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ML received consulting fees from the Pandemic Flu Registry, which is sponsored in part by Roche.

Mathematically simulating an influenza pandemic, Joseph Wu and colleagues predict that using a secondary antiviral drug early in local epidemics would reduce global emergence of resistance to the primary stockpiled drug.

The effectiveness of single-drug antiviral interventions to reduce morbidity and mortality during the next influenza pandemic will be substantially weakened if transmissible strains emerge which are resistant to the stockpiled antiviral drugs. We developed a mathematical model to test the hypothesis that a small stockpile of a secondary antiviral drug could be used to mitigate the adverse consequences of the emergence of resistant strains.

We used a multistrain stochastic transmission model of influenza to show that the spread of antiviral resistance can be significantly reduced by deploying a small stockpile (1% population coverage) of a secondary drug during the early phase of local epidemics. We considered two strategies for the use of the secondary stockpile: early combination chemotherapy (ECC; individuals are treated with both drugs in combination while both are available); and sequential multidrug chemotherapy (SMC; individuals are treated only with the secondary drug until it is exhausted, then treated with the primary drug). We investigated all potentially important regions of unknown parameter space and found that both ECC and SMC reduced the cumulative attack rate (AR) and the resistant attack rate (RAR) unless the probability of emergence of resistance to the primary drug _{A}_{A} = 0.01. If the probability of resistance emergence for the secondary drug was also 0.01, then SMC reduced AR and RAR to 57% and 2%. The effectiveness of ECC was similar if combination chemotherapy reduced the probabilities of resistance emergence by at least ten times. We extended our model using travel data between 105 large cities to investigate the robustness of these resistance-limiting strategies at a global scale. We found that as long as populations that were the main source of resistant strains employed these strategies (SMC or ECC), then those same strategies were also effective for populations far from the source even when some intermediate populations failed to control resistance. In essence, through the existence of many wild-type epidemics, the interconnectedness of the global network dampened the international spread of resistant strains.

Our results indicate that the augmentation of existing stockpiles of a single anti-influenza drug with smaller stockpiles of a second drug could be an effective and inexpensive epidemiological hedge against antiviral resistance if either SMC or ECC were used. Choosing between these strategies will require additional empirical studies. Specifically, the choice will depend on the safety of combination therapy and the synergistic effect of one antiviral in suppressing the emergence of resistance to the other antiviral when both are taken in combination.

Every winter, millions of people catch influenza—a viral infection of the airways—and about half a million people die as a result. These seasonal “epidemics” occur because small but frequent changes in the viral proteins (antigens) to which the human immune system responds mean that an immune response produced one year provides only partial protection against influenza the next year. Influenza viruses also occasionally appear that contain major antigenic changes. Human populations have little or no immunity to such viruses so they can start deadly pandemics (global epidemics). The 1918–19 influenza pandemic, for example, killed 40–50 million people. The last influenza pandemic was in 1968 and many experts fear the next pandemic might strike soon. To prepare for such an eventuality, scientists are trying to develop vaccines that might work against an emerging pandemic influenza virus. In addition, many governments are stockpiling antiviral drugs for the large-scale treatment of influenza and for targeted prophylaxis (prevention). Antiviral drugs prevent the replication of the influenza virus, thereby shortening the length of time that an infected person is ill and protecting uninfected people against infection. Their widespread use should, therefore, slow the spread of pandemic influenza.

Although some countries are stockpiling more than one antiviral drug in preparation for an influenza pandemic, many countries are investing in large stockpiles of a single drug, oseltamivir (Tamiflu). But influenza viruses can become resistant to antiviral drugs and the widespread use of a single drug (the primary antiviral) is likely to increase the risk that a resistant strain will emerge. If this did happen, the ability of antiviral drugs to slow the spread of a pandemic would be greatly reduced. In this study, the researchers use a mathematical model of influenza transmission to investigate whether a small stockpile of a secondary antiviral drug could be used to prevent the adverse consequences of the emergence of antiviral-resistant pandemic influenza viruses.

The researchers used their model of influenza transmission to predict how two strategies for the use of a small stockpile of a secondary antiviral might affect the cumulative attack rate (AR; the final proportion of the population infected) and the resistant attack rate (RAR; the proportion of the population infected with an influenza virus strain resistant to the primary drug, a measure that may reflect the impact of antiviral resistance on death rates during a pandemic). In a large, closed population, the model predicted that both “early combination chemotherapy” (treatment with both drugs together while both are available) and “sequential multi-drug chemotherapy” (treatment with the secondary drug until it is exhausted, then treatment with the primary drug) would reduce the AR and the RAR compared with monotherapy unless the probability of emergence of resistance to the primary drug was very low (resistance rarely occurred) or very high (resistance emerged as soon as the primary drug was used). The researchers then introduced international travel data into their model to investigate whether these two strategies could limit the development of antiviral resistance at a global scale. This analysis predicted that, provided the population that was the main source of resistant strains used one of the strategies, both strategies in distant, subsequently affected populations would be able to reduce the AR and RAR even if some intermediate populations failed to control resistance.

