ABSTRACT Influenza viruses annually kill 290,000–650,000 people worldwide. Antivirals can reduce death tolls. Baloxavir, the recently approved influenza antiviral, inhibits initiation of

viral mRNA synthesis, whereas oseltamivir, an older drug, inhibits release of virus progeny. Baloxavir blocks virus replication more rapidly and completely than oseltamivir, reducing the

duration of infectiousness. Hence, early baloxavir treatment may indirectly prevent transmission. Here, we estimate impacts of ramping up and accelerating baloxavir treatment on

population-level incidence using a new model that links viral load dynamics from clinical trial data to between-host transmission. We estimate that ~22 million infections and >6,000

virus that function like baloxavir might similarly curtail transmission and save lives. SIMILAR CONTENT BEING VIEWED BY OTHERS A UNIFYING MODEL TO EXPLAIN FREQUENT SARS-COV-2 REBOUND AFTER

NIRMATRELVIR TREATMENT AND LIMITED PROPHYLACTIC EFFICACY Article Open access 28 June 2024 A QUANTITATIVE SYSTEMS PHARMACOLOGY MODEL OF THE PATHOPHYSIOLOGY AND TREATMENT OF COVID-19 PREDICTS

OPTIMAL TIMING OF PHARMACOLOGICAL INTERVENTIONS Article Open access 14 April 2023 CHARACTERIZING THE INTERACTIONS BETWEEN INFLUENZA AND RESPIRATORY SYNCYTIAL VIRUSES AND THEIR IMPLICATIONS

FOR EPIDEMIC CONTROL Article Open access 20 November 2024 INTRODUCTION Influenza A and B viruses cause a highly contagious respiratory disease in humans that kills 290,000–650,000 people

worldwide every year1. Vaccination is the primary means for controlling influenza transmission but is hampered by the variable efficacy and incomplete population coverage of annual vaccines,

and thus is not yet sufficient for preventing large annual epidemics. Antiviral medications can shorten the duration of symptoms and reduce the likelihood of severe outcomes when

administered to infected individuals shortly after they develop symptoms. Prior to 2018, the only approved influenza antivirals were viral neuraminidase inhibitors2,3. Of these, only

oseltamivir (Tamiflu) can be taken orally, thereby facilitating its widespread usage. Oseltamivir inhibits the release of progeny virus from the cell surface, which is the last step in the

production of infectious virus. Multiple oseltamivir treatments over 5 consecutive days are required to fully arrest virus production. In 2018, a new oral antiviral, baloxavir (Xofluza), was

approved in the United States for use in adults4. Baloxavir inhibits an early step in virus replication, the initiation of viral mRNA synthesis5,6,7. This initiation step requires

cap-snatching, a mechanism in which the viral polymerase binds to the cap structure (m7GpppNm) at the 5’ ends of pre-mRNAs, the nuclear RNA precursors to cellular mRNAs, and then the

endonuclease enzyme in the polymerase itself cleaves the pre-mRNAs at a position 10–14 bases downstream from the cap to generate the capped RNA fragments that serve as primers to initiate

viral mRNA synthesis. Because baloxavir almost completely inhibits the cap-dependent endonuclease, little or no initiation of viral mRNA synthesis occurs, and little or no virus is produced.

Consequently, as predicted, baloxavir treatment of infected patients almost totally inhibits virus production rapidly, within 24 h8. For this reason, only a single dose of baloxavir is

needed to block virus production and shorten symptoms. In addition to reducing the duration of symptoms, influenza antivirals can reduce infectiousness by shortening the period of virus

shedding. In fact, because baloxavir treatment rapidly inhibits virus replication, virus shedding is shortened by 2–3 days. Consequently, widespread baloxavir treatment is predicted to

substantially reduce population-level incidence, analogous to the herd effect attributed to vaccines9. Here, we estimate the impact of increasing baloxavir treatment coverage and varying

times of treatment on population-level incidence using both clinical results and a hierarchical mathematical model that links within-host dynamics of viral load to between-host transmission.

