Computing fractal dimension in supertransient systems directly, fast and reliable

Chaotic transients occur in many experiments including those in fluids, in simulations of the plane Couette flow, and in coupled map lattices and they are a common phenomena in dynamical systems. Superlong chaotic transients are caused by the presence of chaotic saddles whose stable sets have fractal dimensions that are close to phase-space dimension. For many physical systems chaotic saddles have a big impact on laboratory measurements, and it is important to compute the dimension of such stable sets including fractal basin boundaries through a direct method. In this work, we present a new method to compute the dimension of stable sets of chaotic saddles directly, fast, and reliable.Comment: 6 pages, 3 figure

Can Influenza Epidemics Be Prevented by Voluntary Vaccination?

Previous modeling studies have identified the vaccination coverage level necessary for preventing influenza epidemics, but have not shown whether this critical coverage can be reached. Here we use computational modeling to determine, for the first time, whether the critical coverage for influenza can be achieved by voluntary vaccination. We construct a novel individual-level model of human cognition and behavior; individuals are characterized by two biological attributes (memory and adaptability) that they use when making vaccination decisions. We couple this model with a population-level model of influenza that includes vaccination dynamics. The coupled models allow individual-level decisions to influence influenza epidemiology and, conversely, influenza epidemiology to influence individual-level decisions. By including the effects of adaptive decision-making within an epidemic model, we can reproduce two essential characteristics of influenza epidemiology: annual variation in epidemic severity and sporadic occurrence of severe epidemics. We suggest that individual-level adaptive decision-making may be an important (previously overlooked) causal factor in driving influenza epidemiology. We find that severe epidemics cannot be prevented unless vaccination programs offer incentives. Frequency of severe epidemics could be reduced if programs provide, as an incentive to be vaccinated, several years of free vaccines to individuals who pay for one year of vaccination. Magnitude of epidemic amelioration will be determined by the number of years of free vaccination, an individuals' adaptability in decision-making, and their memory. This type of incentive program could control epidemics if individuals are very adaptable and have long-term memories. However, incentive-based programs that provide free vaccination for families could increase the frequency of severe epidemics. We conclude that incentive-based vaccination programs are necessary to control influenza, but some may be detrimental. Surprisingly, we find that individuals' memories and flexibility in adaptive decision-making can be extremely important factors in determining the success of influenza vaccination programs. Finally, we discuss the implication of our results for controlling pandemics

Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees

The spread of infectious diseases crucially depends on the pattern of contacts among individuals. Knowledge of these patterns is thus essential to inform models and computational efforts. Few empirical studies are however available that provide estimates of the number and duration of contacts among social groups. Moreover, their space and time resolution are limited, so that data is not explicit at the person-to-person level, and the dynamical aspect of the contacts is disregarded. Here, we want to assess the role of data-driven dynamic contact patterns among individuals, and in particular of their temporal aspects, in shaping the spread of a simulated epidemic in the population. We consider high resolution data of face-to-face interactions between the attendees of a conference, obtained from the deployment of an infrastructure based on Radio Frequency Identification (RFID) devices that assess mutual face-to-face proximity. The spread of epidemics along these interactions is simulated through an SEIR model, using both the dynamical network of contacts defined by the collected data, and two aggregated versions of such network, in order to assess the role of the data temporal aspects. We show that, on the timescales considered, an aggregated network taking into account the daily duration of contacts is a good approximation to the full resolution network, whereas a homogeneous representation which retains only the topology of the contact network fails in reproducing the size of the epidemic. These results have important implications in understanding the level of detail needed to correctly inform computational models for the study and management of real epidemics

Basin boundary, edge of chaos, and edge state in a two-dimensional model

In shear flows like pipe flow and plane Couette flow there is an extended range of parameters where linearly stable laminar flow coexists with a transient turbulent dynamics. When increasing the amplitude of a perturbation on top of the laminar flow, one notes a a qualitative change in its lifetime, from smoothly varying and short one on the laminar side to sensitively dependent on initial conditions and long on the turbulent side. The point of transition defines a point on the edge of chaos. Since it is defined via the lifetimes, the edge of chaos can also be used in situations when the turbulence is not persistent. It then generalises the concept of basin boundaries, which separate two coexisting attractors, to cases where the dynamics on one side shows transient chaos and almost all trajectories eventually end up on the other side. In this paper we analyse a two-dimensional map which captures many of the features identified in laboratory experiments and direct numerical simulations of hydrodynamic flows. The analysis of the map shows that different dynamical situations in the edge of chaos can be combined with different dynamical situations in the turbulent region. Consequently, the model can be used to develop and test further characterisations that are also applicable to realistic flows.Comment: 24 pages, 9 color figure

