Novel modelling approaches to predict the role of antivirals in reducing influenza transmission.

To aid understanding of the effect of antiviral treatment on population-level influenza transmission, we used a novel pharmacokinetic-viral kinetic transmission model to test the correlation between nasal viral load and infectiousness, and to evaluate the impact that timing of treatment with the antivirals oseltamivir or baloxavir has on influenza transmission. The model was run under three candidate profiles whereby infectiousness was assumed to be proportional to viral titer on a natural-scale, log-scale, or dose-response model. Viral kinetic profiles in the presence and absence of antiviral treatment were compared for each individual (N = 1000 simulated individuals); subsequently, viral transmission mitigation was calculated. The predicted transmission mitigation was greater with earlier administration of antiviral treatment, and with baloxavir versus oseltamivir. When treatment was initiated 12-24 hours post symptom onset, the predicted transmission mitigation was 39.9-56.4% for baloxavir and 26.6-38.3% for oseltamivir depending on the infectiousness profile. When treatment was initiated 36-48 hours post symptom onset, the predicted transmission mitigation decreased to 0.8-28.3% for baloxavir and 0.8-19.9% for oseltamivir. Model estimates were compared with clinical data from the BLOCKSTONE post-exposure prophylaxis study, which indicated the log-scale model for infectiousness best fit the observed data and that baloxavir affords greater reductions in secondary case rates compared with neuraminidase inhibitors. These findings suggest a role for baloxavir and oseltamivir in reducing influenza transmission when treatment is initiated within 48 hours of symptom onset in the index patient.

Estimating incidence of infection from diverse data sources: Zika virus in Puerto Rico, 2016.

Emerging epidemics are challenging to track. Only a subset of cases is recognized and reported, as seen with the Zika virus (ZIKV) epidemic where large proportions of infection were asymptomatic. However, multiple imperfect indicators of infection provide an opportunity to estimate the underlying incidence of infection. We developed a modeling approach that integrates a generic Time-series Susceptible-Infected-Recovered epidemic model with assumptions about reporting biases in a Bayesian framework and applied it to the 2016 Zika epidemic in Puerto Rico using three indicators: suspected arboviral cases, suspected Zika-associated Guillain-Barré Syndrome cases, and blood bank data. Using this combination of surveillance data, we estimated the peak of the epidemic occurred during the week of August 15, 2016 (the 33rd week of year), and 120 to 140 (50% credible interval [CrI], 95% CrI: 97 to 170) weekly infections per 10,000 population occurred at the peak. By the end of 2016, we estimated that approximately 890,000 (95% CrI: 660,000 to 1,100,000) individuals were infected in 2016 (26%, 95% CrI: 19% to 33%, of the population infected). Utilizing multiple indicators offers the opportunity for real-time and retrospective situational awareness to support epidemic preparedness and response.

Impacts of Zika emergence in Latin America on endemic dengue transmission.

In 2015 and 2016, Zika virus (ZIKV) swept through dengue virus (DENV) endemic areas of Latin America. These viruses are of the same family, share a vector and may interact competitively or synergistically through human immune responses. We examine dengue incidence from Brazil and Colombia before, during, and after the Zika epidemic. We find evidence that dengue incidence was atypically low in 2017 in both countries. We investigate whether subnational Zika incidence is associated with changes in dengue incidence and find mixed results. Using simulations with multiple assumptions of interactions between DENV and ZIKV, we find cross-protection suppresses incidence of dengue following Zika outbreaks and low periods of dengue incidence are followed by resurgence. Our simulations suggest correlations in DENV and ZIKV reproduction numbers could complicate associations between ZIKV incidence and post-ZIKV DENV incidence and that periods of low dengue incidence are followed by large increases in dengue incidence.

Reassessing Serosurvey-Based Estimates of the Symptomatic Proportion of Zika Virus Infections.

Since the 2007 Zika epidemic in the Micronesian state of Yap, it has been apparent that not all people infected with Zika virus (ZIKV) experience symptoms. However, the proportion of infections that result in symptoms remains unclear. Existing estimates have varied in their interpretation of symptoms due to other causes and the case definition used, and they have assumed perfect test sensitivity and specificity. Using a Bayesian model and data from ZIKV serosurveys in Yap (2007), French Polynesia (2013-2014), and Puerto Rico (2016), we found that assuming perfect sensitivity and specificity generally led to lower estimates of the symptomatic proportion. Incorporating reasonable assumptions for assay sensitivity and specificity, we estimated that 27% (95% credible interval (CrI): 15, 37) (Yap), 44% (95% CrI: 26, 66) (French Polynesia), and 50% (95% CrI: 34, 92) (Puerto Rico) of infections were symptomatic, with variation due to differences in study populations, study designs, and case definitions. The proportion of ZIKV infections causing symptoms is critical for surveillance system design and impact assessment. Here, we accounted for key uncertainties in existing seroprevalence data and found that estimates for the symptomatic proportion ranged from 27% to 50%, suggesting that while the majority of infections are asymptomatic or mildly symptomatic, symptomatic infections might be more common than previously estimated.

