Modelling pandemic influenza and antiviral drug resistance
The recent emergence of antiviral resistance against oseltamivir in seasonal influenza viruses has led to a spate of exercises using modelling techniques to suggest how transmission of antiviral resistant viruses would develop in a pandemic under different circumstances, especially concerning use of antivirals. Here ECDC considers and comments on three recent examples.
Handel, A., I. M. Longini, Jr., et al. (2009). "Antiviral resistance and the control of pandemic influenza: the roles of stochasticity, evolution and model details." J Theor Biol 256(1): 117-25
This study aims to study on the random effects of resistance generation and spread and the possibilities for ongoing evolution of the strains during an outbreak. It is suggested that taking into account the ongoing evolution does not increase the probability of resistant emergence but it does increase the number of infected individuals if an outbreak of resistant viruses occurs. The random effects at the beginning of an outbreak have strong effects on rapid and strong control measures, not only in terms of controlling the outbreak but in addition on preventing resistance outbreak from occurring. In the model it is assumed that resistance can emerge during treatment and these can produce new infections that can cause infections that are dominated by the resistant strain. Resistance can emerge in untreated patients, with 100 times less probability compared with a treated patient. In the model is including a factor for the evolution of the resistance strain during the outbreak. The study finds that the attack rate increases by approximately 20% if a resistant strain emerges compared with only a susceptible strain. If containment is impossible the study find that intermediate control is the best solution as the risk of getting a resistant strain is considerably lower. The effects of using a random model compared with a deterministic model for effects of resistance development and using more control strategies at the beginning of the outbreak is used. Previous modelling studies  have shown that two separate strains (susceptible and resistant) are evolving, and that resistance leads to rapid generation of resistance and an increased attack rate. The random model can account for the realistic case that strong control can lead quick containment of the outbreak.
The study also compared the results in claiming that the best strategy is little control at the beginning and more when the outbreak increases in size . With the random model they find that little initial control is more likely to lead to a generation of a secondary outbreak, while a strong control might contain not only the sensitive outbreak, but also prevent resistance generation. The results can be used in, if a secondary resistant outbreak is unavoidable. But the study suggests that control measures should be implemented for preventing this scenario.
ECDC comment (10/02/2009)
This is the strongest of the papers as its one of the few articles in the field where the researchers have thought of including random effects. Though the experience of the 2008/8 season and the differences in the national levels of antiviral resistance in A(H1N1) viruses suggests this is very important. Due to the random behavioural of genetic changes, this approach is greatly appreciated. The study compares previous studies using deterministic models and possible effects of having random effects. Of great value is the modelled differences on effects of how using different levels of control during the outbreak. Not everything in the model is of random nature yet, as stated by the authors, for example the randomness of the length of the infectious time period and its effects should be investigated. Also what effects changing the probabilities for developing resistance in treated and non-treated patients would benefit this study. We find the developed model very useful and the results should assist pandemic planners.
Arino, J., C. S. Bowman, et al. (2009). "Antiviral resistance during pandemic influenza: implications for stockpiling and drug use." BMC Infect Dis 9(1): 8.
The authors have developed a deterministic (a model with no random effects) mathematical model. Modelling is undertaken for situations with and without a supply of antivirals. The authors estimate that for a pandemic with the features of 1918/9 an antiviral stockpile of 20% of the population is needed. The paper assumes there are three strains of pathogens: drug-sensitive, drug-resistant with low transmission ability (LTFitness) and drug-resistant with high transmission ability (HTFitness). It is assumed that individuals hosting resistance with LTFitness make no contribution to the spread of the resistant virus. Individuals infected are assumed to be symptomatic (two thirds) or asymptomatic (one third). Values of R0 between 1.5 and 2.5 are investigated. The model is seeded by one index case arriving on day 0. The rate of de novo resistance that generates mutants with LTF is assumed a value of 0.018 per day. The simulation is looking at both an adequate (20%) and a 12% supply of antivirals for the population in the illustrations.
