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Stochastic modeling and combined spatial pattern analysis of epidemic spreading
Abstract
We present analysis of spatial patterns of generic disease spread simulated by a stochastic long-range correlation SIR model, where individuals can be infected at long distance in a power law distribution. We integrated various tools, namely perimeter, circularity, fractal dimension, and aggregation index to characterize and investigate spatial pattern formations. Our primary goal was to understand for a given model of interest which tool has an advantage over the other and to what extent. We found that perimeter and circularity give information only for a case of strong correlation- while the fractal dimension and aggregation index exhibit the growth rule of pattern formation, depending on the degree of the correlation exponent (β). The aggregation index method used as an alternative method to describe the degree of pathogenic ratio (α). This study may provide a useful approach to characterize and analyze the pattern formation of epidemic spreading.
... The analysis methods of spatial pattern for the ecological analysis based on the research objectives according to Legendre and Fortin (1989) The approach of the spatial patterns allows the predictive modeling and detailed mapping to be compiled in order to get a better understanding of the formation of an endemic pattern of a disease. The method of determining spatial patterns of endemicity can be done by the measurement of the studied area (Chadsuthi et al., 2010). The methods of characterization of the spatial patterns based on the research objective divided two categories: the measurement of population distribution pattern by the NNA and QA method, detecting the spatial pattern of organisms attack by the method of SAA. ...
This study aims to predict the population dynamics of Brown Planthopper (BPH) in highly endemic areas of Central Java province, Indonesia. The research was conducted by modifying the method proposed by Legendre and Fortin (1989), through three stages. Those were predicting BPH attacks using Exponential Smoothing Holt Winter, analyzing spatial structure using I, C and Z test on Local Statistic, and making the connectivity inter the periodic predictions of planting season. The results showed that, the studied areas will experience the hotspots phenomenon based on the analysis by the method of Moran's I, Geary's C and Getis Ord Statistic. The analysis of Local Moran's and Getis Ord showed that, four counties namely Boyolali, Klaten, Karanganyar and Sragen experienced a local migration current from region to region around them, whereas other counties are independent. The migration current was influenced by topography, biotic interactions, and anthropogenic factor. Viewed from the spatial scalability in the studied areas, there are four categories of BPH population distribution; point, site, local, and landscape. BPH local migration interregion happened in the County of Klaten, Boyolali, Karanganyar and Sragen. It was caused by some factors: (1) the local climate, (2) the repetition of the use of rice plant variety in a long time, (3) the use of insecticide intensively (3-4 times in one planting period/season), and (4) the irrigation, allowing the spread of BPH larvae and eggs into its surroundings.
This paper studies a discrete dynamical system of interacting particles that evolve by interacting among them. The computational model is an abstraction of the natural world, and real systems can range from the huge cosmological scale down to the scale of biological cell, or even molecules. Different conditions for the system evolution are tested. The emerging patterns are analysed by means of fractal dimension and entropy measures. It is observed that the population of particles evolves towards geometrical objects with a fractal nature. Moreover, the time signature of the entropy can be interpreted at the light of complex dynamical systems.
Stochastic differential equations are rapidly becoming the most popular format in which to express the mathe-matical models of such diverse areas as neural networks, ecosystem dynamics, population genetics, and macro-economic systems. It seems only a question of time before the social sciences begin to rephrase their dynamic models in these terms, and indeed, in some isolated cases the process has already begun. This paper is designed to introduce social scientists to the fundamental concepts and uses of stochastic differential equations, as applied to several models of current interest: linear feedback, epidemics, and the cusp catastrophe. The approach taken here is to focus on the stationary probability density function of the model, which avoids most of the advanced mathematical techniques that are ordinarily required to describe the solutions of the equations. Further, it will be seen that this approach yields new statistical insights into the process under study, and in some cases even new descriptive statistics.