Our results indicate that scaling up and accelerating baloxavir treatment would substantially reduce influenza morbidity and mortality every year. RESULTS AND DISCUSSION IMPACT OF ANTIVIRAL

TREATMENT ON THE CELL-TO-CELL PROLIFERATION OF INFLUENZA Our within-host model assumes that infected patients have an initial load of drug-sensitive virus that increases via replication and

decreases via immune response and antiviral treatment10,11 (Supplementary Fig. 1). We estimated the efficacy with which oseltamivir and baloxavir inhibit viral replication by fitting the

model to the results of a recent clinical trial8 that measured the viral loads of 1014 influenza virus-infected patients after treatment with oseltamivir, baloxavir, or a placebo (Table 1).

Our model produces viral titer estimates similar to the clinical data, and, like the clinical data, shows that baloxavir inhibits influenza virus replication more effectively than

oseltamivir (Fig. 1). Within 1 day of initiating baloxavir or oseltamivir treatment, virus load decreases by an estimated 84% or 56%, respectively, compared with an expected reduction in

untreated cases of 39%. The observed differences in the time between symptom onset and the initiation of treatment for patients in the clinical trial accounts for most of the observed

variability in virus replication (Fig. 1, standard deviations). We used the fitted model to predict the effectiveness of drug treatment scenarios beyond those tested in the clinical trial,

including the initiation of baloxavir or oseltamivir regimens at different times after symptom onset (Supplementary Fig. 3). IMPACT OF BALOXAVIR TREATMENT ON THE TRANSMISSION DYNAMICS OF

INFLUENZA We incorporated this viral replication model into a stochastic individual-based model of influenza transmission that tracks the daily evolution of infectiousness with disease

progression. The infectiousness of a case at any given time depends on viral load, treatment status, and baseline transmission rates estimated from influenza surveillance data12,13

(Supplementary Table 2). Consistent with previous studies14,15, we assume a logarithmic relationship between viral load and infectiousness (Fig. 2). Unless otherwise specified, each course

of treatment is initiated within the first 48 h of symptom onset, with the exact treatment times following the distribution reported in the recent clinical trial8 (Table 1). A day after

initiating treatment with baloxavir or oseltamivir, the model projects that infectiousness is reduced by 95% or only 21%, respectively, relative to a comparable untreated patient (Fig. 2a).

In addition, baloxavir-treated patients are likely to become non-infectious within two days, whereas oseltamivir-treated patients are predicted to remain infectious for ~4 or 5 days. To

project the population-level impacts of both scaling up and accelerating antiviral treatment, we fit our model to the 2017–2018 influenza epidemic in the United States, a severe epidemic

which resulted in an estimated 63.3 million people infected, over 900,000 hospitalizations and more than 79,000 deaths16. In the absence of scaling up antiviral coverage, the timing and

magnitude of the epidemiological trajectories projected by the model match the 2017–2018 seasonal epidemic (Fig. 3a). Treatment of 30% of infected cases with baloxavir or oseltamivir within

48 h after symptoms onset reduces the expected number of influenza infections throughout the virus season by 38% or 26%, respectively. We estimate the reduction in the number of overall

infections at other treatment levels, ranging from 10% to 50% (Fig. 3a). As the percent of cases receiving antiviral treatment is increased, the estimated herd effect increases as reflected

by a proportional decline in expected incidence. Baloxavir treatment is predicted to reduce the overall burden of influenza more than oseltamivir treatment across all treatment rates. If

half of all cases are treated, baloxavir or oseltamivir are expected to reduce incidence by 58% or 39%, respectively. Similar herd effects are estimated for models that are fit to incidence

data from the 2016–2017 and 2018–2019 influenza seasons in the United States (Supplementary Figs. 4 and 5). For each intervention scenario in the 2017–2018 season, we also calculated the

basic reproduction number (_R_0), the average number of secondary infections generated by a typical infectious case at the outset of the epidemic (Supplementary Table 2). For example,

treatment of 30% of cases with baloxavir would reduce _R_0 from a 2017–2018 baseline of ~1.15 (95% CI 1.12, 1.17) to ~1.08 (95% CI 1.05, 1.10). Using our model based on the 2017–2018

influenza season, we consider the population-level impacts of treatment initiation time within the 48 h period after symptom onset. Both the efficacy of baloxavir treatment and the increased

benefit of baloxavir relative to oseltamivir are greatest in the first 24 h period (Fig. 4a). For a single infected individual, baloxavir treatment administered within the first 24 h period

is expected to achieve nearly double the reduction in infectiousness (87%) than treatment administered within the second 24 h period. On a population level, baloxavir treatment within the

first 24 h after symptoms onset results in a significantly greater reduction in total incidence than treatment within the second 24 h window following symptom onset (Fig. 4b). At the 30% and

