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.

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.

The emerging collective motions of swarms of interacting agents are a subject of great interest in application areas ranging from biology to physics and robotics. In this paper, we conduct a careful analysis of the collective dynamics of a swarm of self-propelled heterogeneous, delay-coupled agents. We show the emergence of collective motion patterns and segregation of populations of agents with different dynamic properties; both of these behaviors (pattern formation and segregation) emerge naturally in our model, which is based on self-propulsion and attractive pairwise interactions between agents. We derive the bifurcation structure for emergence of different swarming behaviors in the mean field as a function of physical parameters and verify these results through simulation.

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.

We consider a general swarm model of self-propelling agents interacting through a pairwise potential in the presence of noise and communication time delay. Previous work has shown that a communication time delay in the swarm induces a pattern bifurcation that depends on the size of the coupling amplitude. We extend these results by completely unfolding the bifurcation structure of the mean field approximation. Our analysis reveals a direct correspondence between the different dynamical behaviors found in different regions of the coupling-time delay plane with the different classes of simulated coherent swarm patterns. We derive the spatiotemporal scales of the swarm structures, as well as demonstrate how the complicated interplay of coupling strength, time delay, noise intensity, and choice of initial conditions can affect the swarm. In particular, our studies show that for sufficiently large values of the coupling strength and/or the time delay, there is a noise intensity threshold that forces a transition of the swarm from a misaligned state into an aligned state. We show that this alignment transition exhibits hysteresis when the noise intensity is taken to be time dependent.

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.

Time-delays are common in many physical and biological systems and they give rise to complex dynamic phenomena. The elementary processes involved in template biopolymerization, such as mRNA and protein synthesis, introduce significant time delays. However, there is not currently a systematic mapping between the individual mechanistic parameters and the time delays in these networks. We present here the development of mathematical, time-delay models for protein translation, based on PDE models, which in turn are derived through systematic approximations of first-principles mechanistic models. Theoretical analysis suggests that the key features that determine the time-delays and the agreement between the time-delay and the mechanistic models are ribosome density and distribution, i.e., the number of ribosomes on the mRNA chain relative to their maximum and their distribution along the mRNA chain. Based on analytical considerations and on computational studies, we show that the steady-state and dynamic responses of the time-delay models are in excellent agreement with the detailed mechanistic models, under physiological conditions that correspond to uniform ribosome distribution and for ribosome density up to 70%. The methodology presented here can be used for the development of reduced time-delay models of mRNA synthesis and large genetic networks. The good agreement between the time-delay and the mechanistic models will allow us to use the reduced model and advanced computational methods from nonlinear dynamics in order to perform studies that are not practical using the large-scale mechanistic models.