A computer model developed to simulate the interaction between the pathogenic fungus, Entomophaga maimaiga, and the gypsy moth, Lymantria dispar, was used to investigate airborne dispersal of fungal conidial spores. The model used data on egg mass density gathered from 32 sites in an area of Connecticut and information on fungal prevalence, gypsy moth abundance, fungus resting spore load in the soil, and detailed weather records from six intensively sampled plots in the same area. It calculated seasonal survival rates of gypsy moths at the six plots using a variety of dispersal distributions, or kernels, for the conidia. Distributions ranged from normal densities to the exponential, a Bessel and power distribution, along with a “kinked” linear distribution, which had two parts. All kernels gave good fits to the data so long as the dispersion parameter caused each standardized distribution to have an abscissa value near 0.05 at a distance of 1.25 km from the source. However, significant dispersal beyond 10 km only occurred for the kinked linear and power distributions. Thus, mechanisms for short-range dispersal may be different from those for long-distance dispersal. The model was also used to investigate the potential for dispersal of E. maimaiga in the northeastern United States just after it was known to be established in 1989. For the weather conditions prevalent in 1989 and 1990, and assuming a kinked linear dispersal kernel, I predicted that the fungus would spread rapidly, which did indeed happen. Furthermore, in these years rainfall and other weather conditions were very favorable for fungus development, so even if relatively few conidia dispersed long distances, they might easily have initiated viable infections.
In this paper, we investigate a spatial S–I model with non-linear incidence rates βS p I q , and obtain the conditions for transcritical bifurcation, Hopf bifurcation and Turing bifurcation. In particular, the exact Turing domain is found in the parameter space. For parameters are in that domain, a series of numerical simulations reveal that the model has rich dynamics. In our previous paper (Liu and Jin, 2007 J. Stat. Mech. P05002), we considered an epidemic model with constant rate of removal of the infectives and the mass action incidence βSI, in which only a stripe pattern was observed. However, in this paper, we obtain not only a stripe-like pattern but also a spot pattern, or coexistence of the two. The results obtained extend well the finding of pattern formation in the epidemic model and may well explain the field observed in some areas.
There is often need to measure aggregation levels of spatial patterns within a single map class in landscape ecological studies. The contagion index (CI), shape index (SI), and probability of adjacency of the same class (Qi), all have certain limits when measuring aggregation of spatial patterns. We have developed an aggregation index (AI) that is class specific and independent of landscape composition. AI assumes that a class with the highest level of aggregation (AI =1) is comprised of pixels sharing the most possible edges. A class whose pixels share no edges (completely disaggregated) has the lowest level of aggregation (AI =0). AI is similar to SI and Qi, but it calculates aggregation more precisely than the latter two. We have evaluated the performance of AI under varied levels of (1) aggregation, (2) number of patches, (3) spatial resolutions, and (4) real species distribution maps at various spatial scales. AI was able to produce reasonable results under all these circumstances. Since it is class specific, it is more precise than CI, which measures overall landscape aggregation. Thus, AI provides a quantitative basis to correlate the spatial pattern of a class with a specific process. Since AI is a ratio variable, map units do not affect the calculation. It can be compared between classes from the same or different landscapes, or even the same classes from the same landscape under different resolutions.
The behavior of robotic manipulators with backlash is analyzed. Based on the pseudo-phase plane two indices are proposed to evaluate the backlash effect upon the robotic system: the root mean square error and the fractal dimension. For the dynamical analysis the noisy signals captured from the system are filtered through wavelets. Several tests are developed that demonstrate the coherence of the results.
Cancer registries are increasingly mapping residences of patients at time of diagnosis, however, an accepted protocol for spatial analysis of these data is lacking. We undertook a public health practice-research partnership to develop a strategy for detecting spatial clusters of early stage breast cancer using registry data.
Spatial patterns of early stage breast cancer throughout Michigan were analyzed comparing several scales of spatial support, and different clustering algorithms.
Analyses relying on point data identified spatial clusters not detected using data aggregated into census block groups, census tracts, or legislative districts. Further, using point data, Cuzick-Edwards' nearest neighbor test identified clusters not detected by the SaTScan spatial scan statistic. Regression and simulation analyses lent credibility to these findings.