ECDC comment (10/02/2009)
The article makes for difficult reading as there are very many numbers. Different values of input values have been used to see their effects of these on the final outcome (a sensitivity analysis). However the authors have only changed the value of one value and not checked what happens when a number of different values are changed. Also what is not investigated in the model are the random properties of resistance development, and how these can occur. The values of ‘de novo‘ resistance refer to earlier modelling studies by the same researchers  and not to any other independent authorities. What is neither addressed is the effect of random distribution on the length of the infectious time period and how the infectivity during the infectious time is varying due to the type of infection. The results claim that a 20% stockpile of antivirals is necessary, but this is not suppored by the article, as this result also does depend on the rates for resistance development and how treatment is given within a certain country. In addition, it is demonstrated that the emergence of highly transmissible resistant strain has no significant impact, on the use of available stockpiles if treatment is maintained at low level and the policy for how the treatments are distributed is not specified.
Brockmann, S. O., M. Schwehm, et al. (2008). "Modelling the effects of drug resistant influenza virus in a pandemic." Virol J 5: 133.
The study uses a freely available computer program InfluSim  to make calculations. Without drug resistance the model predicts that a drug sensitive pandemic strain lead to a cumulative number of 19500 (19.5%) outpatients and around 260 hospitalisations per 100 000 inhabitants. Imported sensitive strains increase these numbers a little to 20700 (20.7%) and around 310 hospitalisations. When including only ‘de novo’ resistance the number rises to 22,700 (22.7%) and around 420. The model assumes a basic reproductive number (the average number of infected when an infectious person enters a totally susceptible population) R0 of 2.5. Unspecified social distancing is suggested to decrease contacts by 10% and isolation of cases reduces the number of contacts by between 10% and 30%. One third of those infected are assumed to be asymptomatic, one third become moderately sick and one third seek medical help (these would be offered antiviral treatment). The model is initiated at day 0 when one infectious person arrives to the population; on day 21, one other infectious person arrives - these can be either drug sensitive or resistant. The paper states that wide-spread use of antivirals will make it likely that drug resistant strains will predominate if it has fitness but highlights the chance effect of whether or not a resistant strain is imported into the population at an early stage in the pandemic.
ECDC comment (10/02/2009)
This paper uses a readily available computer program has ‘pros’ but more ‘cons’. The program is fast and easy to use but even after reading the documentation the assumptions in the model remain unclear which therefore remains rather a ‘black box’. The model is intended for European (Swiss) conditions and other considerations may apply elsewhere. There are no estimations on the uncertainty of the products estimations and little or no validation. For example the assumption of one third of cases being asymptomatic would be challenged by some. The assumption of reduction of contacts by social distancing would benefit of more scientific input than only an assumption of 10%. This article would have benefited from more statistical methodology and more explanation of parameters and assumptions.
The three compared articles have shown a broad span on available methodology to model antiviral resistance. Most of the papers in general and also in this summary are based on deterministic models, these are models which are easy to develop and the calculations are quick. Deterministic models are robust is some situations, for example to estimate the size of a large outbreak. In this situation the results will be the same as from a random model. But their use also has a number of limitations as there is no estimation on the uncertainty of the estimations. In addition deterministic models do not necessarily work well at the beginning or the end of an epidemic when random effects can have a major effect on the final outcome. That was seen in reality last influenza season (2007-8) year with the very different proportions of A(H1N1) viruses that were resistant to oseltamivier in European countries. Presumably those like Norway with high proportion happened by chance alone to have some resistant viruses among the first that entered the country. The two papers with deterministic models may be of less use for pandemic planning research. To make a comparison, a large consortium is needed of leading modellers, in Europe the FluModCont  project would be a candidate to do an analysis of this.
The modelling studies in the field on resistance modelling have still not been using all available modelling approaches, a new input would be to use results from a field called competing epidemics. This is still a new field but should be applied to this kind of problems. Another field not addressed yet is some operational modelling, in which manner and how quickly it is possible to distribute antivirals within a country. These constrains would most possibly make some modelling results more difficult to achieve. This is important because of the short natural history of influenza infections. If an antiviral is to exert any selective pressure it has to be given early soon after symptoms start. Hence there will be a much greater selective pressure from antivirals given for prophylaxis than there will be for treatment unless the latter is given soon after the onset of symptoms, This factor is forgotten in some modelling exercises.
 Eichner, M., M. Schwehm, et al. (2007). "The influenza pandemic preparedness planning tool InfluSim." BMC Infect Dis 7: 17.
 Moghadas, S. M., C. S. Bowman, et al. (2008). "Population-wide emergence of antiviral resistance during pandemic influenza." PLoS ONE 3(3): e1839.
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