Attack rate definition

DialysisPrepper · Jan 8, 2007

Does the attack rate (using CDC's 30% figure) mean that after two years, once the initial flu surge has run its course, that 30% of the population will have had the flu? Or does it mean that with each wave (based on the reporting that historically there are three waves) 30% of the people who have not caught the bug during the previous waves, will catch the virus? This would mean 30% sick in the first wave, and 21% in the second, etc. I think it is the first meaning because I have read that it is expected that the attack rate will differ during each wave, peaking in the second.

If it is the former and assuming three waves, with the second being the "worst" wave: Does the CDC scenario imply wave one ~ 5% sick; wave two ~15% sick; wave three ~10% sick?

MHSC · Jan 8, 2007

Re: Attack rate definition

Hmmm... good question.

I was under the impression that it was 30% in each wave, (3 waves) so potentially 90% of the population would have had it by the time it is over. Having it in one wave does not guarantee immunity, you could catch it again, because it could mutate enough that you may not be immune.

JetStuuby · Jan 8, 2007

Re: Attack rate definition

This is a good question.

For example, in 1918 did everyone on the planet eventually get infected with h1n1?

I assume that lets say within 3 years everyone did, although by the later stages the virus itself had evolved into a less deadly strain.

I'm just guessing here, but if no one has a natural immunity to it, then surely over some period of time almost everyone is likely to become infected?

THus to hazard an answer at your question, i think the 30% CDC estimate must refer to the initial "deadly pandemic" strain of the virus, and does not refer to the later stages where the virus has evolved to survive in its new host (humans) without the high initial CFR?

Snicklefritz · Jan 8, 2007

Re: Attack rate definition

I think that if you look at the related figure - the CFR - and do the math, you'll find it is 30% of the entire population, for the entire pandemic. Not sure, but it seems likely.

Laidback Al · Jan 8, 2007

Re: Attack rate definition

In August of last year, we had a discussion about the R0 factor in the Garut cluster and there was some discussion of the definition of attack rate.

http://www.flutrackers.com/forum/showthread.php?p=34153

As I understand it, the attack rate is simply the percent of the population that becomes infected over a specific period of time.

I believe that 30% figure is based on historical human influenza statistics. Whether a novel virus that causes a pandemic will only have an overall attack rate of 30% is a question that I would like to know as well. One thing is certain; the actual attack rate for a pandemic can only be calculated after it is over.

The point that JetStuuby has made is a good one. People were being infected and dying from the Spanish Flu well into the 1920's, but just not as frequently as 1918. I believe there are some scientists who think that by the 1940's everyone in the world had been exposed and infected, and either died or survived. That would be an attack rate of 100% over a 20+ year period.

Perhaps some specialists will weigh here with more information and discussion.

Shannon Bennett · Jan 9, 2007

Re: Attack rate definition

I too have read that virtually everyone had antibodies to variants of the flu of 1918 by the time testing was available. It is also my understanding that the entire population has immunity to new strains within one to two years. I am sorry I cannot remember where I read this so I cannot verify its validity. However, testing of subsequent novel strains gives a base line for the spread of flu virus within a population and I am certain this had been done.

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[SIZE=-1]JAC Advance Access originally published online on March 13, 2003 [/SIZE][SIZE=-1]
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Journal of Antimicrobial Chemotherapy (2003) 51, 977-990
? 2003 The British Society for Antimicrobial Chemotherapy [/SIZE]

A population-dynamic model for evaluating the potential spread of drug-resistant influenza virus infections during community-based use of antivirals

Neil M. Ferguson1,*, Susan Mallett2, Helen Jackson3, Noel Roberts4 and Penelope Ward3

1 Department of Infectious Disease Epidemiology, Imperial College London, St Mary?s Campus, Norfolk Place, London W2 1PG; 2 The UK Cochrane Centre, NHS R & D Programme, Oxford; 3 Roche Global Development, Welwyn Garden City; 4 Roche Discovery Welwyn, Welwyn Garden City, UK 
[SIZE=-1]Received 18 February 2002; returned 23 September 2002; revised 6 December 2002; accepted 2 January 2003[/SIZE]

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A mathematical model of influenza transmission dynamics is used to simulate the impact of neuraminidase inhibitor therapy on infection rates and transmission of drug-resistant viral strains. The model incorporates population age structure, seasonal transmission, immunity and inclusion of elderly nursing home residents or non-residents. Key parameter values are estimated from epidemiological, clinical and experimental data. The analysis examines the factors determining the population spread of antiviral resistance, and predicts no significant transmission of neuraminidase inhibitor resistant virus. This conclusion is robust even at high therapy levels and under conservative assumptions regarding the likely frequency of transmission of resistant virus. The predicted incidence of resistance following protracted usage reflects primary drug resistance, currently estimated as

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2% for neuraminidase inhibitor therapy. It is also shown that until high levels of therapy are attained, early treatment of symptomatic cases is more efficient (per unit of drug) at preventing infections than prophylactic therapy. 

