Optimizing the early detection of low pathogenic avian influenza H7N9 virus in live bird markets

In Southeast Asia, surveillance at live bird markets (LBMs) has been identified as crucial for detecting avian influenza viruses (AIV) and reducing the risk of human infections. However, the design of effective surveillance systems in LBMs remains complex given the rapid turn-over of poultry. We developed a deterministic transmission model to provide guidance for optimizing AIV surveillance efforts. The model was calibrated to fit one of the largest LBMs in northern Vietnam at high risk of low pathogenic H7N9 virus introduction from China to identify the surveillance strategy that optimizes H7N9 detection. Results show that (i) using a portable diagnostic device would slightly reduce the number of infected birds leaving the LBM before the first detection, as compared to a laboratory-based diagnostic strategy, (ii) H7N9 detection could become more timely by sampling birds staying overnight, just before new susceptible birds are introduced at the beginning of a working day, and (iii) banning birds staying overnight would represent an effective intervention to reduce the risk of H7N9 spread but would decrease the likelihood of virus detection if introduced. These strategies should receive high priority in Vietnam and other Asian countries at risk of H7N9 introduction.     

Detection of mortality clusters associated with highly pathogenic avian influenza in poultry: a theoretical analysis

Rapid detection of infectious disease outbreaks is often crucial for their effective control. One example is highly pathogenic avian influenza (HPAI) such as H5N1 in commercial poultry flocks. There are no quantitative data, however, on how quickly the effects of HPAI infection in poultry flocks can be detected. Here, we study, using an individual-based mathematical model, time to detection in chicken flocks. Detection is triggered when mortality, food or water intake or egg production in layers pass recommended thresholds suggested from the experience of past HPAI outbreaks. We suggest a new threshold for caged flocks—the cage mortality detection threshold—as a more sensitive threshold than current ones. Time to detection is shown to depend nonlinearly on R₀ and is particularly sensitive for R₀<10. It also depends logarithmically on flock size and number of birds per cage. We also examine how many false alarms occur in uninfected flocks when we vary detection thresholds owing to background mortality. The false alarm rate is shown to be sensitive to detection thresholds, dependent on flock size and background mortality and independent of the length of the production cycle. We suggest that current detection thresholds appear sufficient to rapidly detect the effects of a high R₀ HPAI strain such as H7N7 over a wide range of flock sizes. Time to detection of the effects of a low R₀ HPAI strain such as H5N1 can be significantly improved, particularly for large flocks, by lowering detection thresholds, and this can be accomplished without causing excessive false alarms in uninfected flocks. The results are discussed in terms of optimizing the design of disease surveillance programmes in general.     

Spatial dynamics of bar-headed geese migration in the context of H5N1

Virulent outbreaks of highly pathogenic avian influenza (HPAI) since 2005 have raised the question about the roles of migratory and wild birds in the transmission of HPAI. Despite increased monitoring, the role of wild waterfowl as the primary source of the highly pathogenic H5N1 has not been clearly established. The impact of outbreaks of HPAI among species of wild birds which are already endangered can nevertheless have devastating consequences for the local and non-local ecology where migratory species are established. Understanding the entangled dynamics of migration and the disease dynamics will be key to prevention and control measures for humans, migratory birds and poultry. Here, we present a spatial dynamic model of seasonal migration derived from first principles and linking the local dynamics during migratory stopovers to the larger scale migratory routes. We discuss the effect of repeated epizootic at specific migratory stopovers for bar-headed geese (Anser indicus). We find that repeated deadly outbreaks of H5N1 on stopovers during the autumn migration of bar-headed geese could lead to a larger reduction in the size of the equilibrium bird population compared with that obtained after repeated outbreaks during the spring migration. However, the opposite is true during the first few years of transition to such an equilibrium. The age-maturation process of juvenile birds which are more susceptible to H5N1 reinforces this result.     