In these cluster analyses of early stage breast cancer in Michigan, spatial analyses of point data are more sensitive than analyses relying on data aggregated into polygons, and the Cuzick-Edwards' test is more sensitive than the SaTScan spatial scan statistic, with acceptable Type I error. Cuzick-Edwards' test also enables presentation of results in a manner easily communicated to public health practitioners. The approach outlined here should help cancer registries conduct and communicate results of geographic analyses.
Air travel plays a key role in the spread of many pathogens. Modeling the long distance spread of infectious disease in these cases requires an air travel model. Highly detailed air transportation models can be over determined and computationally problematic. We compared the predictions of a simplified air transport model with those of a model of all routes and assessed the impact of differences on models of infectious disease.
Using U.S. ticket data from 2007, we compared a simplified "pipe" model, in which individuals flow in and out of the air transport system based on the number of arrivals and departures from a given airport, to a fully saturated model where all routes are modeled individually. We also compared the pipe model to a "gravity" model where the probability of travel is scaled by physical distance; the gravity model did not differ significantly from the pipe model. The pipe model roughly approximated actual air travel, but tended to overestimate the number of trips between small airports and underestimate travel between major east and west coast airports. For most routes, the maximum number of false (or missed) introductions of disease is small (<1 per day) but for a few routes this rate is greatly underestimated by the pipe model.
If our interest is in large scale regional and national effects of disease, the simplified pipe model may be adequate. If we are interested in specific effects of interventions on particular air routes or the time for the disease to reach a particular location, a more complex point-to-point model will be more accurate. For many problems a hybrid model that independently models some frequently traveled routes may be the best choice. Regardless of the model used, the effect of simplifications and sensitivity to errors in parameter estimation should be analyzed.
Control of animal-born diseases is a major challenge faced by applied ecologists and public health managers. To improve cost-effectiveness, the effort required to control such pathogens needs to be predicted as accurately as possible. In this context, we reviewed the anti-rabies vaccination schemes applied around the world during the past 25 years.
We contrasted predictions from classic approaches based on theoretical population ecology (which governs rabies control to date) with a newly developed individual-based model. Our spatially explicit approach allowed for the reproduction of pattern formation emerging from a pathogen's spread through its host population.
We suggest that a much lower management effort could eliminate the disease than that currently in operation. This is supported by empirical evidence from historic field data. Adapting control measures to the new prediction would save one-third of resources in future control programmes.
The reason for the lower prediction is the spatial structure formed by spreading infections in spatially arranged host populations. It is not the result of technical differences between models.
Synthesis and applications. For diseases predominantly transmitted by neighbourhood interaction, our findings suggest that the emergence of spatial structures facilitates eradication. This may have substantial implications for the cost-effectiveness of existing disease management schemes, and suggests that when planning management strategies consideration must be given to methods that reflect the spatial nature of the pathogen–host system.
A percolation model with long-range correlations was introduced to investigate the phenomena of epidemic spreading by Monte Carlo simulations. The correlation exponent alpha and pathogenic ratio s correspond to different spreading methods and pathogenicity of variant epidemics. As the correlation changes from a weak one to a strong one, the patterns change from site percolation to Eden cluster when pathogenic ratio s=1, or Leath percolation cluster when s<1. Corresponding to change of patterns, the fractal dimension increases up to space dimension. The critical behavior in epidemic spreading has been examined based on the model. It is found that correlation has a great influence on the threshold of spreading percolation.
The probability of Trypanosoma cruzi transmission to opossums by independent events of predation and fecal contamination during feeding ("biting") with positive Triatoma infestans was estimated. Negative female opossums were challenged for 23 hr with 10 infected third and fourth instars of T. infestans, and tests for positivity for T. cruzi by xenodiagnosis were performed at 30, 60, and 90 days. From these data, seven probability parameters were estimated by maximum likelihood, and likelihood ratio statistics confidence intervals were calculated. Simultaneous estimation of p1 (probability that a "bite" will infect an opossum), p3 (probability that a bug that has been eaten by an opossum will infect it), and p6 (probability that the opossum will become infected if faced with an infected triatomine), resulted in p1 = 0.06, p3 = 0.075, and p6 = 0.059. On average, each opossum should be exposed to an average of 700 encounters with bugs during its life, resulting in about eight potentially infective contacts, to produce the 35% opossum prevalence found in the field.
