A Discrete Velocity Kinetic Model with Food Metric: Chemotaxis Traveling Waves

We introduce a mesoscopic scale chemotaxis model for traveling wave phenomena which is induced by food metric. The organisms of this simplified kinetic model have two discrete velocity modes, \(\pm s\) and a constant tumbling rate. The main feature of the model is that the speed of organisms is constant \(s\,{>}\,0\) with respect to the food metric, not the Euclidean metric. The uniqueness and the existence of the traveling wave solution of the model are obtained. Unlike the classical logarithmic model case there exist traveling waves under super-linear consumption rates and infinite population pulse-type traveling waves are obtained. Numerical simulations are also provided.     

West Nile Virus: High Transmission Rate in North-Western European Mosquitoes Indicates Its Epidemic Potential and Warrants Increased Surveillance

Background

West Nile virus (WNV) is a highly pathogenic flavivirus transmitted by Culex spp. mosquitoes. In North America (NA), lineage 1 WNV caused the largest outbreak of neuroinvasive disease to date, while a novel pathogenic lineage 2 strain circulates in southern Europe. To estimate WNV lineage 2 epidemic potential it is paramount to know if mosquitoes from currently WNV-free areas can support further spread of this epidemic.

Methodology/Principal Findings

We assessed WNV vector competence of Culex pipiens mosquitoes originating from north-western Europe (NWE) in direct comparison with those from NA. We exposed mosquitoes to infectious blood meals of lineage 1 or 2 WNV and determined the infection and transmission rates. We explored reasons for vector competence differences by comparing intrathoracic injection versus blood meal infection, and we investigated the influence of temperature. We found that NWE mosquitoes are highly competent for both WNV lineages, with transmission rates up to 25%. Compared to NA mosquitoes, transmission rates for lineage 2 WNV were significantly elevated in NWE mosquitoes due to better virus dissemination from the midgut and a shorter extrinsic incubation time. WNV infection rates further increased with temperature increase.

Conclusions/Significance

Our study provides experimental evidence to indicate markedly different risk levels between both continents for lineage 2 WNV transmission and suggests a degree of genotype-genotype specificity in the interaction between virus and vector. Our experiments with varying temperatures explain the current localized WNV activity in southern Europe, yet imply further epidemic spread throughout NWE during periods with favourable climatic conditions. This emphasizes the need for intensified surveillance of virus activity in current WNV disease-free regions and warrants increased awareness in clinics throughout Europe.     

Spreading speeds as slowest wave speeds for cooperative systems

It is well known that in many scalar models for the spread of a fitter phenotype or species into the territory of a less fit one, the asymptotic spreading speed can be characterized as the lowest speed of a suitable family of traveling waves of the model. Despite a general belief that multi-species (vector) models have the same property, we are unaware of any proof to support this belief. The present work establishes this result for a class of multi-species model of a kind studied by Lui [Biological growth and spread modeled by systems of recursions. I: Mathematical theory, Math. Biosci. 93 (1989) 269] and generalized by the authors [Weinberger et al., Analysis of the linear conjecture for spread in cooperative models, J. Math. Biol. 45 (2002) 183; Lewis et al., Spreading speeds and the linear conjecture for two-species competition models, J. Math. Biol. 45 (2002) 219]. Lui showed the existence of a single spreading speed c(*) for all species. For the systems in the two aforementioned studies by the authors, which include related continuous-time models such as reaction-diffusion systems, as well as some standard competition models, it sometimes happens that different species spread at different rates, so that there are a slowest speed c(*) and a fastest speed c(f)(*). It is shown here that, for a large class of such multi-species systems, the slowest spreading speed c(*) is always characterized as the slowest speed of a class of traveling wave solutions.     