Outbreaks of H5N1 in poultry in Thailand: the relative role of poultry production types in sustaining transmission and the impact of active surveillance in control

H5N1, highly pathogenic avian influenza, continues to pose a public health risk in the countries of southeast Asia where it has become endemic. However, in Thailand, which experienced two of the largest recorded epidemics in 2004–2005, the disease has been successfully reduced to very low levels. We fitted a spatio-temporal model of the spread of infection to outbreak data collected during the second wave of outbreaks to assess the extent to which different poultry types were responsible for propagating infection. Our estimates suggest that the wave of outbreaks would not have been possible without the contribution of backyard flocks to the susceptibility of a sub-district. However, we also estimated that outbreaks involving commercial poultry, a much larger sector in Thailand than in neighbouring countries, were disproportionately infectious, a factor which was also crucial in sustaining the wave. As a result, implemented measures that aim to reduce the role of commercial farms in the spread of infection, such as the drive to bring aspects of the supply chain ‘in house’, may help to explain the subsequent success in controlling H5N1 in Thailand. We also found that periods of active surveillance substantially improved the rate of outbreak detection.     

Preventable H5N1 avian influenza epidemics in the British poultry industry network exhibit characteristic scales

Epidemics are frequently simulated on redundantly wired contact networks, which have many more links between sites than are minimally required to connect all. Consequently, the modelled pathogen can travel numerous alternative routes, complicating effective containment strategies. These networks have moreover been found to exhibit ‘scale-free’ properties and percolation, suggesting resilience to damage. However, realistic H5N1 avian influenza transmission probabilities and containment strategies, here modelled on the British poultry industry network, show that infection dynamics can additionally express characteristic scales. These system-preferred scales constitute small areas within an observed power law distribution that exhibit a lesser slope than the power law itself, indicating a slightly increased relative likelihood. These characteristic scales are here produced by a network-pervading intranet of so-called hotspot sites that propagate large epidemics below the percolation threshold. This intranet is, however, extremely vulnerable; targeted inoculation of a mere 3–6% (depending on incorporated biosecurity measures) of the British poultry industry network prevents large and moderate H5N1 outbreaks completely, offering an order of magnitude improvement over previously advocated strategies affecting the most highly connected ‘hub’ sites. In other words, hotspots and hubs are separate functional entities that do not necessarily coincide, and hotspots can make more effective inoculation targets. Given the ubiquity and relevance of networks (epidemics, Internet, power grids, protein interaction), recognition of this spreading regime elsewhere would suggest a similar disproportionate sensitivity to such surgical interventions.     

Distribution of vaccine/antivirals and the ‘least spread line’ in a stratified population

We describe a prioritization scheme for an allocation of a sizeable quantity of vaccine or antivirals in a stratified population. The scheme builds on an optimal strategy for reducing the epidemic''s initial growth rate in a stratified mass-action model. The strategy is tested on the EpiSims network describing interactions and influenza dynamics in the population of Utah, where the stratification we have chosen is by age (0–6, 7–13, 14–18, adults). No prior immunity information is available, thus everyone is assumed to be susceptible—this may be relevant, possibly with the exception of persons over 50, to the 2009 H1N1 influenza outbreak. We have found that the top priority in an allocation of a sizeable quantity of seasonal influenza vaccinations goes to young children (0–6), followed by teens (14–18), then children (7–13), with the adult share being quite low. These results, which rely on the structure of the EpiSims network, are compared with the current influenza vaccination coverage levels in the US population.     

Future climates: Markov blankets and active inference in the biosphere

We formalize the Gaia hypothesis about the Earth climate system using advances in theoretical biology based on the minimization of variational free energy. This amounts to the claim that non-equilibrium steady-state dynamics—that underwrite our climate—depend on the Earth system possessing a Markov blanket. Our formalization rests on how the metabolic rates of the biosphere (understood as Markov blanket''s internal states) change with respect to solar radiation at the Earth''s surface (i.e. external states), through the changes in greenhouse and albedo effects (i.e. active states) and ocean-driven global temperature changes (i.e. sensory states). Describing the interaction between the metabolic rates and solar radiation as climatic states—in a Markov blanket—amounts to describing the dynamics of the internal states as actively inferring external states. This underwrites climatic non-equilibrium steady-state through free energy minimization and thus a form of planetary autopoiesis.     

Interplay of population genetics and dynamics in the genetic control of mosquitoes

Some proposed genetics-based vector control methods aim to suppress or eliminate a mosquito population in a similar manner to the sterile insect technique. One approach under development in Anopheles mosquitoes uses homing endonuclease genes (HEGs)—selfish genetic elements (inherited at greater than Mendelian rate) that can spread rapidly through a population even if they reduce fitness. HEGs have potential to drive introduced traits through a population without large-scale sustained releases. The population genetics of HEG-based systems has been established using discrete-time mathematical models. However, several ecologically important aspects remain unexplored. We formulate a new continuous-time (overlapping generations) combined population dynamic and genetic model and apply it to a HEG that targets and knocks out a gene that is important for survival. We explore the effects of density dependence ranging from undercompensating to overcompensating larval competition, occurring before or after HEG fitness effects, and consider differences in competitive effect between genotypes (wild-type, heterozygotes and HEG homozygotes). We show that population outcomes—elimination, suppression or loss of the HEG—depend crucially on the interaction between these ecological aspects and genetics, and explain how the HEG fitness properties, the homing rate (drive) and the insect''s life-history parameters influence those outcomes.     