Natural exposure to prion disease is likely to occur throughout successive challenges, yet most experiments focus on single large doses of infectious material. We analyze the results from an experiment in which rodents were exposed to multiple doses of feed contaminated with the scrapie agent. We formally define hypotheses for how the doses combine in terms of statistical models. The competing hypotheses are that only the total dose of infectivity is important (cumulative model), doses act independently, or a general alternative that interaction between successive doses occurs (to raise or lower the risk of infection). We provide sample size calculations to distinguish these hypotheses. In the experiment, a fixed total dose has a significantly reduced probability of causing infection if the material is presented as multiple challenges, and as the time between challenges lengthens. Incubation periods are shorter and less variable if all material is consumed on one occasion. We show that the probability of infection is inconsistent with the hypothesis that each dose acts as a cumulative or independent challenge. The incubation periods are inconsistent with the independence hypothesis. Thus, although a trend exists for the risk of infection with prion disease to increase with repeated doses, it does so to a lesser degree than is expected if challenges combine independently or in a cumulative manner.
Wild birds are important to public health because they carry emerging zoonotic pathogens, either as a reservoir host or by dispersing infected arthropod vectors. In addition, bird migration provides a mechanism for the establishment of new endemic foci of disease at great distances from where an infection was acquired. Birds are central to the epidemiology of West Nile virus (WNV) because they are the main amplifying host of the virus in nature. The initial spread of WNV in the U.S. along the eastern seaboard coincided with a major bird migration corridor. The subsequent rapid movement of the virus inland could have been facilitated by the elliptical migration routes used by many songbirds. A number of bird species can be infected with Borrelia burgdorferi, the etiologic agent of Lyme disease, but most are not competent to transmit the infection to Ixodes ticks. The major role birds play in the geographic expansion of Lyme disease is as dispersers of B. burgdorferi-infected ticks. Aquatic waterfowl are asymptomatic carriers of essentially all hemagglutinin and neuraminidase combinations of influenza A virus. Avian influenza strains do not usually replicate well in humans, but they can undergo genetic reassortment with human strains that co-infect pigs. This can result in new strains with a marked increase in virulence for humans. Wild birds can acquire enteropathogens, such as Salmonella and Campylobacter spp., by feeding on raw sewage and garbage, and can spread these agents to humans directly or by contaminating commercial poultry operations. Conversely, wild birds can acquire drug-resistant enteropathogens from farms and spread these strains along migration routes. Birds contribute to the global spread of emerging infectious diseases in a manner analogous to humans traveling on aircraft. A better understanding of avian migration patterns and infectious diseases of birds would be useful in helping to predict future outbreaks of infections due to emerging zoonotic pathogens.
Recent outbreaks of highly pathogenic avian influenza (HPAI) viruses in poultry and their threatening zoonotic consequences emphasize the need for effective control measures. Although vaccination of poultry against avian influenza provides a potentially attractive control measure, little is known about the effect of vaccination on epidemiologically relevant parameters, such as transmissibility and the infectious period. We used transmission experiments to study the effect of vaccination on the transmission characteristics of HPAI A/Chicken/Netherlands/03 H7N7 in chickens. In the experiments, a number of infected and uninfected chickens is housed together and the infection chain is monitored by virus isolation and serology. Analysis is based on a stochastic susceptible, latently infected, infectious, recovered (SEIR) epidemic model. We found that vaccination is able to reduce the transmission level to such an extent that a major outbreak is prevented, important variables being the type of vaccine (H7N1 or H7N3) and the moment of challenge after vaccination. Two weeks after vaccination, both vaccines completely block transmission. One week after vaccination, the H7N1 vaccine is better than the H7N3 vaccine at reducing the spread of the H7N7 virus. We discuss the implications of these findings for the use of vaccination programs in poultry and the value of transmission experiments in the process of choosing vaccine.