An Agent-Based Model to study the epidemiological and evolutionary dynamics of Influenza viruses

<p>Abstract</p> <p>Background</p> <p>Influenza A viruses exhibit complex epidemiological patterns in a number of mammalian and avian hosts. Understanding transmission of these viruses necessitates taking into account their evolution, which represents a challenge for developing mathematical models. This is because the phrasing of multi-strain systems in terms of traditional compartmental ODE models either requires simplifying assumptions to be made that overlook important evolutionary processes, or leads to complex dynamical systems that are too cumbersome to analyse.</p> <p>Results</p> <p>Here, we develop an Individual-Based Model (IBM) in order to address simultaneously the ecology, epidemiology and evolution of strain-polymorphic pathogens, using Influenza A viruses as an illustrative example.</p> <p>Conclusions</p> <p>We carry out careful validation of our IBM against comparable mathematical models to demonstrate the robustness of our algorithm and the sound basis for this novel framework. We discuss how this new approach can give critical insights in the study of influenza evolution.</p

Rapid Emergence of Free-Riding Behavior in New Pediatric Immunization Programs

BACKGROUND: Mathematical models have formalized how free-rider effects can threaten the stability of high vaccine coverage levels under established voluntary vaccination programs. However, little research has addressed the question of when free-riding begins to develop when a new vaccine is first introduced in a population. METHODOLOGY/PRINCIPAL FINDINGS: Here, we combine a game theoretical model of vaccinating behavior with an age-structured compartmental model to analyze rational vaccinating behavior in the first years of a universal immunization program, where a new vaccine is free to all children of a specified age. The model captures how successive birth cohorts face different epidemiological landscapes that have been shaped by the vaccinating decisions of previous birth cohorts, resulting in a strategic interaction between individuals in different birth cohorts. The model predicts a Nash equilibrium coverage level of for the first few birth cohorts under the new program. However, free-riding behavior emerges very quickly, with the Nash equilibrium vaccine coverage dropping significantly within 2-5 years after program initiation. Subsequently, a rich set of coupled dynamics between infection prevalence and vaccinating behaviors is possible, ranging from relatively stable (but reduced) coverage in later birth cohorts to wide fluctuations in vaccine coverage from one birth cohort to the next. Individual tolerance for vaccine risk also starts out at relatively high levels before dropping significantly within a few years. CONCLUSIONS/SIGNIFICANCE: These results suggest that even relatively new immunization programs can be vulnerable to drops in vaccine coverage caused by vaccine scares and exacerbated by herd immunity effects, necessitating vigilance from the start

Erratic Flu Vaccination Emerges from Short-Sighted Behavior in Contact Networks

The effectiveness of seasonal influenza vaccination programs depends on individual-level compliance. Perceptions about risks associated with infection and vaccination can strongly influence vaccination decisions and thus the ultimate course of an epidemic. Here we investigate the interplay between contact patterns, influenza-related behavior, and disease dynamics by incorporating game theory into network models. When individuals make decisions based on past epidemics, we find that individuals with many contacts vaccinate, whereas individuals with few contacts do not. However, the threshold number of contacts above which to vaccinate is highly dependent on the overall network structure of the population and has the potential to oscillate more wildly than has been observed empirically. When we increase the number of prior seasons that individuals recall when making vaccination decisions, behavior and thus disease dynamics become less variable. For some networks, we also find that higher flu transmission rates may, counterintuitively, lead to lower (vaccine-mediated) disease prevalence. Our work demonstrates that rich and complex dynamics can result from the interaction between infectious diseases, human contact patterns, and behavior