As with all mathematical models, the accuracy of these predictions depends on the assumptions used to build the model and the data fed into it. Nevertheless, these findings suggest that both of the proposed strategies for the use of small stockpiles of secondary antiviral drugs should limit the spread of drug-resistant influenza virus more effectively than monotherapy with the primary antiviral drug. Thus, small stockpiles of secondary antivirals could provide a hedge against the development of antiviral resistance during the early phases of an influenza pandemic and are predicted to be a worthwhile public-health investment. However, note the researchers, experimental studies—including determinations of which drugs are safe to use together, and how effectively a given combination prevents resistance compared with each drug used alone—are now needed to decide which of the strategies to recommend in real-life situations. In the context of the 2009 global spread of swine flu, these findings suggest that public health officials might consider zanamivir (Relenza) as the secondary antiviral drug for resistance-limiting strategies in countries that have stockpiled oseltamivir.

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Large-scale antiviral treatment and targeted prophylaxis may provide substantial public health benefits by slowing the spread of pandemic influenza

We adopted the natural history model (Figure A in _{s}_{s}_{T}_{0} = 1.8 _{G}_{T}_{i}_{i}_{T}ε

Our objective was to investigate the possible benefits of multidrug strategies over monotherapy in terms of reducing the impact of treatment-induced resistance. Therefore, we considered antiviral therapies in a generic sense: drug A was the primary antiviral in national stockpiles and drug B was the secondary antiviral to be used to reduce the emergence and spread of resistance. In the context of currently available influenza antivirals and pandemic preparedness, drug A would be oseltamivir because that is the drug that has been stockpiled. Drug B could be zanamivir (Relenza) or an adamantane derivative (amantadine [Symmetrel] or rimantadine [Flumadine]). Although there are few data from humans (or from good animals models of human influenza) that combination antiviral therapy can reduce the emergence of resistance _{A}_{B}

We used a discrete-time stochastic multistrain transmission model to simulate the spread of pandemic influenza in a global network of 105 major cities (see

Our main outcome variables were attack rate (AR, the final proportion of the population infected, both with and without symptoms) and resistant attack rate (RAR, the final proportion infected with a strain resistant to the primary antiviral). AR and RAR are both important measures for the impact of the spread of antiviral resistance. For example, AR reflects the overall societal impact (e.g., burden on the health care system, work absenteeism) posed by the pandemic; RAR indicates the number of infections not treatable by the primary antiviral and therefore may reflect the impact of antiviral resistance on pandemic mortality.

We investigated the dynamics of resistance emergence and mitigation in the first large population to implement large-scale antiviral treatment (assumed to have 6.8 million individuals, the size of Hong Kong). Our baseline scenario was that resistance to the primary antiviral (drug A) emerged with probability _{A}_{0} = 1.8, the demand created by a treatment probability of _{T}

Under monotherapy, there was substantial stochastic variation in AR and RAR among different stochastic realizations, even in a large population, across a wide range of probabilities of emergence of resistance _{A}

Outcome variables were calculated using 10,000 simulations of 365 d in a population of 6.8 million individuals. See main text for baseline natural history parameters. (A) The baseline monotherapy scenario was associated with substantial stochasticity for a wide range of values of _{A}_{A}_{A}

In view of the dramatic impact of early emergence of resistance on AR and RAR, we considered next the effect of a deterministic delay in the emergence of resistance (_{100} to be the time at which the number of resistant cases first reached 100 and _{100} to be the cumulative number of wild-type infections at _{100}. As _{100} increased, the final attack rates AR and RAR decreased because (i) there were more wild-type infectors competing with resistant infectors for susceptible individuals, and (ii) the number of susceptible individuals available for the resistant strain decreased. While the reduction in AR might appear to be limited (a maximal drop of 17% from 73% when all cases were resistant to 56% when resistance was absent;

The results in ^{5} (1.5% of the population). This threshold was robust against variations in population size (Figure J in

We considered two alternative strategies for the deployment of the secondary antiviral. Under early combination chemotherapy (ECC), at the start of the epidemic, symptomatic individuals were treated (with probability _{T}

Both SMC and ECC were effective in reducing the spread of resistance across a wide range of _{A}_{B}_{B}_{B}_{A}_{B}_{B}_{A}

_{A} |
AR or RAR | Mono | SMC | ECC1 | ECC0 with _{B} |
ECC0 with _{B} |
ECC0 with _{B} |