• SEIR model
• highly pathogenic avian influenza
• final size
• generalized linear model
• reproduction ratio
1. Direct interactions between individuals play an important part in the sociality of group-living animals, their mating system and disease transmission. Here, we devise a methodology to quantify relative rates of proximity interaction from radio-tracking data and highlight potential asymmetries within the contact network of a moderate-density badger population in the north-east of England. 2. We analysed radio-tracking data from four contiguous social groups, collected over a 3-year period. Dynamic interaction analysis of badger dyads was used to assess the movement of individuals in relation to the movement of others, both within and between social groups. Dyads were assessed with regard to season, sex, age and sett use pattern of the badgers involved. 3. Intragroup separation distances were significantly shorter than intergroup separation distances, and interactions between groups were rare. Within groups, individuals interacted with each other more often than expected, and interaction patterns varied significantly with season and sett use pattern. Non-mover dyads (using the main sett for day-resting on > 50% of occasions) interacted more frequently than mover dyads (using an outlier sett for day-resting on > 50% of occasions) or mover-non-mover dyads. Interactions between group members occurred most frequently in winter. 4. Of close intragroup interactions (< 50 m separation distance), 88.6% were associated with a main sett and only 4.4% with outlier setts. Non-mover dyads and non-mover-mover dyads interacted significantly more often at the main sett than mover-only dyads. These results highlight the importance of the main sett to badger sociality and support the suggestion that badger social groups are comprised of different subgroups, in our case based on differential sett use patterns. 5. Asymmetries in contact structure within a population will affect the way in which diseases are transmitted through a social network. Assessment of these networks is essential for understanding the persistence and spread of disease within populations which do not mix freely or which exhibit heterogeneities in their spatial or social behaviour.
This paper addresses the question of how population diffusion affects the formation of the
spatial patterns in the spatial epidemic model by Turing mechanisms. In particular, we
present a theoretical analysis of results of the numerical simulations in two dimensions.
Moreover, there is a critical value for the system within the linear regime. Below the critical
value the spatial patterns are impermanent, whereas above it stationary spot and stripe
patterns can coexist over time. We have observed the striking formation of spatial patterns
during the evolution, but the isolated ordered spot patterns do not emerge in the space.
The non-equilibrium phase transition in models for epidemic spreading with long-range infections in combination with incubation times is investigated by field-theoretical and numerical methods. Here the spreading process is modelled by spatio-temporal Levy flights, i.e., it is assumed that both spreading distance and incubation time decay algebraically. Depending on the infection rate one observes a phase transition from a fluctuating active phase into an absorbing phase, where the infection becomes extinct. This transition between spreading and extinction is characterized by continuously varying critical exponents, extending from a mean-field regime to a phase described by the universality class of directed percolation. We compute the critical exponents in the vicinity of the upper critical dimension by a field-theoretic renormalization group calculation and verify the results in one spatial dimension by extensive numerical simulations.
A class of non-local contact processes is introduced and studied using the mean field
approximation and numerical simulations. In these processes particles are created at a rate
which decays algebraically with the distance from the nearest particle. It is found that the
transition into the absorbing state is continuous and is characterized by continuously
varying critical exponents. This model differs from the previously studied non-local directed
percolation model, where particles are created by unrestricted Levy flights. It is
motivated by recent studies of non-equilibrium wetting indicating that such non-local
processes play a role in the unbinding transition. Other non-local processes which
have been suggested to exist within the context of wetting are considered as well.
An autonomous model of HIV recombination is proposed and analyzed. The necessary and sufficient conditions for the existence of all equilibria are obtained. Stability and global attraction of these equilibria are also fully studied. The principle of competitive exclusion is no longer valid, interclade recombination effect confers competitive advantages to the recombinant virus. An optimal vaccine strategy also is suggested.