Guillain-Barré syndrome risk among individuals infected with Zika virus: a multi-country assessment.

BACKGROUND: Countries with ongoing outbreaks of Zika virus have observed a notable rise in reported cases of Guillain-Barré syndrome (GBS), with mounting evidence of a causal link between Zika virus infection and the neurological syndrome. However, the risk of GBS following a Zika virus infection is not well characterized. In this work, we used data from 11 locations with publicly available data to estimate the risk of GBS following an infection with Zika virus, as well as the location-specific incidence of infection and the number of suspect GBS cases reported per infection. METHODS: We built a mathematical inference framework utilizing data from 11 locations that had reported suspect Zika and GBS cases, two with completed outbreaks prior to 2015 (French Polynesia and Yap) and nine others in the Americas covering partial outbreaks and where transmission was ongoing as of early 2017. RESULTS: We estimated that 2.0 (95% credible interval 0.5-4.5) reported GBS cases may occur per 10,000 Zika virus infections. The frequency of reported suspect Zika cases varied substantially and was highly uncertain, with a mean of 0.11 (95% credible interval 0.01-0.24) suspect cases reported per infection. CONCLUSIONS: These estimates can help efforts to prepare for the GBS cases that may occur during Zika epidemics and highlight the need to better understand the relationship between infection and the reported incidence of clinical disease.

Mosquitoes on a plane: Disinsection will not stop the spread of vector-borne pathogens, a simulation study.

Mosquito-borne diseases are increasingly being recognized as global threats, with increased air travel accelerating their occurrence in travelers and their spread to new locations. Since the early days of aviation, concern over the possible transportation of infected mosquitoes has led to recommendations to disinsect aircraft. Despite rare reports of mosquitoes, most likely transported on aircraft, infecting people far from endemics areas, it is unclear how important the role of incidentally transported mosquitoes is compared to the role of traveling humans. We used data for Plasmodium falciparum and dengue viruses to estimate the probability of introduction of these pathogens by mosquitoes and by humans via aircraft under ideal conditions. The probability of introduction of either pathogen by mosquitoes is low due to few mosquitoes being found on aircraft, low infection prevalence among mosquitoes, and high mortality. Even without disinsection, introduction via infected human travelers was far more likely than introduction by infected mosquitoes; more than 1000 times more likely for P. falciparum and more than 200 times more likely for dengue viruses. Even in the absence of disinsection and under the most favorable conditions, introduction of mosquito-borne pathogens via air travel is far more likely to occur as a result of an infected human travelling rather than the incidental transportation of infected mosquitoes. Thus, while disinsection may serve a role in preventing the spread of vector species and other invasive insects, it is unlikely to impact the spread of mosquito-borne pathogens.

Guillain-Barré Syndrome and Healthcare Needs during Zika Virus Transmission, Puerto Rico, 2016.

To assist with public health preparedness activities, we estimated the number of expected cases of Zika virus in Puerto Rico and associated healthcare needs. Estimated annual incidence is 3.2-5.1 times the baseline, and long-term care needs are predicted to be 3-5 times greater than in years with no Zika virus.

The Long-Term Safety, Public Health Impact, and Cost-Effectiveness of Routine Vaccination with a Recombinant, Live-Attenuated Dengue Vaccine (Dengvaxia): A Model Comparison Study.