The global spread of drug-resistant influenza

Resistance to oseltamivir, the most widely used influenza antiviral drug, spread to fixation in seasonal influenza A(H1N1) between 2006 and 2009. This sudden rise in resistance seemed puzzling given the low overall level of the oseltamivir usage and the lack of a correlation between local rates of resistance and oseltamivir usage. We used a stochastic simulation model and deterministic approximations to examine how such events can occur, and in particular to determine how the rate of fixation of the resistant strain depends both on its fitness in untreated hosts as well as the frequency of antiviral treatment. We found that, for the levels of antiviral usage in the population, the resistant strain will eventually spread to fixation, if it is not attenuated in transmissibility relative to the drug-sensitive strain, but not at the speed observed in seasonal H1N1. The extreme speed with which the resistance spread in seasonal H1N1 suggests that the resistant strain had a transmission advantage in untreated hosts, and this could have arisen from genetic hitchhiking, or from the mutations responsible for resistance and compensation. Importantly, our model also shows that resistant virus will fail to spread if it is even slightly less transmissible than its sensitive counterpart—a finding of relevance given that resistant pandemic influenza (H1N1) 2009 may currently suffer from a small, but nonetheless experimentally perceptible reduction in transmissibility.     

Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin

Groups of eukaryotic cilia and flagella are capable of coordinating their beating over large scales, routinely exhibiting collective dynamics in the form of metachronal waves. The origin of this behaviour—possibly influenced by both mechanical interactions and direct biological regulation—is poorly understood, in large part due to a lack of quantitative experimental studies. Here we characterize in detail flagellar coordination on the surface of the multicellular alga Volvox carteri, an emerging model organism for flagellar dynamics. Our studies reveal for the first time that the average metachronal coordination observed is punctuated by periodic phase defects during which synchrony is partial and limited to specific groups of cells. A minimal model of hydrodynamically coupled oscillators can reproduce semi-quantitatively the characteristics of the average metachronal dynamics, and the emergence of defects. We systematically study the model''s behaviour by assessing the effect of changing intrinsic rotor characteristics, including oscillator stiffness and the nature of their internal driving force, as well as their geometric properties and spatial arrangement. Our results suggest that metachronal coordination follows from deformations in the oscillators'' limit cycles induced by hydrodynamic stresses, and that defects result from sufficiently steep local biases in the oscillators'' intrinsic frequencies. Additionally, we find that random variations in the intrinsic rotor frequencies increase the robustness of the average properties of the emergent metachronal waves.     

Modelling the initial phase of an epidemic using incidence and infection network data: 2009 H1N1 pandemic in Israel as a case study

This paper presents new computational and modelling tools for studying the dynamics of an epidemic in its initial stages that use both available incidence time series and data describing the population''s infection network structure. The work is motivated by data collected at the beginning of the H1N1 pandemic outbreak in Israel in the summer of 2009. We formulated a new discrete-time stochastic epidemic SIR (susceptible-infected-recovered) model that explicitly takes into account the disease''s specific generation-time distribution and the intrinsic demographic stochasticity inherent to the infection process. Moreover, in contrast with many other modelling approaches, the model allows direct analytical derivation of estimates for the effective reproductive number (R_e) and of their credible intervals, by maximum likelihood and Bayesian methods. The basic model can be extended to include age–class structure, and a maximum likelihood methodology allows us to estimate the model''s next-generation matrix by combining two types of data: (i) the incidence series of each age group, and (ii) infection network data that provide partial information of ‘who-infected-who’. Unlike other approaches for estimating the next-generation matrix, the method developed here does not require making a priori assumptions about the structure of the next-generation matrix. We show, using a simulation study, that even a relatively small amount of information about the infection network greatly improves the accuracy of estimation of the next-generation matrix. The method is applied in practice to estimate the next-generation matrix from the Israeli H1N1 pandemic data. The tools developed here should be of practical importance for future investigations of epidemics during their initial stages. However, they require the availability of data which represent a random sample of the real epidemic process. We discuss the conditions under which reporting rates may or may not influence our estimated quantities and the effects of bias.     