In quality control discipline, pattern classification is focused on the detection of unnatural patterns in process data. In this paper, fractal dimension is proposed as a new classifier for pattern classification. Fractal dimension is an index for measuring the complexity of an object. Its applications were found in such diverse fields as manufacturing, material science, medical, and image processing. A method for detecting patterns in process data using the fractal dimension is proposed in this paper. A Monte Carlo study was carried out to study the fractal dimension (D) and the Y-intercept (Yint) values of process data with patterns of interest. The patterns included in the study are natural pattern, upward linear trend, downward linear trend, cycle, systematic variable, stratification, mixture, upward sudden shift, and downward sudden shift. Based on the results, the approach is effective in detecting such non-periodic patterns as the natural patterns, linear trends (at slope ≥0.2), systematic variable, stratification, mixture, and sudden shifts. For the cyclical pattern, although the D and Yint-values are not stable, the approach can provide useful information when the period of the cycle is greater than 2 and is less than or equal to half the window size (2
It is shown that the shape of the large, random clusters, near the critical percolation concentration c0, is such that their mean boundary 〈b〉 is proportional to their mean bulk 〈n〉 and this is illustrated by an argument which shows that the dimension of the boundary is the same as that of the bulk. The resulting ratio 〈b〉/〈n〉 is simply related to the critical concentration c0. The detailed results of a Monte Carlo calculation, previously reported, are given for c<c0 on a simple square lattice; they yield an empirical formula for the probability distribution P(n,b), for finding a cluster of size n and boundary b, that is proportional to a Gaussian in b/n, which is independent of concentration and which narrows to a δ function at b/n=α0, n→∞. The asymptotic behavior of the Gaussian form gives the critical exponents β=0.19±0.16, and γ=2.34±0.3, and α0, gives the critical concentration c0=0.587±0.14, in agreement with previous determinations.
Dear Sir, The frequent opportunities I have had of receiving pleasure from your writings and conversation, have induced me to prefer offering to the Royal Society through your medium, this Paper on Life Contingencies, which forms part of a continuation of my original paper on the same subject, published among the valuable papers of the Society, as by passing through your hands it may receive the advantage of your judgment.
In this paper we define a new circularity measure. The new measure is easy to compute and, being area based, is robust with
respect to noise. It ranges over (0,1] and gives the measured circularity equal to 1 if and only if the measured shape is
a circle. The new measure is invariant with respect to translations, rotations and scaling.
Grid-based models have been used to understand spatial heterogeneity of the vegetation height in forests and to analyze spatio-temporal
dynamics of the forest regeneration process. In this report, we present two methods of identifying lattice models when spatio-temporal
data are given. The first method detects directionality of regeneration waves based on the timing of local disturbance events.
The second evaluates the forest pattern by recording the fraction of high and low vegetation areas at multiple spatial scales.
We illustrate these methods by applying them to patterns generated using three simple stochastic lattice models: (1) two-state
model, distinguishing sites with high and low vegetation, (2) three-state model, in which sites can be in an additional disturbed
state, and (3) Shimagare model, which considers a continuous range of states. The combination of the two methods provides
efficient means of distinguishing the models. The first method has a more direct ecological meaning, while the second is useful
when forest data are limited in time.
In the paper, we propose a model that tracks the dynamics of many diseases spread by vectors, such as malaria, dengue, or West Nile virus (all spread by mosquitoes). Our model incorporates demographic structure with variable population size which is described by nonlinear birth rate and linear death rate. The stability of the system is analyzed for the existence of the disease-free and endemic equilibria points. We find the basic reproduction number R0 in terms of measurable epidemiological and demographic parameters is the threshold condition that determines the dynamics of disease infection: if R0<1 the disease fades out, and for R0>1 the disease remains endemic. The threshold condition provides important guidelines for accessing control of the vector diseases, and implies that it is an efficient way to halt the spread of vector epidemic by reducing the carrying capacity of the environment for the vector and the host. Moreover, sufficient conditions are also obtained for the global stability of the unique endemic equilibrium E∗.
