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 33^rd 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.

Zika virus (ZIKV) infections, like many infections, are generally underreported due to asymptomatic, mild, or unrecognized cases. Using available surveillance indicators reflecting imperfect proxies of infection, we developed a modeling approach to estimate the weekly incidence of infection by combining independent surveillance indicators and assumptions about system-specific reporting biases in a Bayesian framework. Using our approach, we estimated that approximately 890,000 people in the population were infected with Zika in Puerto Rico in 2016, much higher than the 36,316 reported confirmed infections. Our framework has broad application to other diseases where cases may be underreported through traditional disease surveillance and can provide near real-time changes in incidences.

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.

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.

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.

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.

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.

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.

Noise, Bifurcations, and Modeling of Interacting Particle Systems

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete bifurcation unfolds in the presence of communication delay and coupling amplitude. Relative to the center of mass, the patterns can then be described as transitions between translation, rotation about a stationary point, or a rotating swarm, where the center of mass undergoes a Hopf bifurcation from steady state to a limit cycle. Examples of some of the stochastic patterns will be given for large numbers of particles.

Evolution of two-dimensional lump nanosolitons for the Zakharov-Kuznetsov and electromigration equations

The evolution of lump solutions for the Zakharov-Kuznetsov equation and the surface electromigration equation, which describes mass transport along the surface of nanoconductors, is studied. Approximate equations are developed for these equations, these approximate equations including the important effect of the dispersive radiation shed by the lumps as they evolve. The approximate equations show that lump-like initial conditions evolve into lump soliton solutions for both the Zakharov-Kuznetsov equation and the surface electromigration equations. Solutions of the approximate equations, within their range of applicability, are found to be in good agreement with full numerical solutions of the governing equations. The asymptotic and numerical results predict that localized disturbances will always evolve into nanosolitons. Finally, it is found that dispersive radiation plays a more dominant role in the evolution of lumps for the electromigration equations than for the Zakharov-Kuznetsov equation.