50% case treatment rates, the early baloxavir treatment scenario is expected to avert 3.8 and 5.3 million infections more than the delayed treatment scenario, respectively. We also

evaluated the distribution of treatment times reported in the baloxavir clinical trial:8 approximately equal numbers of patients treated in the 0–24 and 24–48 h time periods following

symptom onset. This mixture is expected to reduce transmission to almost the same extent as accelerating all treatment to within 24 h of symptom onset (Fig. 4b). We restrict our analysis to

treatment initiated within the initial 48 h window, given that later treatment will only negligibly impact incidence and that treatment within 48 h is clearly indicated17,18. In addition,

treatment within 48 h is increasingly feasible with the expansion of telemedicine and online clinics (e.g., through the Xofluza website19 and insurance providers20). Finally, we estimate

influenza-associated mortality and morbidity averted by scaling up baloxavir or oseltamivir treatment (Fig. 4c). Specifically, we calculate the reduction in Disability-Adjusted Life Years

(DALYs)21 between simulated 2017–2018 epidemics with and without scaling up antiviral treatment. For averted cases, we use DALY estimates22 that include losses due to influenza-associated

hospitalization (58%) outpatient care (4%) and mortality (38%). Clinical trial8 results indicate that baloxavir and oseltamivir reduce the duration of illness by at least 23 h. As the

treatment rate increases, the number of courses of treatment required to avert one DALY decreases with baloxavir treatment to a greater extent than with oseltamivir treatment (Fig. 4c). For

example, when only 20% of cases are treated, every 10.6 courses of baloxavir treatment is expected to avert one DALY, whereas 18.6 courses of oseltamivir treatment are needed to avert one

DALY. Hence, each course of baloxavir or oseltamivir treatment is expected to prevent the loss of ~5 weeks or ~3 weeks of healthy life, respectively. Proactive case identification and

antiviral treatment can significantly mitigate the burden of seasonal influenza in the United States. Using an influenza transmission model fitted to a recent clinical trial and incidence

reports from the 2017 to 2018 season, we find that baloxavir offers individual-level and population-level benefits to a greater extent than oseltamivir. For a reasonably attainable scenario

in which only 20% of cases receive baloxavir treatment within 48 h of symptom onset, the estimated herd effect is a 25% reduction in overall incidence, corresponding to ~15 million infected

cases averted in the United States, potentially saving ~4200 lives. With a higher treatment rate (50%), the expected number of cases averted increases to ~37 million, potentially saving

~10,200 lives. Our results indicate that optimal reduction of overall infection occurs when a significant number of infected cases are treated with baloxavir within 24 h after symptom onset.

Consequently, efforts to accelerate the diagnosis and treatment of influenza infections with antivirals such as baloxavir, including potentially cost-saving telemedicine23, should have

far-reaching public health benefits. We expect that ongoing COVID-19 responses will vastly expand the reach and speed of telehealth and increase public awareness of antivirals. Thus,

antiviral treatment of 20–30% of infected patients may be attainable in future influenza epidemics. Influenza A viruses also cause periodic widespread pandemics usually resulting in higher

mortality rates24. The relative benefits of mass treatment with oseltamivir and baloxavir that we have estimated for seasonal influenza epidemics should extend to pandemics, although the

herd effect would likely diminish for more rapidly spreading viruses25,26,27,28. Even at the higher _R_0 values characteristic of rapidly spreading pandemic viruses, baloxavir treatment is

predicted to yield a higher herd effect than oseltamivir (Supplementary Fig. 6). Seminal studies of the mitigation of influenza pandemics suggest that oseltamivir-based interventions can

only partially mitigate a pandemic, with the proportion of cases averted inversely related to the treatment rate, speed of treatment, and transmission rate of the pandemic virus29,30. Our

new estimates of time-dependent baloxavir and oseltamivir efficacy against virus spread are qualitatively consistent with these prior studies and can be readily applied to the evaluation and

updating of antiviral-based mitigation of pandemics. The critical importance of mass treatment by effective antivirals is exemplified by the global pandemic (COVID-19) caused by a novel

coronavirus SARS-CoV2. As of April 2020, COVID-19 has spread to ~200 countries, infected ~2.5 million people, and claimed the lives of more than 170,000 people31. No antivirals specific for