Integrating stochasticity and network structure into an epidemic model

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.     

Coordination of gene expression noise with cell size: analytical results for agent-based models of growing cell populations

The chemical master equation and the Gillespie algorithm are widely used to model the reaction kinetics inside living cells. It is thereby assumed that cell growth and division can be modelled through effective dilution reactions and extrinsic noise sources. We here re-examine these paradigms through developing an analytical agent-based framework of growing and dividing cells accompanied by an exact simulation algorithm, which allows us to quantify the dynamics of virtually any intracellular reaction network affected by stochastic cell size control and division noise. We find that the solution of the chemical master equation—including static extrinsic noise—exactly agrees with the agent-based formulation when the network under study exhibits stochastic concentration homeostasis, a novel condition that generalizes concentration homeostasis in deterministic systems to higher order moments and distributions. We illustrate stochastic concentration homeostasis for a range of common gene expression networks. When this condition is not met, we demonstrate by extending the linear noise approximation to agent-based models that the dependence of gene expression noise on cell size can qualitatively deviate from the chemical master equation. Surprisingly, the total noise of the agent-based approach can still be well approximated by extrinsic noise models.     

Effectiveness of non-pharmaceutical interventions to contain COVID-19: a case study of the 2020 spring pandemic wave in New York City

As COVID-19 continues to pose significant public health threats, quantifying the effectiveness of different public health interventions is crucial to inform intervention strategies. Using detailed epidemiological and mobility data available for New York City and comprehensive modelling accounting for under-detection, we reconstruct the COVID-19 transmission dynamics therein during the 2020 spring pandemic wave and estimate the effectiveness of two major non-pharmaceutical interventions—lockdown-like measures that reduce contact rates and universal masking. Lockdown-like measures were associated with greater than 50% transmission reduction for all age groups. Universal masking was associated with an approximately 7% transmission reduction overall and up to 20% reduction for 65+ year olds during the first month of implementation. This result suggests that face covering can substantially reduce transmission when lockdown-like measures are lifted but by itself may be insufficient to control SARS-CoV-2 transmission. Overall, findings support the need to implement multiple interventions simultaneously to effectively mitigate COVID-19 spread before the majority of population can be protected through mass-vaccination.     

Decreasing stochasticity through enhanced seasonality in measles epidemics

Seasonal changes in the environment are known to be important drivers of population dynamics, giving rise to sustained population cycles. However, it is often difficult to measure the strength and shape of seasonal forces affecting populations. In recent years, statistical time-series methods have been applied to the incidence records of childhood infectious diseases in an attempt to estimate seasonal variation in transmission rates, as driven by the pattern of school terms. In turn, school-term forcing was used to show how susceptible influx rates affect the interepidemic period. In this paper, we document the response of measles dynamics to distinct shifts in the parameter regime using previously unexplored records of measles mortality from the early decades of the twentieth century. We describe temporal patterns of measles epidemics using spectral analysis techniques, and point out a marked decrease in birth rates over time. Changes in host demography alone do not, however, suffice to explain epidemiological transitions. By fitting the time-series susceptible–infected–recovered model to measles mortality data, we obtain estimates of seasonal transmission in different eras, and find that seasonality increased over time. This analysis supports theoretical work linking complex population dynamics and the balance between stochastic and deterministic forces as determined by the strength of seasonality.     

Networks of influence and infection: parental choices and childhood disease

Clusters of unvaccinated individuals are at risk of outbreaks of infection. When an individual''s decision to choose vaccination is influenced by the choices of his social group, such clusters can readily arise. However, when the interactions that influence decision-making and those that permit the transmission of infection are different—for instance, when parents make vaccination decisions on behalf of their children—it is unclear how large the impact of this social influence will be. Here we use a modelling approach to represent social influence within a network of parents and the transmission of infection through a network of children. We show that the effect of social influence depends on the amount of overlap between the two different networks; large overlap means that clusters of parents who choose not to vaccinate are likely to have interacting children, generating clusters of unvaccinated children. Spatially local connections can further increase the impact of social influence. Outbreaks are most likely when parents who do not vaccinate have children who interact.     