Australia produces one of the highest volumes of agricultural, industrial, and municipal wastes per capita in the world. Increasingly, the public is demanding statutory authorities investigate environmentally sound methods of land application. However, a real danger associated with land disposal of wastes, in particular sewage, is the possible contamination of groundwater and threats to public health resulting from transport of pathogenic micro-organisms through the vadose zone. The study of the transport and fate of micro-organisms in soils is also of vital importance in the fields of oil recovery, biological control of plant root diseases, and in-situ bioremediation of contaminated soils and aquifers from industrial accidents. The objectives of this paper are 1.(a) to explore the extent of spatial and temporal heterogeneity found in the soil-water patterns in Australian soils, and2.(b) to establish the framework for a mathematical model of the population dynamics and mobility of soil bacterial transport through the unsaturated zone of soils.
The model explicitly incorporates spatial and temporal heterogeneity in describing these dynamics.
Epidemic spreading in percolation worlds has been investigated by Monte Carlo simulations, based on a correlated percolation model. It is found that the spreading behavior is greatly influenced by the spreading worlds. When the correlation changes from the weak limit to a strong one, the pattern consisting of sick individuals converts from the pattern of site percolation to that of Leath percolation in a percolation world. Correspondingly, the fractal dimension varies from the dimension of the random pattern to that of dense growth morphology. The critical correlation exponent αc=dw, where dw is the fractal dimension of the percolation world. Furthermore, the critical behavior of epidemic spreading is obviously affected by the spreading world also. The threshold of pathogenic ratio sc=1 (for uniform world) and 0.593 (for the critical percolation one), respectively, in the strong correlation limit.
The aim of this study was to explore the suggestion that fractal characteristics may play a role in aesthetic experiences by providing possible empirical evidence for connections between landscape preference and fractal properties. This approach was motivated by the knowledge that many natural forms are fractal and that, in preference research, naturalness has been found an important predictor. For reasons described in the paper, in this study we chose to focus on landscape silhouette outlines. The results indicate that there is a relationship between preference and the fractal dimension, which in turn gives rise to the hypothesis that the fractal dimension could provide part of the explanation to the well-documented connection between preference and naturalness.
A new perimeter for shapes composed of cells is defined. This perimeter is called the contact perimeter, which corresponds to the sum of the boundaries of neighboring cells of the shape. Also, a relation between the perimeter of the shape and the contact perimeter is presented. The contact perimeter corresponds to the measure of compactness proposed here called discrete compactness. In this case, the term compactness does not refer to point-set topology, but is related to intrinsic properties of objects.
Factors governing the rate and direction of prairie dog (Cynomys spp.) colony expansion remain poorly understood. However, increased knowledge and ability to control these factors may lead to more effective reintroductions of prairie dogs and restoration of grassland habitats. We present density and directional analyses of the establishment of new burrows on three reintroduced colonies of Black-tailed prairie dog (Cynomys ludovicianus) in southern New Mexico; the study colonies had been subjected to mow and burn treatments in the second year of the study. Our hypotheses were that prairie dogs will preferentially dig new burrows in the treatment plots versus control plots and that the colonies will expand in the direction of the treatment plots. The results support these hypotheses; analysis of burrow counts by site and treatment shows that prairie dogs preferentially colonized both mow and burn treatments compared to untreated areas at the periphery of the colonies. Directional analysis showed a significant posttreatment orientation of new burrows toward the treatment plots for all colonies. Our results show that the direction of expansion of prairie dog colonies can be manipulated. Effective control of the expansion of prairie dog colonies may lead to more successful reintroductions.