COVID-19 are currently available to treat patients and mitigate the spread of this virus during the time that an effective vaccine is being developed and deployed. Our results indicate that

the rapid development of an antiviral against COVID-19 that, like baloxavir, quickly and almost completely inhibits COVID-19 virus replication could vastly reduce morbidity and mortality

worldwide. However, the likelihood of pre-symptomatic transmission32 and persistent disparities in access to healthcare may hinder the efficacy of future antiviral campaigns. We assume that

the efficacy and timing of antiviral treatment estimated from a clinical trial8 applies to the population as a whole, and have not modeled possible biases in the data with respect to disease

severity or timing of treatment. Future epidemiological studies and clinical trials may allow us to address such biases and capture two key complexities not yet considered in our models.

First, we have not considered that viral kinetics and the efficacy of treatment may substantially vary across age groups and risk groups, as demonstrated by others33. We expect that

incorporating such heterogeneity will enhance intervention assessments and the prioritization of medical resources, but not qualitatively change the results of this analysis. Second, we do

not yet model the evolution and transmission of baloxavir-resistant viruses, which may alter the population-level benefits of ramping up treatment rates. In recent clinical trials,

baloxavir-resistant viruses emerged in 23% of baloxavir-treated children34 and 9.7% of baloxavir-treated adults8, and in some cases prolonged symptoms and viral shedding. Combination therapy

with baloxavir and a neuraminidase inhibitor (oseltamivir) may prevent the generation of baloxavir-resistant viruses, whereas preserving the strong herd effect provided by baloxavir

treatment. Clinical evaluation of this combination therapy is currently underway with results expected in March 2021 (ref. 35). A prior study provides a flexible framework for estimating the

efficacy of combination therapy depending on the timing of administration36. As another caveat, we follow prior studies14,15 in assuming that the infectiousness of a case is logarithmically

related to their viral load. Although there is little doubt that infectiousness and viral load are positively correlated, transmission also depends on contact patterns during the time that

an individual is infectious37. We do not consider infection-mediated changes in contact rates, such as when individuals choose to stay home from school or work when ill. In conclusion, our

results indicate that both the scaling up and acceleration of baloxavir treatment would avert substantial influenza morbidity and mortality every year. Even modest baloxavir treatment rates

can potentially spare millions of people from influenza virus infections during epidemics, thereby substantially reducing hospitalizations, morbidity, and deaths. This prediction provides an

added incentive for accelerated healthcare delivery systems such as telemedicine and the development of rapid, sensitive assays for influenza virus infection. METHODS Our hierarchical

method includes three steps (Supplementary Table 1): (i) fitting a within-host model of antiviral-induced inhibition of influenza virus replication to clinical trial data to estimate the

impact of treatment on the infectiousness of patients (2) fitting a between-host model of person-to-person virus transmission to seasonal influenza surveillance data to estimate influenza

transmission rates, and (3) incorporate both sets of estimates into our simulation model to project the impacts of expanding and accelerating antiviral treatment during emerging epidemics.

WITHIN-HOST MODEL OF INFLUENZA A REPLICATION DYNAMICS We applied a published model that includes viral suppression by both the immune response and antiviral treatment10,11, as given by dU/dt

 = −bUV;  dF/dt = bUV−δF; dZ/dt = rZ; dV/dt = (1−ϵ)pF-cV-kZV. The variables _U, F_, _Z_, and _V_ represent the numbers of uninfected target cells, the numbers of infected target cells, the

intensity of the immune response (i.e., antibody levels), and the amount of free virus (in TCID50/ml), respectively. The parameters _p_, _c, b_, _r_, and \(\epsilon\) denote the viral

replication rate, viral death rate, cell infection rate, growth rate of the immune response, and the antiviral efficacy. Using published estimates for the initial values of _F_ and _U_10, we

applied simulated annealing and approximate Bayesian computation38,39 to fit the model to clinical trial data8 to estimate all model parameters. We assumed that the time from infection to

symptom onset follows a lognormal distribution, _L_, and the time from symptom onset to treatment follows a gamma distribution truncated at 48 h, _G_0–48 (ref. 40) the two distributions were

estimated from data provided in refs. 8,41 using the interior-point method to minimize the root-mean-square error (Supplementary Fig. 2). We do not explicitly consider other sources of

heterogeneity in viral replication or immune response rates. Although most of the patients in the trial were infected by influenza A viruses, ~10% were infected by influenza B viruses. When

we consider the reduced efficacy of baloxavir against influenza B viruses relative to influenza A viruses42, the predictions are relatively unchanged (Supplementary Fig. 7). Following refs.