Interactions between Social Structure,Demography, and Transmission Determine Disease Persistence in Primates

Catastrophic declines in African great ape populations due to disease outbreaks have been reported in recent years, yet we rarely hear of similar disease impacts for the more solitary Asian great apes, or for smaller primates. We used an age-structured model of different primate social systems to illustrate that interactions between social structure and demography create ‘dynamic constraints’ on the pathogens that can establish and persist in primate host species with different social systems. We showed that this varies by disease transmission mode. Sexually transmitted infections (STIs) require high rates of transmissibility to persist within a primate population. In particular, for a unimale social system, STIs require extremely high rates of transmissibility for persistence, and remain at extremely low prevalence in small primates, but this is less constrained in longer-lived, larger-bodied primates. In contrast, aerosol transmitted infections (ATIs) spread and persist at high prevalence in medium and large primates with moderate transmissibility;, establishment and persistence in small-bodied primates require higher relative rates of transmissibility. Intragroup contact structure – the social network - creates different constraints for different transmission modes, and our model underscores the importance of intragroup contacts on infection prior to intergroup movement in a structured population. When alpha males dominate sexual encounters, the resulting disease transmission dynamics differ from when social interactions are dominated by mother-infant grooming events, for example. This has important repercussions for pathogen spread across populations. Our framework reveals essential social and demographic characteristics of primates that predispose them to different disease risks that will be important for disease management and conservation planning for protected primate populations.     

Landscape mosaic induces traveling waves of insect outbreaks

The effect of landscape mosaic on recurrent traveling waves in spatial population dynamics was studied via simulation modeling across a theoretical landscape with varying levels of connectivity. Phase angle analysis was used to identify locations of wave epicenters on patchy landscapes. Simulations of a tri-trophic model of the larch budmoth (Zeiraphera diniana) with cyclic population dynamics on landscapes with a single focus of high-density habitat produced traveling waves generally radiating outwardly from single and multiple foci and spreading to isolated habitats. We have proposed two hypotheses for this result: (1) immigration subsidies inflate population growth rates in the high connectivity habitat and, thus, reduce the time from valleys to peaks in population cycles; (2) populations in the high connectivity habitat crash from peaks to valleys faster than in an isolated habitat due to over-compensatory density dependence. While population growth rates in the high connectivity habitat benefitted from immigration subsidies, times from population valleys to peaks were greater in high connectivity habitat due to a greater magnitude of fluctuations. Conversely, the mean time of the crash from population peaks to valleys was shorter in high connectivity habitat, supporting the second hypothesis. Results of this study suggest over-compensatory density dependence as an underlying mechanism for recurrent traveling waves originating in high connectivity habitats aggregated around a single focus.Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Multiple-spike waves in a one-dimensional integrate-and-fire neural network

This paper builds on the past study of single-spike waves in one-dimensional integrate-and-fire networks to provide a framework for the study of waves with arbitrary (finite or countably infinite) collections of spike times. Based on this framework, we prove an existence theorem for single-spike traveling waves, and we combine analysis and numerics to study two-spike traveling waves, periodic traveling waves, and general infinite spike trains. For a fixed wave speed, finite-spike waves, periodic waves, and other infinite-spike waves may all occur, and we discuss the relationships among them. We also relate the waves considered analytically to waves generated in numerical simulations by the transient application of localized excitation.Key words or phrases:Traveling waves, Integrate-and-fire network, Excitatory synaptic coupling     

Learning poly-synaptic paths with traveling waves

Traveling waves are commonly observed across the brain. While previous studies have suggested the role of traveling waves in learning, the mechanism remains unclear. We adopted a computational approach to investigate the effect of traveling waves on synaptic plasticity. Our results indicate that traveling waves facilitate the learning of poly-synaptic network paths when combined with a reward-dependent local synaptic plasticity rule. We also demonstrate that traveling waves expedite finding the shortest paths and learning nonlinear input/output mapping, such as exclusive or (XOR) function.     