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Influenza A and B virus (and associated co-infections) are estimated to be responsible for 18?20 million excess respiratory illnesses and 20 000 deaths per annum in the USA alone.1?3 Influenza A pandemics have induced even greater levels of mortality in the past, 40 million in the 1918 pandemic4 and a total of 6 million in 1957 and 1968 pandemics,5 and remain one of the major global public health threats posed by emerging infections in the coming century. Vaccination remains the primary public health intervention and has been demonstrated to reduce influenza-related morbidity. However, the antigenic variability of influenza virus necessitates continuous surveillance to identify new vaccine candidate strains, and vaccine efficacy is reduced in key target groups such as the elderly and immunocompromised.6 
Antiviral agents therefore represent a useful additional tool for the control and treatment of influenza infection. The amantadines were the first such agents identified, but have the drawbacks of being effective only against influenza A, significant contraindications and a high frequency of development of drug resistance. Recently, a new class of antivirals with a different biological action, the neuraminidase inhibitors (NAIs), have been developed. Two NAI drugs have been approved for clinical use, oseltamivir (Roche) and zanamivir (GlaxoSmithKline). These drugs are active against both influenza A and B infections and have greater potency and tolerability compared with the amantadines. The current heightened concern over influenza morbidity and mortality is likely to result in the use of these drugs expanding rapidly in the future. 
In such a context, past experience with antimicrobial treatments for a variety of infectious diseases has highlighted the importance of understanding the potential for emergence of drug resistance at a community level. This paper uses experimental and clinical trial data in a mathematical model of influenza transmission to predict potential trends in evolution of resistance to the NAIs. The early development of this model provides information concerning the critical factors predicted to drive development of resistance, and offers the ability to highlight areas where collection of additional data could be used to monitor the spread of resistance in future surveillance studies. 
The use of mathematical models to explain observed patterns of drug-resistant microorganisms and predict future trends is well established7?11 and has proved a powerful tool for understanding the processes determining the evolution and frequency of resistance of drug-resistant pathogens in hospital and community settings. The only previous analysis of the spread of drug resistance to influenza treatment focused on amantadine use in a small closed population (a boarding school) during a single outbreak.12 Resistance to NAIs has been documented both in vitro and in vivo.13,14 In contrast to amantadine-resistant mutants, which exhibit fitnesses close to that of wild-type infectivity and appear to be transmissible, NAI-resistant viruses appear to be 100- to 1000-fold less infectious than wild-type and do not appear to transmit readily in animal models.13,14 
The model developed in this paper describes the dynamics of influenza transmission and treatment and uses these characteristics to predict the potential emergence of drug resistance over many years in a large population with demographic characteristics typical of most developed countries. The model captures heterogeneity of transmission within an age-structured population, and allows the effect of a wide range of targeted treatment scenarios for NAI usage on incidence of drug-susceptible and -resistant influenza to be simulated. The relatively complex framework used enables exploration of a range of realistic future treatment and prophylaxis scenarios. Predictions of the frequency of resistant virus are placed in the context of the effect of treatment on influenza transmission, and susceptibility analyses are carried out to test the robustness of model predictions to varying assumptions about the value of key parameters. 

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Model structure
A deterministic modelling framework was used, since the intention was to capture influenza transmission dynamics in a large population with characteristics representative of the USA or other developed countries. This framework is appropriate to represent average seasonal epidemic behaviour, since for large populations the relative magnitude of random fluctuations around the mean (demographic stochasticity) is small. 
The model (see Figure 1 for overall structure and the Appendix for details and parameter values) divides the population into five compartments as a function of disease status: susceptible, exposed but not infected, asymptomatic infected, symptomatic infected and immune. An ?exposed? state (corresponding to people who have recently been in contact with an infected individual but not infected) is used to allow realistic modelling of treatment involving post-contact (but perhaps pre-infection) prophylactic drug use. Symptomatic infected individuals are defined as those with severe clinical symptoms including a fever. Asymptomatic infected are defined as those with either no or only mild clinical symptoms and who would typically not display health seeking behaviour but would continue normal behavioural patterns in terms of workplace, school and family contacts. The infected population is split into these two stages since experimental influenza infections clearly demonstrate viral shedding before development of symptoms20?22 and a proportion of infected individuals never develop significant symptoms.23,24 This stratification is also necessary if both prophylactic and symptomatic treatment regimens are to be modelled. 


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</TD><TD vAlign=top align=left>Figure 1. Outline of model structure showing population flows between epidemiological compartments. Each epidemiological compartment is further stratified by age class, and infection compartments also into wild-type/resistant categories.