0.001 | AR | 58 (56, 68) | 57 (56, 57) | 56 (56, 56) | 56 (56, 57) | 56 (56, 60) | 58 (56, 66) |

RAR | 7 (1, 42) | 0 (0, 0) | 0 (0, 0) | 1 (0, 4) | 2 (0, 11) | 5 (1, 33) | |

0.01 | AR | 67 (62, 72) | 58 (57, 58) | 57 (57, 57) | 59 (58, 64) | 61 (58, 68) | 65 (60, 71) |

RAR | 38 (18, 64) | 2 (2, 3) | 3 (3, 3) | 9 (5, 24) | 14 (6, 43) | 29 (12, 59) | |

0.1 | AR | 72 (71, 73) | 63 (63, 63) | 63 (63, 63) | 67 (66, 71) | 69 (67, 72) | 72 (70, 73) |

RAR | 66 (60, 71) | 17 (15, 18) | 18 (18, 18) | 39 (32, 57) | 49 (38, 65) | 62 (54, 69) |

We conducted an extensive sensitivity analysis to investigate explicitly how the benefits of ECC and SMC in hedging against resistance varied across the space of unknown parameter values (_{0}, where large-scale antiviral intervention was able to make a significant reduction in attack rate (up to 40%) yet the spread of resistance was likely under monotherapy. In all cases, a hedge was more useful for higher values of _{A}_{0} and _{A}_{A}_{B}_{0} and _{A}_{B}_{A}_{B}

We used Latin-hypercube sampling to generate 1,000 combinations of the following parameters: basic reproductive number _{0}, linear scale on interval (1,3); generation time _{G}_{A}^{−5}, 1); probability of emergence of resistance to the secondary antiviral _{B}^{−5}, 1); synergistic effects of combination therapy in reducing the rates of emergence of resistance ^{−7}, 1)). A probability of treatment of _{T}_{T}_{A}_{B}_{A}_{0} determined the usefulness of a hedge against the emergence of resistance. Main chart, frequency of parameter combinations versus the increase in monotherapy AR due to resistance, AR(MONO)−AR(MONO/R); inset charts, parameter subsets for AR(MONO)−AR(MONO/R)<1% (left) and >1% (right, Set H), points are colored as per the _{A}_{B}_{B}_{A}_{c}_{c}_{c}_{c}_{B}_{A}_{B}

The choice between ECC and SMC is particularly sensitive to the synergy parameter _{T}_{T}

In the global context, the analysis described so far applies to a “source population,” one whose epidemic takes off early enough in the pandemic so that the importation of resistant viruses is not a significant risk. However, given the high connectivity among populations in the global network, it was not apparent that ECC or SMC would also be effective for other populations (downstream populations), because they would more likely be seeded by resistant strains than would source populations. Therefore, to investigate the effectiveness of ECC and SMC at a global scale, we simulated the international spread of a multistrain influenza pandemic over a network of 105 major cities with Hong Kong as the source

Hong Kong (HK) is the source of infection in the network with 30 wild-type seeds on day 0. Twenty-eight cities implement large-scale antiviral intervention: Hong Kong, London, New York, Geneva, and 24 other cities (randomly chosen for each stochastic realization). Cities that implemented SMC had a drug B stockpile coverage of 1%. In this 4-by-4 chart panel, each row corresponds to a city (Hong Kong, London, New York or Geneva) and each column (A–D) corresponds to a different scenario. Each panel is the 2-D histogram (1,000 realizations) of attack rate (_{s}

If only monotherapy was used, the importation of resistance promoted the spread of the resistant strain and downstream populations had higher ARs and RARs, e.g., New York had a higher AR and RAR than London because the pandemic reached New York later, with a higher proportion of introduced infections being resistant (

If all 28 populations that had stockpiles of antivirals implemented SMC rather than monotherapy, reductions in AR and RAR in these populations were similar to those in a single source population (

The source population was the key to the robustness of SMC as a resistance-limiting strategy at the global scale. If the source population implemented only monotherapy, then SMC had little benefit in any downstream population (_{A}

Our model predicts that the spread of treatment-induced antiviral resistance during an influenza pandemic can be effectively reduced by deploying a small stockpile of a secondary drug during the early phase of local epidemics. By investigating all potentially important regions of unknown parameter space we found that both ECC and SMC reduced the cumulative AR and the RAR unless the probability of emergence of resistance to the primary drug was so low that resistance was unlikely to be a problem or so high that resistance emerged as soon as primary drug monotherapy began. Using a global model of large cities, we found that as long as populations that were the main source of resistant strains employed these strategies (SMC or ECC), then those same strategies were also effective for populations far from the source even when some intermediate populations failed to control resistance.