14,15, we assume that infectiousness is a logarithmic function of viral load, as given by \(1 - e^{ - {\mathrm{log}}_{10}{\mathrm{V}}(t)/100}\) where _V(t)_ denotes the virus load at time

_t_ since infection (Supplementary Section 2). To estimate total reduction in infectiousness attributable to treatment, we calculate the area between the infectiousness curves estimated for

placebo and treatment throughout the entire period of viremia. BETWEEN-HOST INFLUENZA TRANSMISSION MODELS Using approximate Bayesian computation38,39, we fit a deterministic compartmental

susceptible-exposed-symptomatic-recovered (SEYR) model43 to incidence time series for the 2016–2017, 2017–2018, and 2018–2019 influenza seasons in the United States to estimate seasonal

transmission parameters (Table 1 and Supplementary Table 3). Following refs. 44,45, flu incidence is estimated as the product of CDC-reported ILINet activity and WHO lab percent positive

influenza tests12,13. We then incorporated viral replication dynamics and antiviral treatment into a stochastic agent-based version of the fitted SEYR model (Supplementary Section 3). We

replace the discrete exposed and symptomatic states with continuously changing infectiousness from the moment of infection that is governed by our within-host model. Exposed individuals

become symptomatic (and thus eligible for treatment) according to _L_; treated cases obtain their first dose within a 48 h window following distribution _G_0–48 (unless otherwise specified);

symptomatic recover when their virus load falls below zero yielding average infectious periods of 9, 4, and 7 days, as infection for untreated, baloxavir-treated, and oseltamivir-treated

cases, respectively (assuming treatment times follow _G_0–48). The force of infection (the probability that a susceptible individual becomes exposed) is given by \(\lambda = \frac{{\mathop

{\sum }\nolimits_{j \in Y\mathop { \cup }\nolimits^ T}^{} \beta _j(t)}}{N}\), where _N_ is the population size and _β__j_(_t_) is the transmission rate of the _j_th infectious individual

(symptomatic or treated) at time _t_, which is determined by the product of a population-wide scaling factor _Φ_ estimated from seasonal influenza incidence data and the individual’s

infectiousness at time _t_ based on the within-host viral load model. Supplementary Section 6 addresses the assumptions and robustness of the model with respect to influenza virus type.

ESTIMATING EPIDEMIOLOGICAL QUANTITIES FROM SIMULATION DATA _R_0: To obtain the _R_0 of a single simulation, we calculate the average number of secondary cases produced by all individuals

infected during the first week. For each scenario, we compute the mean and 95% confidence interval for _R_0 over 100 stochastic simulations (Supplementary Section 4). TREATMENT EFFECTS To

estimate the epidemiological benefits of various interventions, we conduct pairwise experiments in which we repeatedly run baseline and treatment simulations in tandem, assuming a total

population of 10,000. For each pair _i_, we record the difference in total incidence between the baseline and treatment simulations, _d__i_ = _I_0_ − I__t_, the total number of cases treated

in the treatment simulation _n__i_. For each treatment scenario, we report medians and other distributional statistics over 1000 pairs of simulations. To obtain the expected _number_ of

cases averted on a national-scale in the United States, we multiply the median value of _d__i__/I_0 by a CDC reported estimated for number of infections during the 2017–2018 influenza

season12,13. DALYS AVERTED To estimate the DALYs averted by mass antiviral treatment, we again pair baseline and treatment simulations. To translate infections averted into healthy life

years gained, we apply a published model22 that considers US age-specific risks, disability weights, and durations of clinical outcomes. To quantify the direct benefits for treated cases, we

estimate the years averted owing to alleviation of influenza symptoms using baloxavir or oseltamivir8 (Supplementary Section 5). REPORTING SUMMARY Further information on research design is

available in the Nature Research Reporting Summary linked to this article. DATA AVAILABILITY The clinical trial data used is publicly available in ref. 8. All other data are available from

the corresponding author upon reasonable requests. CODE AVAILABILITY Code developed R (Version 3.6.3) and Matlab (Matlab R2018b) for both the within-host and between-host models and for

estimating epidemiological parameters are available from github (https://github.com/MeyersLabUTexas/baloxavir). REFERENCES * World Health Organization. Influenza (seasonal) (WHO, 2018). *

von Itzstein, M. The war against influenza: discovery and development of sialidase inhibitors. _Nat. Rev. Drug Discov._ 6, 967–974 (2007). Article  Google Scholar  * McClellan, K. &