BACKGROUND: Large Phase III trials across Asia and Latin America have recently demonstrated the efficacy of a recombinant, live-attenuated dengue vaccine (Dengvaxia) over the first 25 mo following vaccination. Subsequent data collected in the longer-term follow-up phase, however, have raised concerns about a potential increase in hospitalization risk of subsequent dengue infections, in particular among young, dengue-naïve vaccinees. We here report predictions from eight independent modelling groups on the long-term safety, public health impact, and cost-effectiveness of routine vaccination with Dengvaxia in a range of transmission settings, as characterised by seroprevalence levels among 9-y-olds (SP9). These predictions were conducted for the World Health Organization to inform their recommendations on optimal use of this vaccine. METHODS AND FINDINGS: The models adopted, with small variations, a parsimonious vaccine mode of action that was able to reproduce quantitative features of the observed trial data. The adopted mode of action assumed that vaccination, similarly to natural infection, induces transient, heterologous protection and, further, establishes a long-lasting immunogenic memory, which determines disease severity of subsequent infections. The default vaccination policy considered was routine vaccination of 9-y-old children in a three-dose schedule at 80% coverage. The outcomes examined were the impact of vaccination on infections, symptomatic dengue, hospitalised dengue, deaths, and cost-effectiveness over a 30-y postvaccination period. Case definitions were chosen in accordance with the Phase III trials. All models predicted that in settings with moderate to high dengue endemicity (SP9 ≥ 50%), the default vaccination policy would reduce the burden of dengue disease for the population by 6%-25% (all simulations: -3%-34%) and in high-transmission settings (SP9 ≥ 70%) by 13%-25% (all simulations: 10%- 34%). These endemicity levels are representative of the participating sites in both Phase III trials. In contrast, in settings with low transmission intensity (SP9 ≤ 30%), the models predicted that vaccination could lead to a substantial increase in hospitalisation because of dengue. Modelling reduced vaccine coverage or the addition of catch-up campaigns showed that the impact of vaccination scaled approximately linearly with the number of people vaccinated. In assessing the optimal age of vaccination, we found that targeting older children could increase the net benefit of vaccination in settings with moderate transmission intensity (SP9 = 50%). Overall, vaccination was predicted to be potentially cost-effective in most endemic settings if priced competitively. The results are based on the assumption that the vaccine acts similarly to natural infection. This assumption is consistent with the available trial results but cannot be directly validated in the absence of additional data. Furthermore, uncertainties remain regarding the level of protection provided against disease versus infection and the rate at which vaccine-induced protection declines. CONCLUSIONS: Dengvaxia has the potential to reduce the burden of dengue disease in areas of moderate to high dengue endemicity. However, the potential risks of vaccination in areas with limited exposure to dengue as well as the local costs and benefits of routine vaccination are important considerations for the inclusion of Dengvaxia into existing immunisation programmes. These results were important inputs into WHO global policy for use of this licensed dengue vaccine.

Benefits and risks of the Sanofi-Pasteur dengue vaccine: Modeling optimal deployment.

The first approved dengue vaccine has now been licensed in six countries. We propose that this live attenuated vaccine acts like a silent natural infection in priming or boosting host immunity. A transmission dynamic model incorporating this hypothesis fits recent clinical trial data well and predicts that vaccine effectiveness depends strongly on the age group vaccinated and local transmission intensity. Vaccination in low-transmission settings may increase the incidence of more severe "secondary-like" infection and, thus, the numbers hospitalized for dengue. In moderate transmission settings, we predict positive impacts overall but increased risks of hospitalization with dengue disease for individuals who are vaccinated when seronegative. However, in high-transmission settings, vaccination benefits both the whole population and seronegative recipients. Our analysis can help inform policy-makers evaluating this and other candidate dengue vaccines.

Collective motion patterns of swarms with delay coupling: Theory and experiment.

The formation of coherent patterns in swarms of interacting self-propelled autonomous agents is a subject of great interest in a wide range of application areas, ranging from engineering and physics to biology. In this paper, we model and experimentally realize a mixed-reality large-scale swarm of delay-coupled agents. The coupling term is modeled as a delayed communication relay of position. Our analyses, assuming agents communicating over an Erdös-Renyi network, demonstrate the existence of stable coherent patterns that can be achieved only with delay coupling and that are robust to decreasing network connectivity and heterogeneity in agent dynamics. We also show how the bifurcation structure for emergence of different patterns changes with heterogeneity in agent acceleration capabilities and limited connectivity in the network as a function of coupling strength and delay. Our results are verified through simulation as well as preliminary experimental results of delay-induced pattern formation in a mixed-reality swarm.

Potential opportunities and perils of imperfect dengue vaccines.

Dengue vaccine development efforts have focused on the development of tetravalent vaccines. However, a recent Phase IIb trial of a tetravalent vaccine indicates a protective effect against only 3 of the 4 serotypes. While vaccines effective against a subset of serotypes may reduce morbidity and mortality, particular profiles could result in an increased number of cases due to immune enhancement and other peculiarities of dengue epidemiology. Here, we use a compartmental transmission model to assess the impact of partially effective vaccines in a hyperendemic Thai population. Crucially, we evaluate the effects that certain serotype heterogeneities may have in the presence of mass-vaccination campaigns. In the majority of scenarios explored, partially effective vaccines lead to 50% or greater reductions in the number of cases. This is true even of vaccines that we would not expect to proceed to licensure due to poor or incomplete immune responses. Our results show that a partially effective vaccine can have significant impacts on serotype distribution and mean age of cases.