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Age structure

The model adopted here, unlike earlier models,12 explicitly stratifies the population by age, since we wished to explore how treatment in an age-restricted patient group (e.g. elderly persons) might impact on potential development of viral resistance in the population. This allows age-targeted treatment strategies to be modelled, more realistic heterogeneous contact patterns between age groups to be captured25?29 and enables other key parameters (viral shedding, infectivity, mortality, immunity, vaccination) to vary with age. The model further subdivides the population aged >65 years into two subgroups corresponding to those in residential nursing homes and those remaining in the general community. This allows different mixing, treatment, vaccination efficacy and mortality parameters to be assigned to these groups of elderly persons. 
Symptomatic/asymptomatic states
We assumed that 50% of individuals in the age range 18?65 years who are infected with influenza develop severe symptoms (including a fever) and hence enter the symptomatic model state.30 The other 50% move straight from the asymptomatic to the immune state on clearing infection. To reflect higher morbidity and longer durations of viral shedding15?18,31 in the young and old compared with the general population, we assumed that 75% of infected individuals in the age range 0?18 and 65+ years develop severe symptoms and enter the symptomatic model state. Consistent with reported data,20?22,31,32 the duration of the asymptomatic phase of infection was assigned to be 2 days, and the symptomatic phase 4 days, although model results are not highly sensitive to small changes in these values. 
Given that viral shedding before development of severe symptoms accounts for

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25% of total virus shedding,20?22,32 the net infectiousness of asymptomatic individuals was calculated as approximately twice that of symptomatic individuals. This estimate was based on the additional assumption that the contact rate of symptomatic individuals is one-third that of asymptomatics (since most symptomatic patients will not attend work/school), and also allows for the different durations of the asymptomatic and symptomatic periods. 
Epidemic characteristics
Cohort studies and population surveillance have generated data showing variation in influenza attack rates across different age groups, measuring either infection incidence using serology (change in antiviral antibody titres), viral isolation33?36 or disease incidence.30,37 Model transmission parameters were conservatively selected to reproduce the higher attack rates seen when viral antigenicity changes significantly, rather than the lower rates seen (as in the last few years) when antigenic change is limited. 
The seasonal characteristics of epidemic influenza are evident in collated incidence data from many different countries and communities. In the UK influenza incidence figures, the peak of cases is seen from December to March.37?39 A variety of mechanisms may be responsible for this pattern, including seasonal fluctuations in contact patterns in children caused by school terms and holidays, and temperature dependence in influenza transmissibility. We represented this variability through a sinusoidal oscillation of the transmission coefficients with a period of 1 year. This follows the example of much previous modelling of childhood diseases.25,26,29 However, while the model captures average seasonal epidemic behaviour well, we do not attempt to reproduce inter-season variability in epidemic size. To do so would require incorporation of antigenic drift and demographic stochasticity. 
Immunity
Recovery from influenza infection results in the acquisition of immunity, resulting in partial protection from re-infection with similar strains of the virus (we assume that NAI treatment of an infected individual has no effect on this process). However, circulating strains of influenza strains are continuously changing, with a typical strain being extinct in three to four seasons due to competitive exclusion by new, antigenically distinct strains.40 As multi-strain models are computationally complex, we have modelled a single strain and captured the effect of drift generating antigenically novel strains by assuming acquired immunity to the circulating strain wanes over time. Average duration of immunity was set to 5 years (for 18?60 year olds) to reproduce an age-related attack profile typical of influenza A,34 although influenza B differs relatively little.41 The parameter values used to represent decreased immunocompetence and immune experience in older and younger age groups are given in the Appendix. 
As the effects of antigenic drift are not included in this model, the competitive pressures imposed on both wild-type and resistant virus by new, antigenically novel strains are not reproduced. Thus the model is likely to over-estimate the probability that resistant virus generated in one season will survive to the next. 
Wild-type and resistant virus
Two classes of virus are modelled, wild-type and drug resistant. Modelling a single wild-type influenza strain limits model complexity and thus enhances tractability. A single drug-resistant strain is modelled, based on the characteristics of resistant mutants identified during studies with oseltamivir. All resistant viruses isolated in NAI treatment and in vitro studies share very similar properties. Genotyping shows all involve single point mutations in the neuraminidase gene sequence, and most have similar viral pathogenicity and transmission characteristics in animal studies in mice and ferrets.14,42,43 
Resistance can arise in a treated population in two ways. The first is through fixation of mutants that arise de novo in a treated patient. Oseltamivir trial data indicate this to occur with an average frequency of 1.8% across all ages.44 There are insufficient published data available from zanamivir studies to estimate the frequency of emergence of drug-resistant viruses during treatment. One influenza B-resistant mutant was identified during zanamivir treatment of an immunocompromised child.42 We therefore conservatively assume a fixed 1.8% frequency across all treated patients for both agents for the majority of our analyses, but also examine the effect of age-related heterogeneity in oseltamivir resistance rates, given reports of a 4% rate in children and a <1% rate in adults.45 No resistant virus has been isolated during prophylaxis with either NAI, but since the number of such individuals who became infected with influenza in such trials was low, the proportion that might exhibit resistance cannot currently be reliably estimated. We therefore assumed the same 1.8% incidence of resistance in prophylactically treated individuals who become infected as for symptomatic treatment. This is likely to be pessimistic since prophylactic treatment results in a much more significant reduction of total viral shedding20,22 than later symptomatic use, reducing net viral turnover rates and therefore the expected probability of resistant virus emerging. 
The second way for resistance to develop is for an individual infected with resistant virus to transmit that virus to another person. The rate of such transmission is critically dependent on the absolute transmissibility of resistant virus, and its transmissibility relative to wild-type. Transmissibility must be correlated with viral shedding and infectivity measures estimated in experimental infection studies in animals, but the precise quantitative relationships between these covariates has not been established. The relationship is unlikely to be linear, one possibility being that viral shedding needs to exceed some threshold (dependent on the nature of the contact process involved) before transmission becomes likely. In view of this uncertainty, we made the assumption that the relative fitness of resistant virus is