Alternative Feeding Strategies and Potential Disease Transmission in Wisconsin White-Tailed Deer

ABSTRACT We conducted experimental feeding using 3 feeding methods (pile, spread, trough) and 2 quantities (rationed, ad libitum) of shelled corn to compare deer activity and behavior with control sites and evaluate potential direct and indirect transmission of infectious disease in white-tailed deer (Odocoileus virginianus) in central Wisconsin, USA. Deer use was higher at 2 of the feeding sites than at natural feeding areas (P ≤ 0.02). Deer spent a higher proportion of time (P < 0.01) feeding at pile (49%) and spread (61%) treatments than at natural feeding areas (36%). We found higher deer use for rationed than ad libitum feeding quantities and feeding intensity was greatest at rationed piles and lowest at ad libitum spreads. We also observed closer pairwise distances (≤0.3 m) among deer when corn was provided in a trough relative to spread (P=0.03). Supplemental feeding poses risks for both direct and indirect disease transmission due to higher deer concentration and more intensive use relative to control areas. Concentrated feeding and contact among deer at feeding sites can also increase risk for disease transmission. Our results indicated that restrictions on feeding quantity would not mitigate the potential for disease transmission. None of the feeding strategies we evaluated substantially reduced the potential risk for disease transmission and banning supplemental feeding to reduce transmission is warranted.     

Meteorological factors and non-pharmaceutical interventions explain local differences in the spread of SARS-CoV-2 in Austria

The drivers behind regional differences of SARS-CoV-2 spread on finer spatio-temporal scales are yet to be fully understood. Here we develop a data-driven modelling approach based on an age-structured compartmental model that compares 116 Austrian regions to a suitably chosen control set of regions to explain variations in local transmission rates through a combination of meteorological factors, non-pharmaceutical interventions and mobility. We find that more than 60% of the observed regional variations can be explained by these factors. Decreasing temperature and humidity, increasing cloudiness, precipitation and the absence of mitigation measures for public events are the strongest drivers for increased virus transmission, leading in combination to a doubling of the transmission rates compared to regions with more favourable weather. We conjecture that regions with little mitigation measures for large events that experience shifts toward unfavourable weather conditions are particularly predisposed as nucleation points for the next seasonal SARS-CoV-2 waves.     

Traveling waves and pulses in a one-dimensional network of excitable integrate-and-fire neurons

 We study the existence and stability of traveling waves and pulses in a one-dimensional network of integrate-and-fire neurons with synaptic coupling. This provides a simple model of excitable neural tissue. We first derive a self-consistency condition for the existence of traveling waves, which generates a dispersion relation between velocity and wavelength. We use this to investigate how wave-propagation depends on various parameters that characterize neuronal interactions such as synaptic and axonal delays, and the passive membrane properties of dendritic cables. We also establish that excitable networks support the propagation of solitary pulses in the long-wavelength limit. We then derive a general condition for the (local) asymptotic stability of traveling waves in terms of the characteristic equation of the linearized firing time map, which takes the form of an integro-difference equation of infinite order. We use this to analyze the stability of solitary pulses in the long-wavelength limit. Solitary wave solutions are shown to come in pairs with the faster (slower) solution stable (unstable) in the case of zero axonal delays; for non-zero delays and fast synapses the stable wave can itself destabilize via a Hopf bifurcation. Received: 27 October 1998     

Infectious disease modeling of social contagion in networks

Many behavioral phenomena have been found to spread interpersonally through social networks, in a manner similar to infectious diseases. An important difference between social contagion and traditional infectious diseases, however, is that behavioral phenomena can be acquired by non-social mechanisms as well as through social transmission. We introduce a novel theoretical framework for studying these phenomena (the SISa model) by adapting a classic disease model to include the possibility for 'automatic' (or 'spontaneous') non-social infection. We provide an example of the use of this framework by examining the spread of obesity in the Framingham Heart Study Network. The interaction assumptions of the model are validated using longitudinal network transmission data. We find that the current rate of becoming obese is 2 per year and increases by 0.5 percentage points for each obese social contact. The rate of recovering from obesity is 4 per year, and does not depend on the number of non-obese contacts. The model predicts a long-term obesity prevalence of approximately 42, and can be used to evaluate the effect of different interventions on steady-state obesity. Model predictions quantitatively reproduce the actual historical time course for the prevalence of obesity. We find that since the 1970s, the rate of recovery from obesity has remained relatively constant, while the rates of both spontaneous infection and transmission have steadily increased over time. This suggests that the obesity epidemic may be driven by increasing rates of becoming obese, both spontaneously and transmissively, rather than by decreasing rates of losing weight. A key feature of the SISa model is its ability to characterize the relative importance of social transmission by quantitatively comparing rates of spontaneous versus contagious infection. It provides a theoretical framework for studying the interpersonal spread of any state that may also arise spontaneously, such as emotions, behaviors, health states, ideas or diseases with reservoirs.     