The implications of our results are straightforward: a small stockpile of a secondary antiviral could be used to hedge against the threat of drug-induced antiviral resistance during the next influenza pandemic in terms of reducing the overall AR and the RAR (and hence significantly protect the therapeutic value of the primary antiviral). We have proposed two ways to use such an antiviral, either as combination therapy (ECC) or as sequential monotherapy (SMC). Crucially, under a wide range of possible parameter values, both are superior to the current policy of monotherapy. Therefore, we recommend that a stockpile of a second drug be assembled for use in likely source populations at least (we discuss choices for this drug below), and downstream populations where possible, and that studies be commenced to assess the key drivers of the choice between SMC and ECC. Those drivers are the safety of combination regimens and the degree of synergy between the drugs in vivo. Safety can and should be assessed prior to a pandemic, while synergy could be studied further using seasonal and zoonotic strains of influenza A to provide a basis for studies of a pandemic strain when it emerges.

At the global scale, the success of these strategies requires source populations to minimize their prevalence of resistance so that downstream populations will not be seeded by large numbers of resistant cases. This prediction suggests that likely downstream populations have a strong incentive to assist likely source populations, perhaps with the WHO managing a globally vested stockpile of secondary antivirals. Although it seems that SMC and ECC reduce AR by only a small margin (e.g., by about 10% in

More specifically, in the context of currently implemented pandemic preparedness plans, oseltamivir is the only primary antiviral. Adamantane derivatives and zanamivir are possible secondary antivirals for the hedging strategies we propose here (SMC and ECC). Despite high rates of emergence of resistance to amantadine (e.g., 30% in outpatient adults

Zanamivir is a neuraminidase inhibitor that is comparable to oseltamivir in efficacy against seasonal influenza

Nonetheless, there are some potential implementation issues. Despite the comparable efficacies of oseltamivir and zanamivir

We have used a stochastic model throughout this study. In

Our study has several limitations due to the assumptions we used. First, we assumed that the pandemic virus was sensitive to both drugs when it arrived at the first major city of the global air-travel network. Second, we assumed that resistance was induced by treatment only and ignored other ways by which resistance might emerge (e.g., reassortment with circulating seasonal strains). Third, we assumed that resistant strains had no fitness cost and might therefore overestimate the threat of antiviral resistance. Fourth, the 105-city air travel network that we used might not accurately reflect the global spread of pandemic influenza. Finally, there was not sufficient evidence to choose definitively between the two alternative strategies, SMC and ECC. We discuss the implications of each of these limitations below.

A key premise of this study is that the wild-type pandemic strain was sensitive to both drugs. The effectiveness of our hedging strategies will be much reduced if the pandemic strain acquires resistance to the primary antiviral early at the source by means that are independent of drug pressure, e.g., de novo resistance among pandemic viruses or reassortment with a circulating seasonal strain that is resistant. As shown in the global model (

We used a four-strain model in which all strains were fully fit. The strain infecting a given infectious individual could be sensitive to (i) both drugs, (ii) only drug A, (iii) only drug B, or (iv) neither drug. Because the objective of this study was to devise strategies for hedging against the risk of antiviral resistance, we assumed fully fit resistant strains as the worst-case scenario and showed that SMC and ECC with a small stockpile of secondary antivirals were effective even under such extreme scenarios. We conducted an additional analysis regarding the implications of less fit emergent strains and found that the spread of antiviral resistance under monotherapy was limited if resistant strains were at most 80% as transmissible as the wild type (see Figure L in

We used our model of 105 large, well-mixed cities connected by a flight network as a proxy for the global spread of infection, which is consistent with a previous analysis of the seasonal spread of influenza

We present a flowchart (

Some of the data needed can be collected before the pandemic strikes, e.g., whether the side effects of combination chemotherapy are tolerable. Other data needed can be collected in real time after the pandemic virus has been observed, e.g., drug sensitivity of the pandemic virus and whether combination chemotherapy shows high synergy in reducing emergence of resistance for the pandemic strain.

We chose to investigate incremental additions to current pandemic preparedness plans, rather than more extreme strategies. If safe combinations of antivirals were developed, then the use of combination chemotherapy for the full duration of national epidemics would necessarily be more effective than ECC. However, the additional investment in drug B beyond the levels we considered here is unlikely to be justified by the relatively small marginal benefit (Figure I in

For nations that are currently maintaining a stockpile of a single antiviral with the intention of mitigating the effects of the next influenza pandemic, the inclusion of a small stockpile of a second antiviral does not represent a substantial additional investment. However, our model predicts substantial potential benefits for populations that use a second antiviral early in their epidemic to limit the impact of the emergence of resistance. These benefits are unlikely to be attenuated by the global spread of resistance unless early users of antiviral intervention fail to control resistance. Hence, a small stockpile of a secondary antiviral therapy is an attractive public health hedge.

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We thank the School of Industrial and Systems Engineering at Georgia Institute of Technology for access to their computational equipment. We are grateful to Malik Peiris, Tim Uyeki, and Arnold Monto for helpful discussions.

attack rate

early combination chemotherapy

resistant attack rate

sequential multidrug chemotherapy