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10% that of wild-type. This is a deliberately pessimistic value, given that all oseltamivir-resistant isolates show a >100-fold drop in infectivity in animal studies, and all zanamivir-resistant isolates (except one, which has only been identified in vitro) show a 60-fold or more drop.14,42 The sensitivity of results to this assumption is discussed later. 
Treatment model
We concentrate on two forms of therapy in this paper, post-contact prophylaxis (equal treatment of the exposed and asymptomatic infected model compartments) and symptomatic disease treatment (affecting only the symptomatic infected compartment). NAI treatment is assumed to have the following biological effects: 
(i) treatment of symptomatically infected individuals reduces the duration of the symptomatic period and their infectiousness. 
(ii) treatment of asymptomatic infected individuals reduces the probability that symptoms will develop, hastens infection clearance and lowers infectiousness. If symptoms do develop they are reduced as above. 
(iii) treatment of susceptible or exposed individuals results in a lower probability of infection. If infection does occur, its severity is reduced as above. 
Vaccination is also modelled, and when effective is assumed to have the same immune protective effect as infection in the model. Vaccination is characterized by age-specific level of effective immunization, the product of vaccine uptake and efficacy (the latter of which declines markedly in older age classes). Different levels of vaccine uptake and protection afforded are modelled for elderly people in residential care and in the community, based on available published data.6 

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Abstract

Introduction

Materials and methods

Results

Discussion

Appendix: model definition and...

References
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Pre-treatment dynamics
The epidemic transmission model reproduces typical patterns of seasonal influenza epidemics, with realistic age-related attack rates and realistic changes in disease incidence due to vaccination. Figure 2(a) illustrates the seasonal epidemic dynamics generated by the model, showing an

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12 week epidemic ?season? each year, consistent with national influenza reporting data in the USA and Europe.38,39 Average annual age-stratified attack rates produced by the model are shown in Figure 2(b), reproducing, as observed,35?37 the much higher attack rates in young children (who have never previously been exposed to influenza), and in the elderly. The average annual infection attack rate across the whole population in this model is 17%, or 10% if only severely symptomatic infections are considered. 


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</TD><TD vAlign=top align=left>Figure 2. (a) Simulated time series of monthly influenza infection incidence per 100 000 population over a 3 year period, in the absence of treatment and vaccination. (b) Simulated average annual percentage attack rate stratified by age of population. (c) Simulated time series of monthly influenza infection incidence per 100 000 population over a 5 year period, but introducing 25% effective vaccination of adults over 60 years of age at the end of year 2 of the simulation; (d) as (b), but 3 years after the introduction of 25% effective vaccination in adults over 60 years. It should be noted that whereas 95% of cases are modelled to occur within a 12 week ?influenza season? window, a small number of cases occur throughout the year.

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The effect of vaccination targeted at elderly persons in reducing overall incidence through time is shown in Figure 2(c), and the much more significant effect on attack rates in the vaccinated age groups in Figure 2(d). Overall, therefore, the model provides a good ?average? description of seasonal influenza epidemics in a population with characteristics similar to the USA. 

NAI usage: current treatment patterns
We initially consider trends in the incidence of resistance under estimated current patterns of usage of oseltamivir in the USA based on a treatment of 6% of symptomatic influenza infections in individuals aged 18?65 years (licensed treatment population for oseltamivir in 1999/2000 season). Figure 3 shows incidence of resistance per 100 000 per annum for the first 3 years after treatment is introduced in the population. This indicates that current treatment patterns will generate

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4.65 cases of resistance per 100 000 of the population per year. This corresponds to 1.8% of the treated patients, or 0.049% of all symptomatic influenza infections. 


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</TD><TD vAlign=top align=left>Figure 3. Predicted monthly incidence of resistance for the first 3 years where 6% of symptomatic influenza patients (age group 18?65 years) are treated with oseltamivir at start of symptoms per 100 000 of the total population. These figures represent a constant 0.049% of all influenza cases following the introduction of treatment, with no evidence of an increasing trend over time; 25% effective vaccination in adults over 60 years is assumed.