Perry, C. M. Oseltamivir. _Drugs_ 61, 263–283 (2001). Article  CAS  Google Scholar  * US Food and Drug Administration. FDA approves new drug to treat influenza (FDA, 2018). * Plotch, S. J.,

Bouloy, M. & Krug, R. M. Transfer of 5′-terminal cap of globin mRNA to influenza viral complementary RNA during transcription in vitro. _Proc. Natl Acad. Sci. USA_ 76, 1618–1622 (1979).

Article  ADS  CAS  Google Scholar  * Plotch, S. J., Bouloy, M., Ulmanen, I. & Krug, R. M. A unique cap(m7GpppXm)-dependent influenza virion endonuclease cleaves capped RNAs to generate

the primers that initiate viral RNA transcription. _Cell_ 23, 847–858 (1981). Article  CAS  Google Scholar  * Reich, S. et al. Structural insight into cap-snatching and RNA synthesis by

influenza polymerase. _Nature_ 516, 361–366 (2014). Article  ADS  CAS  Google Scholar  * Hayden, F. G. et al. Baloxavir marboxil for uncomplicated influenza in adults and adolescents. _N.

Engl. J. Med._ 379, 913–923 (2018). Article  CAS  Google Scholar  * John, T. J. & Samuel, R. Herd immunity and herd effect: new insights and definitions. _Eur. J. Epidemiol._ 16, 601–606

(2000). Article  CAS  Google Scholar  * Handel, A., Longini, I. M. & Antia, R. Neuraminidase inhibitor resistance in influenza: assessing the danger of its generation and spread. _PLoS

Comput. Biol._ 3, e240 (2007). Article  ADS  MathSciNet  Google Scholar  * Smith, A. M. & Perelson, A. S. Influenza A virus infection kinetics: quantitative data and models. _Wiley

Interdiscip. Rev. Syst. Biol. Med._ 3, 429–445 (2011). Article  CAS  Google Scholar  * Centers for Disease Control and Prevention. Influenza positive tests reported to CDC by public health

laboratories and ILI activity, national summary. _CDC_ https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html (2018). * Centers for Disease Control and Prevention. Percentage of visits

for ILI, national summary. _CDC_ https://gis.cdc.gov/grasp/fluview/fluportaldashboard.html (2018). * Handel, A., Brown, J., Stallknecht, D. & Rohani, P. A multi-scale analysis of

influenza A virus fitness trade-offs due to temperature-dependent virus persistence. _PLoS Comput. Biol._ 9, e1002989 (2013). Article  ADS  MathSciNet  CAS  Google Scholar  * Handel, A.,

Lebarbenchon, C., Stallknecht, D. & Rohani, P. Trade-offs between and within scales: environmental persistence and within-host fitness of avian influenza viruses. _Proc. Biol. Sci_. 281,

20133051 (2014). Article  Google Scholar  * Centers for Disease Control and Prevention. Archived estimated influenza illnesses, medical visits, hospitalizations, and deaths in the United

States—2017–2018 influenza season (CDC, 2019). * Centers for Disease Control and Prevention. Influenza antiviral medications: clinician summary (CDC, 2020). * Genentech. Prescription flu

treatment, XOFLUZA (baloxavir marboxil). _Genentech_ https://www.xofluza.com/ (2018). * Genentech. Treating the flu. _Genentech_ https://www.xofluza.com/patient/treating-the-flu.html (2020).

* MDLIVE. Visit with an MDLIVE doctor remotely. _MDLIVE_ https://members.mdlive.com/bcbstx/landing_home (2020). * World Health Organization. Metrics: disability-adjusted life year (DALY)

(WHO, 2020). * Sah, P., Medlock, J., Fitzpatrick, M. C., Singer, B. H. & Galvani, A. P. Optimizing the impact of low-efficacy influenza vaccines. _Proc. Natl Acad. Sci. USA_ 115,

5151–5156 (2018). Article  ADS  CAS  Google Scholar  * Granwehr, B. P. In acute uncomplicated influenza, single-dose baloxavir decreased time to symptom relief compared with placebo. _Ann.