Intervention-based stochastic disease eradication.

Disease control is of paramount importance in public health, with infectious disease extinction as the ultimate goal. Although diseases may go extinct due to random loss of effective contacts where the infection is transmitted to new susceptible individuals, the time to extinction in the absence of control may be prohibitively long. Intervention controls are typically defined on a deterministic schedule. In reality, however, such policies are administered as a random process, while still possessing a mean period. Here, we consider the effect of randomly distributed intervention as disease control on large finite populations. We show explicitly how intervention control, based on mean period and treatment fraction, modulates the average extinction times as a function of population size and rate of infection spread. In particular, our results show an exponential improvement in extinction times even though the controls are implemented using a random Poisson distribution. Finally, we discover those parameter regimes where random treatment yields an exponential improvement in extinction times over the application of strictly periodic intervention. The implication of our results is discussed in light of the availability of limited resources for control.

Breaking the symmetry: immune enhancement increases persistence of dengue viruses in the presence of asymmetric transmission rates.

The dengue viruses exist as four antigenically distinct serotypes. These four serotypes co-circulate and interact with each other through multiple immune-mediated mechanisms. Though the majority of previous efforts to understand the transmission dynamics of dengue have assumed identical characteristics for these four serotypes, empirical data suggests that they differ from one another in important ways. Here, we examine dynamics and persistence in models that do not assume symmetry between the dengue viruses. We find that for serotype transmission rates that are only slightly asymmetric, increased transmissibility of secondary infections through immune enhancement increases the persistence of all dengue viruses in opposition to findings in symmetric models. We identify an optimal magnitude of immune enhancement that maximizes the probability of persistence of all four serotypes. In contrast to other pathogen systems where heterogeneity between serotypes in transmissibility facilitates competitive exclusion (Bremmermann and Thieme, 1989), here we find that in the presence of Antibody Dependent Enhancement (ADE) heterogeneity can increase the persistence of multiple serotypes of dengue.

Mechanistically consistent reduced models of synthetic gene networks.

Designing genetic networks with desired functionalities requires an accurate mathematical framework that accounts for the essential mechanistic details of the system. Here, we formulate a time-delay model of protein translation and mRNA degradation by systematically reducing a detailed mechanistic model that explicitly accounts for the ribosomal dynamics and the cleaving of mRNA by endonucleases. We exploit various technical and conceptual advantages that our time-delay model offers over the mechanistic model to probe the behavior of a self-repressing gene over wide regions of parameter space. We show that a heuristic time-delay model of protein synthesis of a commonly used form yields a notably different prediction for the parameter region where sustained oscillations occur. This suggests that such heuristics can lead to erroneous results. The functional forms that arise from our systematic reduction can be used for every system that involves transcription and translation and they could replace the commonly used heuristic time-delay models for these processes. The results from our analysis have important implications for the design of synthetic gene networks and stress that such design must be guided by a combination of heuristic models and mechanistic models that include all relevant details of the process.

Noise Induced Pattern Switching in Randomly Distributed Delayed Swarms.

We study the effects of noise on the dynamics of a system of coupled self-propelling particles in the case where the coupling is time-delayed, and the delays are discrete and randomly generated. Previous work has demonstrated that the stability of a class of emerging patterns depends upon all moments of the time delay distribution, and predicts their bifurcation parameter ranges. Near the bifurcations of these patterns, noise may induce a transition from one type of pattern to another. We study the onset of these noise-induced swarm re-organizations by numerically simulating the system over a range of noise intensities and for various distributions of the delays. Interestingly, there is a critical noise threshold above which the system is forced to transition from a less organized state to a more organized one. We explore this phenomenon by quantifying this critical noise threshold, and note that transition time between states varies as a function of both the noise intensity and delay distribution.

Statistical multimoment bifurcations in random-delay coupled swarms.

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns with certain universal characteristics that depend on distinguished moments of the time delay distribution. Specifically, we show both theoretically and numerically that although bifurcations of simple patterns, such as translations, change stability only as a function of the first moment of the time delay distribution, more complex patterns arising from Hopf bifurcations depend on all of the moments.

Randomly Distributed Delayed Communication and Coherent Swarm Patterns.

Previously we showed how delay communication between globally coupled self-propelled agents causes new spatio-temporal patterns to arise when the delay coupling is fixed among all agents [1]. In this paper, we show how discrete, randomly distributed delays affect the dynamical patterns. In particular, we investigate how the standard deviation of the time delay distribution affects the stability of the different patterns as well as the switching probability between coherent states.