The spatial resolution of epidemic peaks

The emergence of novel respiratory pathogens can challenge the capacity of key health care resources, such as intensive care units, that are constrained to serve only specific geographical populations. An ability to predict the magnitude and timing of peak incidence at the scale of a single large population would help to accurately assess the value of interventions designed to reduce that peak. However, current disease-dynamic theory does not provide a clear understanding of the relationship between: epidemic trajectories at the scale of interest (e.g. city); population mobility; and higher resolution spatial effects (e.g. transmission within small neighbourhoods). Here, we used a spatially-explicit stochastic meta-population model of arbitrary spatial resolution to determine the effect of resolution on model-derived epidemic trajectories. We simulated an influenza-like pathogen spreading across theoretical and actual population densities and varied our assumptions about mobility using Latin-Hypercube sampling. Even though, by design, cumulative attack rates were the same for all resolutions and mobilities, peak incidences were different. Clear thresholds existed for all tested populations, such that models with resolutions lower than the threshold substantially overestimated population-wide peak incidence. The effect of resolution was most important in populations which were of lower density and lower mobility. With the expectation of accurate spatial incidence datasets in the near future, our objective was to provide a framework for how to use these data correctly in a spatial meta-population model. Our results suggest that there is a fundamental spatial resolution for any pathogen-population pair. If underlying interactions between pathogens and spatially heterogeneous populations are represented at this resolution or higher, accurate predictions of peak incidence for city-scale epidemics are feasible

Partial ORF1ab Gene Target Failure with Omicron BA.2.12.1

Mutations in the genome of SARS-CoV-2 can affect the performance of molecular diagnostic assays. In some cases, such as S-gene target failure, the impact can serve as a unique indicator of a particular SARS-CoV-2 variant and provide a method for rapid detection. Here, we describe partial ORF1ab gene target failure (pOGTF) on the cobas SARS-CoV-2 assays, defined by a $2-thermocycle delay in detection of the ORF1ab gene compared to that of the E-gene. We demonstrate that pOGTF is 98.6% sensitive and 99.9% specific for SARS-CoV-2 lineage BA.2.12.1, an emerging variant in the United States with spike L452Q and S704L mutations that may affect transmission, infectivity, and/ or immune evasion. Increasing rates of pOGTF closely mirrored rates of BA.2.12.1 sequences uploaded to public databases, and, importantly, increasing local rates of pOGTF also mirrored increasing overall test positivity. Use of pOGTF as a proxy for BA.2.12.1 provides faster tracking of the variant than whole-genome sequencing and can benefit laboratories without sequencing capabilities

Spatial and Temporal Association of Outbreaks of H5N1 Influenza Virus Infection in Wild Birds with the 0°C Isotherm

Wild bird movements and aggregations following spells of cold weather may have resulted in the spread of highly pathogenic avian influenza virus (HPAIV) H5N1 in Europe during the winter of 2005–2006. Waterbirds are constrained in winter to areas where bodies of water remain unfrozen in order to feed. On the one hand, waterbirds may choose to winter as close as possible to their breeding grounds in order to conserve energy for subsequent reproduction, and may be displaced by cold fronts. On the other hand, waterbirds may choose to winter in regions where adverse weather conditions are rare, and may be slowed by cold fronts upon their journey back to the breeding grounds, which typically starts before the end of winter. Waterbirds will thus tend to aggregate along cold fronts close to the 0°C isotherm during winter, creating conditions that favour HPAIV H5N1 transmission and spread. We determined that the occurrence of outbreaks of HPAIV H5N1 infection in waterbirds in Europe during the winter of 2005–2006 was associated with temperatures close to 0°C. The analysis suggests a significant spatial and temporal association of outbreaks caused by HPAIV H5N1 in wild birds with maximum surface air temperatures of 0°C–2°C on the day of the outbreaks and the two preceding days. At locations where waterbird census data have been collected since 1990, maximum mallard counts occurred when average and maximum surface air temperatures were 0°C and 3°C, respectively. Overall, the abundance of mallards (Anas platyrhynchos) and common pochards (Aythya ferina) was highest when surface air temperatures were lower than the mean temperatures of the region investigated. The analysis implies that waterbird movements associated with cold weather, and congregation of waterbirds along the 0°C isotherm likely contributed to the spread and geographical distribution of outbreaks of HPAIV H5N1 infection in wild birds in Europe during the winter of 2005–2006