Patent market dynamics: In view of the business model of non-practicing entities

The emergence of Non-Practicing Entities (“NPEs”) influences patent market dynamics. Based on a database of NPE activities from 1996 to 2010, this paper attempts to investigate these influences in view of NPEs' heterogeneity. We found NPEs with prominent R&D involvements can integrate knowledge from the innovation and patent markets, and might therefore generate valuable patents and facilitate effective technology transfer. Hence, when compared with NPEs without any R&D involvement, R&D-performing NPEs appeared able to monetize their patents without resorting to excessive litigation. Thus, different NPEs could exert different influences and drive patent market dynamics in their own respective ways.     

Predator confusion is sufficient to evolve swarming behaviour

Swarming behaviours in animals have been extensively studied owing to their implications for the evolution of cooperation, social cognition and predator–prey dynamics. An important goal of these studies is discerning which evolutionary pressures favour the formation of swarms. One hypothesis is that swarms arise because the presence of multiple moving prey in swarms causes confusion for attacking predators, but it remains unclear how important this selective force is. Using an evolutionary model of a predator–prey system, we show that predator confusion provides a sufficient selection pressure to evolve swarming behaviour in prey. Furthermore, we demonstrate that the evolutionary effect of predator confusion on prey could in turn exert pressure on the structure of the predator''s visual field, favouring the frontally oriented, high-resolution visual systems commonly observed in predators that feed on swarming animals. Finally, we provide evidence that when prey evolve swarming in response to predator confusion, there is a change in the shape of the functional response curve describing the predator''s consumption rate as prey density increases. Thus, we show that a relatively simple perceptual constraint—predator confusion—could have pervasive evolutionary effects on prey behaviour, predator sensory mechanisms and the ecological interactions between predators and prey.     

Which features of an outpatient treatment for COVID-19 would be most important for pandemic control? A modelling study

The global pandemic of coronavirus disease 2019 (COVID-19) has challenged healthcare systems worldwide. Lockdown, social distancing, and screening are thought to be the best means of stopping the virus from spreading and thus of preventing hospital capacity from being overloaded. However, it has also been suggested that effective outpatient treatment can control pandemics. We adapted a mathematical model of the beneficial effect of lockdown on viral transmission and used it to determine which characteristics of outpatient treatment would stop an epidemic. The data on confirmed cases, recovered cases, and deaths were collected from Santé Publique France. After defining components of the epidemic flow, we used a Morris global sensitivity analysis with a 10-level grid and 1000 trajectories to determine which of the treatment parameters had the largest effect. Treatment effectiveness was defined as a reduction in the patients'' contagiousness. Early treatment initiation was associated with better disease control—as long as the treatment was highly effective. However, initiation of a treatment with a moderate effectiveness rate (5%) after the peak of the epidemic was still better than poor distancing (i.e. when compliance with social distancing rules was below 60%). Even though most of today''s COVID-19 research is focused on inpatient treatment and vaccines, our results emphasize the potentially beneficial impact of even a moderately effective outpatient treatment on the current pandemic.     

A two-tiered model for simulating the ecological and evolutionary dynamics of rapidly evolving viruses, with an application to influenza

Understanding the epidemiological and evolutionary dynamics of rapidly evolving pathogens is one of the most challenging problems facing disease ecologists today. To date, many mathematical and individual-based models have provided key insights into the factors that may regulate these dynamics. However, in many of these models, abstractions have been made to the simulated sequences that limit an effective interface with empirical data. This is especially the case for rapidly evolving viruses in which de novo mutations result in antigenically novel variants. With this focus, we present a simple two-tiered ‘phylodynamic’ model whose purpose is to simulate, along with case data, sequence data that will allow for a more quantitative interface with observed sequence data. The model differs from previous approaches in that it separates the simulation of the epidemiological dynamics (tier 1) from the molecular evolution of the virus''s dominant antigenic protein (tier 2). This separation of phenotypic dynamics from genetic dynamics results in a modular model that is computationally simpler and allows sequences to be simulated with specifications such as sequence length, nucleotide composition and molecular constraints. To illustrate its use, we apply the model to influenza A (H3N2) dynamics in humans, influenza B dynamics in humans and influenza A (H3N8) dynamics in equine hosts. In all three of these illustrative examples, we show that the model can simulate sequences that are quantitatively similar in pattern to those empirically observed. Future work should focus on statistical estimation of model parameters for these examples as well as the possibility of applying this model, or variants thereof, to other host–virus systems.