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NAI usage: future treatment patterns

We subsequently model levels of resistance based on anticipated future oseltamivir usage in a wider age range (>1 year) of population with characteristics of the USA, resulting in treatment of a larger number of persons. Table 1 shows predicted results for four different treatment scenarios: (a) treatment of 6% of symptomatic infections; (b) treatment of 6% of symptomatic infections and post-contact prophylaxis following 1% of exposure events; (c) treatment of 40% of symptomatic infections; (d) treatment of 40% of symptomatic infections and post-contact prophylaxis following 5% of exposure events. The maximum possible NAI usage level was chosen as 40%, given current proportions of influenza-infected patients estimated to show healthcare seeking behaviour. Whereas we have assumed that the majority of future treatment will be symptomatic, scenarios (b) and (d) examine the effect of a small proportion of post-contact prophylaxis. Detailed population structure (e.g. schools, workplaces) necessary for a full evaluation of the community benefit of prophylaxis is not included in the model, but realism in capturing the individual benefit of prophylaxis is achieved (see Appendix) by explicitly tracking contacts (which may or may not cause infection) as well as infections (a subset of contacts). Under scenarios (a) and (c), 10.4 and 65.1 cases of resistance per 100 000 of the population are predicted to arise, respectively. These levels are only marginally different under low levels of post-contact prophylaxis usage, such that 12.1 and 63.5 cases of resistance per 100 000 are generated, respectively, for scenarios (b) and (d). 


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</TD><TD vAlign=top align=left>Table 1.. Predicted annual incidence of resistance and of all influenza infection (per 100 000 of the total population, averaged over the 3rd and 4th years post-treatment introduction) </TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE></CENTER>
Allowing for heterogeneous rates of generation of resistance changes model results little; e.g. assuming rates of 4% in children under 18 and 0.7% in adults for scenario (a) of Table 1, the number of cases of resistance per 100 000 of the population increases from 10.4 to 10.7, but total infections and cases prevented remain unchanged. 

The low levels of resistance for all the scenarios examined above are due to the predicted lack of significant transmission of resistant virus, due its low relative transmissibility (10%) compared with wild-type virus. At this level, transmissibility is below the critical level required for self-sustaining transmission of an infectious agent (see Discussion). 
It should be noted that the predicted incidence of resistance is always substantially lower than the estimated numbers of influenza infections predicted to be prevented by these levels of treatment (also given in Table 1). The latter quantities are also likely to be underestimates of the true effect of treatment, as the model does not capture the spatially clustered nature of influenza transmission within small populations. 
NAI usage in the elderly
The elderly population represents a high risk group for influenza, with high levels of morbidity and mortality.15?18 This group of patients is targeted for intensive preventative treatment through influenza vaccination;46 however, the outcomes have differed according to setting6,47,48 and there is clearly room for additional preventative measures.6 We therefore explore the effect of highly intensive (90%) post-contact prophylactic treatment of elderly persons in residential homes, and the levels of resistance expected to arise as a result of such treatment programmes. 
Table 2 shows the effect of this NAI treatment regimen on overall influenza incidence to be dramatic within the residential home population. This reflects patterns seen in clinical trials, where it has been shown that prophylaxis in residential homes can reduce the probability of infection by 90%,49 and prophylactic treatment of experimental infections can reduce viral shedding by 70%.22 Table 2 also demonstrates that the predicted level of resistance generated is low, namely 24.4 cases per 100 000 (half of which arise from the background level of 6% symptomatic treatment assumed) or 0.5% of the treated population (assuming treatment is given regardless of vaccination or immune status). This resistance arises nearly entirely through de novo generation of resistance within a treated individual. There is no predicted significant spread of resistant virus to the general population (where 6% of symptomatic infections are assumed treated), again due to its low transmissibility. 


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</TD><TD vAlign=top align=left>Table 2.. Predicted annual incidence of resistance and of severely symptomatic influenza in care home residents per 100 000 of the total population averaged over the 3rd and 4th years after treatment introduction </TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE></CENTER>
Sensitivity of predictions to key parameter values

We explored the robustness of resistance incidence predictions to varying key parameter values, in particular treatment intensity and modality, the relative transmissibility of resistant virus, and the timescale over which the effect of treatment is observed. Predicted levels of resistance were calculated for a grid of values of treatment intensity and relative transmissibility of resistant virus and the results presented as a surface. 
Figure 4 shows predicted incidence of resistance for two treatment scenarios: (a) symptomatic treatment of the general population (>1 year old), with treatment levels varying between 0% and 40%; (b) post-contact prophylactic treatment of the general population, with treatment levels varying between 0% and 40%. Prophylactic treatment at the 40% level could represent an emergency mass treatment programme given a particularly virulent new strain of influenza. The relative transmissibility of resistant virus compared with wild-type varies between 0% and 100%, in order to examine the circumstances required for substantial transmission of resistance. 


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</TD><TD vAlign=top align=left>Figure 4. Predicted annual number of cases of resistance (per 100 000 of the total population averaged over 3rd and 4th years post-treatment introduction) for: (a) symptomatic treatment of general population (>1 year old), with treatment levels varying between 0% and 40%; (b) post-contact prophylactic treatment of general population, with treatment levels varying between 0% and 40%. In both cases, the relative transmissibility of resistant virus varies in the range 0?100%. Case numbers are shown on a log scale to permit system dynamics to be seen across the full range of parameters explored; 25% effective vaccination in adults over 60 years is assumed.