Intern. Med._ 169, JC63 (2018). Article  Google Scholar  * Monto, A. S. & Webster, R. G. Influenza pandemics: history and lessons learned. _Textb. Influenza_ 2, 20–33 (2013). Article 

Google Scholar  * Longini, I. M. Containing pandemic influenza at the source. _Science_ 309, 1083–1087 (2005). Article  ADS  CAS  Google Scholar  * Longini, I. M. Jr, Halloran, M. E., Nizam,

A. & Yang, Y. Containing pandemic influenza with antiviral agents. _Am. J. Epidemiol._ 159, 623–633 (2004). Article  Google Scholar  * Germann, T. C., Kadau, K., Longini, I. M. Jr &

Macken, C. A. Mitigation strategies for pandemic influenza in the United States. _Proc. Natl. Acad. Sci. USA_ 103, 5935–5940 (2006). Article  ADS  CAS  Google Scholar  * Colizza, V.,

Barrat, A., Barthelemy, M., Valleron, A.-J. & Vespignani, A. Modeling the worldwide spread of pandemic influenza: baseline case and containment interventions. _PLoS Med._ 4, e13 (2007).

Article  Google Scholar  * Ferguson, N. M. et al. Strategies for mitigating an influenza pandemic. _Nature_ 442, 448–452 (2006). Article  ADS  CAS  Google Scholar  * Kamal, M. A. et al.

Interdisciplinary pharmacometrics linking oseltamivir pharmacology, influenza epidemiology and health economics to inform antiviral use in pandemics. _Br. J. Clin. Pharmacol._ 83, 1580–1594

(2017). Article  CAS  Google Scholar  * CNN. Live updates: US coronavirus cases top 300 (CNN, 2020). * Wei, W. E. et al. Presymptomatic transmission of SARS-CoV-2 — Singapore, January

23–March 16, 2020. _MMWR. Morbidity Mortal. Wkly. Rep._ 69, 411–415 (2020). Article  CAS  Google Scholar  * Vegvari, C. et al. How can viral dynamics models inform endpoint measures in

clinical trials of therapies for acute viral infections? _PLoS ONE_ 11, e0158237 (2016). Article  Google Scholar  * Hirotsu, N. et al. Baloxavir marboxil in Japanese pediatric patients with

influenza: safety and clinical and virologic outcomes. _Clin. Infect. Dis_. https://doi.org/10.1093/cid/ciz908 (2019). * US National Library of Medicine. _C__linicalTrials.gov_

https://clinicaltrials.gov/ct2/show/NCT03684044 (2018). * Kamal, M. A. et al. A drug-disease model describing the effect of oseltamivir neuraminidase inhibition on influenza virus

progression. _Antimicrob. Agents Chemother._ 59, 5388–5395 (2015). Article  CAS  Google Scholar  * Meyers, L. A., Pourbohloul, B., Newman, M. E. J., Skowronski, D. M. & Brunham, R. C.

Network theory and SARS: predicting outbreak diversity. _J. Theor. Biol._ 232, 71–81 (2005). Article  MathSciNet  Google Scholar  * Tavaré, S., Balding, D. J., Griffiths, R. C. &

Donnelly, P. Inferring coalescence times from DNA sequence data. _Genetics_ 145, 505–518 (1997). PubMed  PubMed Central  Google Scholar  * Marin, J.-M., Pudlo, P., Robert, C. P. & Ryder,

R. J. Approximate Bayesian computational methods. _Stat. Comput._ 22, 1167–1180 (2012). Article  MathSciNet  Google Scholar  * Jiang, H. et al. Preliminary epidemiologic assessment of human

infections with highly pathogenic avian influenza A (H5N6) virus, China. _Clin. Infect. Dis._ 65, 383–388 (2017). Article  Google Scholar  * Lessler, J. et al. Incubation periods of acute

respiratory viral infections: a systematic review. _Lancet Infect. Dis._ 9, 291–300 (2009). Article  Google Scholar  * Koszalka, P., Tilmanis, D., Roe, M., Vijaykrishna, D. & Hurt, A.