Infection dynamics of endemic malaria in a wild bird population: parasite species-dependent drivers of spatial and temporal variation in transmission rates

1.?Investigating the ecological context in which host-parasite interactions occur and the roles of biotic and abiotic factors in forcing infection dynamics is essential to understanding disease transmission, spread and maintenance. 2.?Despite their prominence as model host-pathogen systems, the relative influence of environmental heterogeneity and host characteristics in influencing the infection dynamics of avian blood parasites has rarely been assessed in the wild, particularly at a within-population scale. 3.?We used a novel multievent modelling framework (an extension of multistate mark-recapture modelling) that allows for uncertainty in disease state, to estimate transmission parameters and assess variation in the infection dynamics of avian malaria in a large, longitudinally sampled data set of breeding blue tits infected with two divergent species of Plasmodium parasites. 4.?We found striking temporal and spatial heterogeneity in the disease incidence rate and the likelihood of recovery within this single population and demonstrate marked differences in the relative influence of environmental and host factors in forcing the infection dynamics of the two Plasmodium species. 5.?Proximity to a permanent water source greatly influenced the transmission rates of P.?circumflexum, but not of P.?relictum, suggesting that these parasites are transmitted by different vectors. 6.?Host characteristics (age/sex) were found to influence infection rates but not recovery rates, and their influence on infection rates was also dependent on parasite species: P.?relictum infection rates varied with host age, whilst P.?circumflexum infection rates varied with host sex. 7.?Our analyses reveal that transmission of endemic avian malaria is a result of complex interactions between biotic and abiotic components that can operate on small spatial scales and demonstrate that knowledge of the drivers of spatial and temporal heterogeneity in disease transmission will be crucial for developing accurate epidemiological models and a thorough understanding of the evolutionary implications of pathogens.     

Revealing mechanisms of infectious disease spread through empirical contact networks

The spread of pathogens fundamentally depends on the underlying contacts between individuals. Modeling the dynamics of infectious disease spread through contact networks, however, can be challenging due to limited knowledge of how an infectious disease spreads and its transmission rate. We developed a novel statistical tool, INoDS (Identifying contact Networks of infectious Disease Spread) that estimates the transmission rate of an infectious disease outbreak, establishes epidemiological relevance of a contact network in explaining the observed pattern of infectious disease spread and enables model comparison between different contact network hypotheses. We show that our tool is robust to incomplete data and can be easily applied to datasets where infection timings of individuals are unknown. We tested the reliability of INoDS using simulation experiments of disease spread on a synthetic contact network and find that it is robust to incomplete data and is reliable under different settings of network dynamics and disease contagiousness compared with previous approaches. We demonstrate the applicability of our method in two host-pathogen systems: Crithidia bombi in bumblebee colonies and Salmonella in wild Australian sleepy lizard populations. INoDS thus provides a novel and reliable statistical tool for identifying transmission pathways of infectious disease spread. In addition, application of INoDS extends to understanding the spread of novel or emerging infectious disease, an alternative approach to laboratory transmission experiments, and overcoming common data-collection constraints.     