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Figure 4 illustrates that the level of resistance is a non-linear function of viral fitness and treatment usage. Treatment exerts a selective pressure on the virus by disadvantaging drug-susceptible strains relative to drug-resistant strains. However, for substantial transmission of resistant virus to occur, resistant virus firstly needs to out-compete wild-type in the population as a whole, requiring the net fitness (i.e. a weighted average of transmissibility in the treated and untreated population) of resistant virus to exceed that of wild-type. Secondly, the absolute transmissibility of resistant virus needs to be sufficient to permit sustained transmission: i.e. the average number of individuals infected by a single infected individual in a susceptible population (the basic reproduction number) needs to exceed 1. Figure 4 demonstrates that as soon as both of these criteria are met, resistant virus rapidly dominates wild-type, leading to a very sharp increase in the incidence of resistance. 

For symptomatic treatment, such a negative outcome can only occur if the relative transmissibility of resistant virus is very close to that of wild-type (in excess of 90%). This is because symptomatic treatment, even at high levels, exerts a limited selective pressure, partly because 50% of transmission is estimated to occur before an infectious individual develops severe symptoms (and so before treatment), and because only 50% of individuals develop severe symptoms warranting treatment. Post-contact prophylaxis imposes a much greater selective pressure, as its effect can be either to protect people from being infected with wild-type (if they were not infected when they started treatment), or potentially to allow generation of resistance much earlier in disease pathogenesis and viral shedding (for people who have been infected before start of treatment). Hence the threshold transmissibility of resistant virus for widespread transmission is lower for prophylaxis, so the inverse correlation between treatment usage and the position of this threshold can be seen more easily. 
Duration of usage
Table 3 shows the effect of changing the duration of use of treatment, by reproducing the same scenarios as in Table 1, but showing average incidence of resistance per 100 000 in the 14th and 15th year after treatment starts (as compared with the 3rd and 4th year used earlier). The minimal differences between Tables 1 and 3 are due to short-term dynamic transient effects caused by sudden perturbation of the epidemic dynamics due to introduction of high treatment levels. Long-term clinical use of NAIs is therefore predicted to be unlikely to generate significant increases in the incidence of resistance per treated individual. 


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</TD><TD vAlign=top align=left>Table 3.. As Table 1, but with all predictions calculated per 100 000 for the 15th year after treatment was introduced </TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE></CENTER>
Relative benefits of prophylactic and symptomatic treatment

Figure 5 examines the long-term community benefits of treatment as a function of drug usage and the relative transmissibility of resistant virus. The numbers of infections prevented per individual treated is used as the outcome measure. It is interesting to note that at lower treatment levels, symptomatic treatment outperforms prophylactic treatment, as a significant proportion of those given post-exposure prophylaxis would not be expected to develop influenza infection even without treatment. However, the relationship between benefit and treatment level is more non-linear for prophylaxis than for symptomatic treatment, since the former reduces transmission more significantly, lowering exposure event incidence and consequently net treatment usage. Hence prophylaxis begins to outperform symptomatic treatment once usage exceeds

$sim.gif$

30%. If resistant virus transmissibility is 10% that of wild-type virus, Figure 5 also shows that at (improbably) high levels (80%+) of prophylaxis, influenza transmission could be dramatically lowered or even pushed below self-sustaining levels. For increased resistant virus transmissibility, the community benefits of treatment are reduced by increasing the spread of resistant virus at higher usage levels. 


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</TD><TD vAlign=top align=left>Figure 5. Predicted number of infections prevented per individual treated (across years 15?35 post-introduction of treatment) as a function of treatment level for prophylactic and symptomatic NAI treatments, assuming relative transmissibility of resistant virus is 10%, 60% or 90%; 25% effective vaccination in adults >60 years is assumed.

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Discussion

Appendix: model definition and...

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The analysis demonstrates that while the evolution of virus mutants exhibiting resistance to any antiviral agent is nearly inevitable, the threat such mutants pose to successful treatment of acute respiratory viruses critically depends on the incidence of primary (de novo) resistance within the treated patient, and the relative fitness (transmissibility) of resistant strains compared with wild-type, in the absence of drug treatment. The rate of spread of drug resistance is determined by the balance between the selective pressure for evolution of resistance imposed by drug treatment, and the fitness disadvantage of resistant virus relative to wild-type in the absence of treatment. 