Baloxavir marboxil susceptibility of influenza viruses from the Asia-Pacific, 2012–2018. _Antiviral Res._ 164, 91–96 (2019). Article  CAS  Google Scholar  * Keeling, M. J. & Rohani, P.

_Modeling Infectious Diseases in Humans and Animals_ (Princeton Univ. Press, 2011). * Goldstein, E., Viboud, C., Charu, V. & Lipsitch, M. Improving the estimation of influenza-related

mortality over a seasonal baseline. _Epidemiology_ 23, 829–838 (2012). Article  Google Scholar  * Fox, S. J., Miller, J. C. & Meyers, L. A. Seasonality in risk of pandemic influenza

emergence. _PLoS Comput. Biol._ 13, e1005749 (2017). Article  ADS  Google Scholar  * Xiang, Y., Gubian, S., Suomela, B. & Hoeng, J. Generalized simulated annealing for global

optimization: the GenSA package. _R J_. 5, ISSN 2073-4859 (2013). * Vihola, M. Robust adaptive Metropolis algorithm with coerced acceptance rate. _Stat. Comput._ 22, 997–1008 (2012). Article

  MathSciNet  Google Scholar  Download references ACKNOWLEDGEMENTS Z.D., A.P.G., and L.A.M. would like to acknowledge funding from the Models of Infectious Disease Agent Study (MIDAS)

program grant number U01 GM087719. R.M.K. was supported by NIH grant number R01 AI11772. The funders had no role in study design, data collection and analysis, decision to publish, or

preparation of the manuscript. AUTHOR INFORMATION AUTHORS AND AFFILIATIONS * Department of Integrative Biology, University of Texas at Austin, Austin, TX, USA Zhanwei Du & Lauren Ancel

Meyers * Department of Statistics and Data Science, University of Texas at Austin, Austin, TX, USA Ciara Nugent & Lauren Ancel Meyers * Center for Infectious Disease Modeling and

Analysis, Yale School of Public Health, New Haven, CN, USA Alison P. Galvani * Department of Molecular Biosciences, John Ring LaMontagne Center for Infectious Disease, Institute for Cellular

and Molecular Biology, University of Texas at Austin, Austin, TX, USA Robert M. Krug * Santa Fe Institute, Santa Fe, NM, USA Lauren Ancel Meyers Authors * Zhanwei Du View author

publications You can also search for this author inPubMed Google Scholar * Ciara Nugent View author publications You can also search for this author inPubMed Google Scholar * Alison P.

Galvani View author publications You can also search for this author inPubMed Google Scholar * Robert M. Krug View author publications You can also search for this author inPubMed Google

Scholar * Lauren Ancel Meyers View author publications You can also search for this author inPubMed Google Scholar CONTRIBUTIONS L.A.M., A.P.G., R.M.K., and Z.D. designed this research,

carried out experiments, and data analysis and drafted the manuscript. C.N. carried out data analysis and drafted the manuscript. The authors read and approved the final manuscript.

CORRESPONDING AUTHOR Correspondence to Lauren Ancel Meyers. ETHICS DECLARATIONS COMPETING INTERESTS The authors declare no competing interests. ADDITIONAL INFORMATION PEER REVIEW INFORMATION

_Nature Communications_ thanks Matthew Ferrari and the other, anonymous, reviewer for their contribution to the peer review of this work. PUBLISHER’S NOTE Springer Nature remains neutral

with regard to jurisdictional claims in published maps and institutional affiliations. SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION REPORTING SUMMARY RIGHTS AND PERMISSIONS OPEN

ACCESS This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format,

as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third

party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the

article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright

holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Reprints and permissions ABOUT THIS ARTICLE CITE THIS ARTICLE Du, Z., Nugent, C., Galvani, A.P.

_et al._ Modeling mitigation of influenza epidemics by baloxavir. _Nat Commun_ 11, 2750 (2020). https://doi.org/10.1038/s41467-020-16585-y Download citation * Received: 28 August 2019 *

Accepted: 11 May 2020 * Published: 02 June 2020 * DOI: https://doi.org/10.1038/s41467-020-16585-y SHARE THIS ARTICLE Anyone you share the following link with will be able to read this

content: Get shareable link Sorry, a shareable link is not currently available for this article. Copy to clipboard Provided by the Springer Nature SharedIt content-sharing initiative