Community-Based Measures for Mitigating the 2009 H1N1 Pandemic in China

Since the emergence of influenza A/H1N1 pandemic virus in March–April 2009, very stringent interventions including Fengxiao were implemented to prevent importation of infected cases and decelerate the disease spread in mainland China. The extent to which these measures have been effective remains elusive. We sought to investigate the effectiveness of Fengxiao that may inform policy decisions on improving community-based interventions for management of on-going outbreaks in China, in particular during the Spring Festival in mid-February 2010 when nationwide traveling will be substantially increased. We obtained data on initial laboratory-confirmed cases of H1N1 in the province of Shaanxi and used Markov-chain Monte-Carlo (MCMC) simulations to estimate the reproduction number. Given the estimates for the exposed and infectious periods of the novel H1N1 virus, we estimated a mean reproduction number of 1.68 (95% CI 1.45–1.92) and other A/H1N1 epidemiological parameters. Our results based on a spatially stratified population dynamical model show that the early implementation of Fengxiao can delay the epidemic peak significantly and prevent the disease spread to the general population but may also, if not implemented appropriately, cause more severe outbreak within universities/colleges, while late implementation of Fengxiao can achieve nothing more than no implementation. Strengthening local control strategies (quarantine and hygiene precaution) is much more effective in mitigating outbreaks and inhibiting the successive waves than implementing Fengxiao. Either strong mobility or high transport-related transmission rate during the Spring Festival holiday will not reverse the ongoing outbreak, but both will result in a large new wave. The findings suggest that Fengxiao and travel precautions should not be relaxed unless strict measures of quarantine, isolation, and hygiene precaution practices are put in place. Integration and prompt implementation of these interventions can significantly reduce the overall attack rate of pandemic outbreaks.     

Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive of R₀. We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more general n-patch setting.     

Host and pathogen ecology drive the seasonal dynamics of a fungal disease,white-nose syndrome

Seasonal patterns in pathogen transmission can influence the impact of disease on populations and the speed of spatial spread. Increases in host contact rates or births drive seasonal epidemics in some systems, but other factors may occasionally override these influences. White-nose syndrome, caused by the emerging fungal pathogen Pseudogymnoascus destructans, is spreading across North America and threatens several bat species with extinction. We examined patterns and drivers of seasonal transmission of P. destructans by measuring infection prevalence and pathogen loads in six bat species at 30 sites across the eastern United States. Bats became transiently infected in autumn, and transmission spiked in early winter when bats began hibernating. Nearly all bats in six species became infected by late winter when infection intensity peaked. In summer, despite high contact rates and a birth pulse, most bats cleared infections and prevalence dropped to zero. These data suggest the dominant driver of seasonal transmission dynamics was a change in host physiology, specifically hibernation. Our study is the first, to the best of our knowledge, to describe the seasonality of transmission in this emerging wildlife disease. The timing of infection and fungal growth resulted in maximal population impacts, but only moderate rates of spatial spread.     

Can Vaccination Save a Zika Virus Epidemic?

Zika virus (ZIKV) is a vector-borne disease that has rapidly spread during the year 2016 in more than 50 countries around the world. If a woman is infected during pregnancy, the virus can cause severe birth defects and brain damage in their babies. The virus can be transmitted through the bites of infected mosquitoes as well as through direct contact from human to human (e.g., sexual contact and blood transfusions). As an intervention for controlling the spread of the disease, we study a vaccination model for preventing Zika infections. Although there is no formal vaccine for ZIKV, The National Institute of Allergy and Infectious Diseases (part of the National Institutes of Health) has launched a vaccine trial at the beginning of August 2016 to control ZIKV transmission, patients who received the vaccine are expected to return within 44 weeks to determine if the vaccine is safe. Since it is important to understand ZIKV dynamics under vaccination, we formulate a vaccination model for ZIKV spread that includes mosquito as well as sexual transmission. We calculate the basic reproduction number of the model to analyze the impact of relatively, perfect and imperfect vaccination rates. We illustrate several numerical examples of the vaccination model proposed as well as the impact of the basic reproduction numbers of vector and sexual transmission and the effect of vaccination effort on ZIKV spread. Results show that high levels of sexual transmission create larger cases of infection associated with the peak of infected humans arising in a shorter period of time, even when a vaccine is available in the population. However, a high level of transmission of Zika from vectors to humans compared with sexual transmission represents that ZIKV will take longer to invade the population providing a window of opportunities to control its spread, for instance, through vaccination.     

