable time to detection; B. Short infectious period and fixed detection time; C. Long infectious period and variable time to detection; and D. Long infectious period and fixed detection time. </p> <p>The three curves denote <i>p_c</i>* for different values of the pre-isolation reproduction ratio <i>R</i>₀<i>^pre</i>.</p> <p>Indicated by dashed lines are the average τ_lat for four infections, in the panels with closest correspondence to the actual parameter values (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0000012#pone-0000012-t002" target="_blank">Table 2</a>).</p> <p>Influenza appears in two panels with long and short infectious period, because it corresponds to both parameter sets equally.</p></div

Read me file with details on the R codes from An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to <i>Streptococcus pneumoniae</i>

The frequency of resistance to antibiotics in <i>Streptococcus pneumoniae</i> has been stable over recent decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance in two communities in Israel over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates <i>in phase</i> with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance

Main R code for data analysis from An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to <i>Streptococcus pneumoniae</i>

The frequency of resistance to antibiotics in <i>Streptococcus pneumoniae</i> has been stable over recent decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance in two communities in Israel over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates <i>in phase</i> with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance

R code containing functions for data analysis from An evolutionary model to predict the frequency of antibiotic resistance under seasonal antibiotic use, and an application to <i>Streptococcus pneumoniae</i>

The frequency of resistance to antibiotics in <i>Streptococcus pneumoniae</i> has been stable over the last decades. For example, penicillin non-susceptibility in Europe has fluctuated between 12% and 16% without any major time trend. In spite of long-term stability, resistance fluctuates over short time-scales, presumably in part due to seasonal fluctuations in antibiotic prescriptions. Here, we develop a model that describes the evolution of antibiotic resistance under selection by multiple antibiotics prescribed at seasonally changing rates. This model was inspired by, and fitted to, published data on monthly antibiotics prescriptions and frequency of resistance, in two communities in Israel, over 5 years. Seasonal fluctuations in antibiotic usage translate into small fluctuations of the frequency of resistance around the average value. We describe these dynamics using a perturbation approach that encapsulates all ecological and evolutionary forces into a generic model, whose parameters quantify a force stabilizing the frequency of resistance around the equilibrium, and the sensitivity of the population to antibiotic selection. Fitting the model to the data revealed a strong stabilizing force, typically two to five times stronger than direct selection due to antibiotics. The strong stabilizing force explains that resistance fluctuates <i>in phase</i> with usage, as antibiotic selection alone would result in resistance fluctuating behind usage with a lag of three months when antibiotic use is seasonal. While most antibiotics selected for increased resistance, intriguingly, cephalosporins selected for decreased resistance to penicillins and macrolides, an effect consistent in the two communities. One extra monthly prescription of cephalosporins per 1000 children decreased the frequency of penicillin-resistant strains by 1.7%. This model emerges under minimal assumptions, quantifies the forces acting on resistance and explains up to 43% of the temporal variation in resistance

The effectiveness of single-step and iterative contact tracing for control of influenza, smallpox, SARS, and foot-and-mouth disease.

<p>Effectiveness is expressed as the minimum proportion of contacts that need to be traced for effective control (critical tracing probability <i>p_c</i>*); <i>p_c</i>* is plotted as a function of the relative delay (δ, proportion of the incubation period) or the absolute delay (days).</p

Is HIV short-sighted? - Matlab codes

Is HIV short-sighted? - Matlab code