This paper has shown that the currently isolated strains of influenza exhibiting high level NAI resistance are unlikely to be transmitted at a frequency that would significantly interfere with the efficacy of even high levels of drug usage. A critical inference in the analysis underlying this conclusion is that within host measures of viral fitness from animal and clinical studies (viral shedding, infectious dose) are strongly correlated with transmissibility. Given the 2?3 log reduction in viral shedding and experimental infectivity14,42,43 seen in animal infections with resistant virus, our assumption that transmissibility is reduced only 10-fold is conservative, but the precise transmission fitness disadvantage of mutant strains can only precisely be measured with experimental host to host transmission studies. Passive surveillance studies of the type often used to monitor resistance are highly problematic tools for estimating viral transmissibility. This is because healthcare seeking behaviour following influenza infection in the general population is currently limited, so necessitating a study design involving highly intensive surveillance of a large yet relatively isolated population (such as multiple residential care homes). 
The other key determinants of the population incidence of drug-resistant strains of virus are their de novo rate of generation and the ease with which they dominate the viral populations of treated individuals sufficiently to be detected. The former depends on the intrinsic error rate of influenza viral replication machinery and so is proportional to the total viral turnover rate in an individual. Hence the probability that resistant mutants pre-exist before initiation of therapy can be minimized by treating the infection as early as possible following exposure, when the viral population size within the patient remains small. 
The probability that a mutant, once generated, will out-compete wild-type virus and dominate the viral population sufficiently to be detected depends on its relative replicative fitness compared with wild-type. Before the start of treatment, the intrinsic fitness difference between resistant mutants and wild-type is sufficient to make the probability of mutant out-growth very low. However, treatment, once started, imposes a massive fitness cost on wild-type such that it can be out-competed by even relatively unfit resistant strains. If resistant mutants do not pre-exist at frequencies sufficient to make fixation likely, maximal inhibition of viral replication immediately on initiation of therapy will minimize the net residual rate of viral replication, and thus minimize the likelihood that resistant mutants will evolve after the start of therapy. Thus maximizing the potency of antiviral treatment is predicted both to optimize clinical outcome and minimize the occurrence of resistance. 
In this context, it is interesting to compare the estimate of 1.8% or less (based on Phase III trial results to date) measured incidence of NAI resistance in treated patients with the 30% incidence of resistance measured following treatment with amantadines.50?52 This difference suggests that amantadine-resistant mutants have much higher replicative fitness than NAI-resistant mutants. This inference is supported by data indicating that amantadine resistance mutations in the M2 virus protein are not associated with a detectable loss in viral function, and that transmissibility, experimental infectivity and pathogenesis of resistant mutants are comparable to wild-type.51?56 For such parameter values, our analysis predicts that widespread use of amantadines for the treatment of symptomatic influenza could result in substantial transmission of resistant virus. 
Influenza strains are continuously changing such that when followed longitudinally particular antigenic variants typically circulate for three to four seasons before extinction due to competitive exclusion by new, more antigenically novel strains.40 As this model does not include antigenic diversity explicitly, the predictions of the incidence of oseltamivir-resistant infections must be regarded as pessimistic, as even relatively transmissible drug-resistant strains would be subject to the same competitive pressures from antigenically fitter new strains generated in populations without significant drug use. 
Our analysis indicates that higher transmissibility mutants would be required for NAI resistance to reach high frequencies. The greater potential for generation of viral diversity in immunocompromised patients, for whom influenza infection can become a chronic infection, is reflected in reports of resistance to zanamivir42 and isolation of multiple sequential amantadine-resistant mutations57,58 within such individuals. Surveillance for potentially higher fitness NAI multipoint resistant mutants (and care in prescribing treatment) should therefore be directed towards this patient group. 

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This project was partly funded by a research contract from Hoffmann-La Roche to Oxford Biologica Ltd. N.M.F. also thanks the Royal Society for fellowship support and the Howard Hughes Medical Institute for research grant funding. N.M.F. was a paid consultant of Hoffmann-La Roche, and S.M. was an employee of Oxford Biologica Ltd at the time this study was undertaken. 

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We adopt a deterministic, age-structured compartmental epidemic model of a similar form to that used for many past studies of childhood disease,26?29 but modified to take account of waning immunity against the pathogen and co-circulation of both wild-type and drug-resistant viral strains:11,12 
Scheme 1 


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Here x, u, h, y and z are, respectively, used to represent those susceptible, exposed but not infected, infected but not severely symptomatic, infected and severely symptomatic, and immune to the currently circulating viral strain. Figure 1 shows the model structure in schematic form. The model is novel in modelling contacts with infectives not leading to infection of the susceptible, the aim being to more realistically describe post-exposure prophylaxis where treatment is used before infection is confirmed. The parameter c represents the ratio of all contacts to infections, whilst

$xgr.gif$

represents the rate at which those exposed but uninfected move back into the unexposed susceptible class?in essence representing the time period after which uninfected individuals would be unlikely to suspect infection via exposure to a particular infected individual. 

The subscript i specifies the age category, with the following age classes being used: 0?<1, 1?<2, 2?<3, 3?<4, 4?<5, 5?<6, 6?<7, 7?<8, 8?<9, 9?<11, 11?<18, 18?<22, 22?<30, 30?<40, 40?<50, 50?<60, 60?<65, 65?<70, 70?<75, 75+ years. The last three age classes (i = 18...20) representing 65+ year olds in the community are duplicated (i = 21...23) so that elderly people in residential care homes could be distinguished from the rest of the population. The rate of movement between age classes is determined by the following function 
Scheme 2 


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where mi represents any age-specific state variable,

$ohgr.gif$

i is the width (in years) of age class i, and Ii is the proportion of individuals who enter residential care homes when entering age class i. 