Estimation of Parameters Influencing Waterborne Transmission of Infectious Hematopoietic Necrosis Virus (IHNV) in Atlantic Salmon (Salmo salar)

Understanding how pathogenic organisms spread in the environment is crucial for the management of disease, yet knowledge of propagule dispersal and transmission in aquatic environments is limited. We conducted empirical studies using the aquatic virus, infectious hematopoietic necrosis virus (IHNV), to quantify infectious dose, shedding capacity, and virus destruction rates in order to better understand the transmission of IHN virus among Atlantic salmon marine net-pen aquaculture. Transmission of virus and subsequent mortality in Atlantic salmon post-smolts was initiated with as low as 10 plaque forming units (pfu) ml⁻¹. Virus shedding from IHNV infected Atlantic salmon was detected before the onset of visible signs of disease with peak shed rates averaging 3.2×10⁷ pfu fish⁻¹ hour⁻¹ one to two days prior to mortality. Once shed into the marine environment, the abundance of free IHNV is modulated by sunlight (UV A and B) and the growth of natural biota present in the seawater. Virus decayed very slowly in sterilized seawater while rates as high as k =  4.37 d⁻¹ were observed in natural seawater. Decay rates were further accelerated when exposed to sunlight with virus infectivity reduced by six orders of magnitude within 3 hours of full sunlight exposure. Coupling the IHNV transmission parameter estimates determined here with physical water circulation models, will increase the understanding of IHNV dispersal and provide accurate geospatial predictions of risk for IHNV transmission from marine salmon sites.     

Genetic assessment of environmental features that influence deer dispersal: implications for prion-infected populations

The landscape can influence host dispersal and density, which in turn, affect infectious disease transmission, spread, and persistence. Understanding how the landscape influences wildlife dispersal and pathogen epidemiology can enhance the efficacy of disease management in natural populations. We applied landscape genetics to examine relationships among landscape variables, dispersal of white-tailed deer hosts and transmission/spread of chronic wasting disease (CWD), a fatal prion encephalopathy. Our focus was on quantifying movements and population structure of host deer in infected areas as a means of predicting the spread of this pathology and promoting its adaptive management. We analyzed microsatellite genotypes of CWD-infected and uninfected deer from two disease foci (Southern Wisconsin, Northern Illinois). We quantified gene flow and population structure using F _ST, assignment tests, and spatial autocorrelation analyses. Gene flow estimates were then contrasted against a suite of landscape variables that potentially mediate deer dispersal. Forest fragmentation and grassland connectivity promoted deer movements while rivers, agricultural fields and large urbanized areas impeded movement. Landscape variables, deer dispersal, and disease transmission covaried significantly and positively in our analyses. Habitats with elevated host gene flow supported the concept of dispersal-mediated CWD transmission by reflecting a concomitant, rapid CWD expansion. Large, interrelated social groups isolated by movement barriers overlapped disease foci, suggesting that philopatry exacerbated CWD transmission. Our results promote adaptive management of CWD by predicting patterns of its spread and identifying habitats at risk for invasion. Further, our landscape genetics approach underscores the significance of topography and host behavior in wildlife disease transmission.     

Contact networks and transmission of an intestinal pathogen in bumble bee (Bombus impatiens) colonies

In socially living animals, individuals interact through complex networks of contact that may influence the spread of disease. Whereas traditional epidemiological models typically assume no social structure, network theory suggests that an individual’s location in the network determines its risk of infection. Empirical, especially experimental, studies of disease spread on networks are lacking, however, largely due to a shortage of amenable study systems. We used automated video-tracking to quantify networks of physical contact among individuals within colonies of the social bumble bee Bombus impatiens. We explored the effects of network structure on pathogen transmission in naturally and artificially infected hives. We show for the first time that contact network structure determines the spread of a contagious pathogen (Crithidia bombi) in social insect colonies. Differences in rates of infection among colonies resulted largely from differences in network density among hives. Within colonies, a bee’s rate of contact with infected nestmates emerged as the only significant predictor of infection risk. The activity of bees, in terms of their movement rates and division of labour (e.g., brood care, nest care, foraging), did not influence risk of infection. Our results suggest that contact networks may have an important influence on the transmission of pathogens in social insects and, possibly, other social animals.