Much of the apparent complexity of the above equations lies in the detailed representation of the impact of antiviral treatment. Treatment and vaccination are modelled via the three age-specific and time-varying functions Ei(t), Di(t) and Vi(t). The first represents the proportion of exposure events that are treated via post-contact prophylaxis, the second the proportion of severely symptomatic influenza cases treated and the third the per capita vaccination rate of susceptibles. For instance, 6% prophylactic treatment from time t = 20 across all ages corresponds to Ei(t) = 0 for t < 20 and 0

$le.gif$

i

$le.gif$

20, and Ei(t) = 0.06 for t <IMG alt=">=" src="http://jac.oxfordjournals.org/math/ge.gif" border=0> 20 and 0

$le.gif$

i

$le.gif$

20. 
In the equations above, superscripts S, R, T and U, respectively, denote state variables or parameters specific to infection with drug-susceptible virus, infection with drug-resistant virus, treatment with NAI or those remaining untreated. 
The forces of infection for susceptible and resistant strains of virus are given by: 
Scheme 3 


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where

$psi.gif$

H,

$psi.gif$

T and

$psi.gif$

R, respectively, represent differences in infectiousness (relative to a symptomatic, untreated wild-type infection) in latent (non-severely symptomatic) infection, treated infection and infections with resistant virus. The sinusoidally varying term in the force of infection is employed (as in previous work25?27) to reproduce the seasonal pattern of infection incidence observed. Heterogeneity of mixing patterns between different age classes is represented in the force of infection equations via the mixing matrix ?ij: 

Scheme 4 


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where the numerical values shown are largely derived from prior modelling studies of childhood diseases,26,27 and

$tgr.gif$

is the baseline transmission coefficient (estimated by matching to incidence data). 

Values of model parameters used in this study are listed in Table A1. 


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</TD><TD vAlign=top align=left>Table A1.. Values of model parameters </TD></TR></TBODY></TABLE></TD></TR></TBODY></TABLE></CENTER>



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* Corresponding author. Fax: +44-20-7262-3495; E-mail: neil.ferguson@imperial.ac.uk<SCRIPT type=text/javascript></SCRIPT>

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Materials and methods

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37 . Hope-Simpson, R. E. (1984). Age and secular distributions of virus-proven influenza patients in successive epidemics 1961?1976 in Cirencester: epidemiological significance discussed. Journal of Hygiene 92, 303?36.[ISI][Medline]
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http://www.pandemicflu.gov/general/h...loverview.html

http://www.globalsecurity.org/securi...ansmission.htm

DialysisPrepper · Jan 9, 2007

Re: Attack rate definition

Laidback Al said:
In August of last year, we had a discussion about the R0 factor in the Garut cluster and there was some discussion of the definition of attack rate.

http://www.flutrackers.com/forum/showthread.php?p=34153

As I understand it, the attack rate is simply the percent of the population that becomes infected over a specific period of time.

I did see that thread, in fact that thread may have been the one that triggered my question initially. I think we have the same understanding of attack rate but I have not seen it clearly stated (other than just now).

What I am trying to do is explain the CDC planning scenario to people. I am putting aside my personal feelings about the relevance of the CDC scenario because I feel that it is as far as my audience will go. I am a civilian (union carpenter) I need official credibility, thus the CDC scenario: Attack rate 30%; CFR 2%; Ro < 1.7; three waves over a two year period, each wave lasting 2 to 8 weeks. (I know, we should be so lucky) Does that sound like what the CDC planning scenario uses for assuptions?

I guess the question now becomes which time period is the CDC attack rate in reference to? In Shannon?s post that paper seems to imply that the attack rate is percentage over a year (mostly based on figure 2) which does make some sense but the wave nature of flu doesn?t follow the calendar ? see 1918 ? so where does that leave us with regard to the CDC scenario? I think I have to present the CDC scenario as I wrote:

DialysisPrepper said:
wave one ~ 5% sick; wave two ~15% sick; wave three ~10% sick

total attack rate over the event ~30%

I think this breakdown will have to be the bases for my justification of what I will be asking people to prepare for and anticipate. I?m trying to avoid being in a meeting and having a highly credentialed individual push back that my scenario is too alarmist. And frankly, in my situation it is not necessary to go beyond the CDC scenario to be alarmed.

As my user name implies I am on dialysis which I am sure you agree puts me at a distinct disadvantage re: pandemic planning. However, optimist that I am I do not feel hopeless. Dialysis-wise I do think we can try to organize a rational response if H5N1 or anything else goes Stage 6 but right now there really isn't a lot (just like every where else). Give me two years okay?

JetStuuby · Jan 9, 2007

Re: Attack rate definition

I think Liad back Al nailed it with this comment........."As I understand it, the attack rate is simply the percent of the population that becomes infected over a specific period of time."

I don't think that there is a set quantifiable period of time like 8 weeks, 3 months, 1 year etc, instead i think that a CFR is a figure calculated for an arbitrary period of time.

For example we speak now of a 65% CFR for h5n1, the time frame being from when the first human cases were recorded until the present time.

In the case of a pandemic i think the CFR determined after the pandemic will be based upon the number of deaths per number of infections over the generalised first wave time period. That maybe considered to be 6, 8 or 12 weeks i guess depending upon who is making the CFR calculation.

Just my thoughts, but i think the time frame is arbitrary

Attack rate definition

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