Geographic information systems (GIS), global positioning systems (GPS), remote sensing, and spatial statistics are tools to analyze and integrate the spatial component in epidemiology of vector-borne disease into research, surveillance, and control programs based on a landscape ecology approach. Landscape ecology, which deals with the mosaic structure of landscapes and ecosystems, considers the spatial heterogeneity of biotic and abiotic components as the underlying mechanism which determines the structure of ecosystems. The methodologies of GIS, GPS, satellite imagery, and spatial statistics, and the landscape ecology--epidemiology approach are described, and applications of these methodologies to vector-borne diseases are reviewed. Collaborative studies by the author and colleagues on malaria in Israel and tsetse flies in Kenya, and Lyme disease, LaCrosse encephalitis, and eastern equine encephalitis in the north-central United States are presented as examples for application of these tools to research and disease surveillance. Relevance of spatial tools and landscape ecology to emerging infectious diseases and to studies of global change effects on vector-borne diseases are discussed.
We present a model that describes adsorption and clustering of particles on a surface. A clustering transition is found that separates between a phase of weakly correlated particle distributions and a phase of strongly correlated distributions in which the particles form localized fractal clusters. The order parameter of the transition is identified and the fractal nature of both phases is examined. The model is relevant to a large class of clustering phenomena such as aggregation and growth on surfaces, population distribution in cities, and plant and bacterial colonies, as well as gravitational clustering.
We introduce a class of small-world networks--homogeneous small-worlds--which, in contrast with the well-known Watts-Strogatz small-worlds, exhibit a homogeneous connectivity distribution, in the sense that all nodes have the same number of connections. This feature allows the investigation of pure small-world effects, detached from any associated heterogeneity. Furthermore, we use at profit the remarkable similarity between the properties of homogeneous small worlds and the heterogeneous small-worlds of Watts-Strogatz to assess the separate roles of heterogeneity and small-world effects. We investigate the dependence on these two mechanisms of the threshold for epidemic outbreaks and also of the coevolution of cooperators and defectors under natural selection. With respect to the well-studied regular homogeneous limits, we find a subtle interplay between these mechanisms. While they both contribute to reduce the threshold for an epidemic outburst, they exhibit opposite behavior in the evolution of cooperation, such that the overall results mask the true nature of their individual contribution to this process.
The classification of 3 common breast lesions, fibroadenomas, cysts, and cancers, was achieved using computerized image analysis of tumor shape in conjunction with patient age. The process involved the digitization of 69 mammographic images using a video camera and a commercial frame grabber on a PC-based computer system. An interactive segmentation procedure identified the tumor boundary using a thresholding technique which successfully segmented 57% of the lesions. Several features were chosen based on the gross and fine shape describing properties of the tumor boundaries as seen on the radiographs. Patient age was included as a significant feature in determining whether the tumor was a cyst, fibroadenoma, or cancer and was the only patient history information available for this study. The concept of a radial length measure provided a basis from which 6 of the 7 shape describing features were chosen, the seventh being tumor circularity. The feature selection process was accomplished using linear discriminant analysis and a Euclidean distance metric determined group membership. The effectiveness of the classification scheme was tested using both the apparent and the leaving-one-out test methods. The best results using the apparent test method resulted in correctly classifying 82% of the tumors segmented using the entire feature space and the highest classification rate using the leaving-one-out test method was 69% using a subset of the feature space. The results using only the shape descriptors, and excluding patient age resulted in correctly classifying 72% using the entire feature space (except age), and 51% using a subset of the feature space.
The fractal properties of models of randomly placed n-dimensional spheres (n=1,2,3) are studied using standard techniques for calculating fractal dimensions in empirical data (the box counting and Minkowski-sausage techniques). Using analytical and numerical calculations it is shown that in the regime of low volume fraction occupied by the spheres, apparent fractal behavior is observed for a range of scales between physically relevant cut-offs. The width of this range, typically spanning between one and two orders of magnitude, is in very good agreement with the typical range observed in experimental measurements of fractals. The dimensions are not universal and depend on density. These observations are applicable to spatial, temporal and spectral random structures. Polydispersivity in sphere radii and impenetrability of the spheres (resulting in short range correlations) are also introduced and are found to have little effect on the scaling properties. We thus propose that apparent fractal behavior observed experimentally over a limited range may often have its origin in underlying randomness. Comment: 19 pages, 12 figures. More info available at http://www.fh.huji.ac.il/~dani/
- J Rabinovich
- N Schweigmann
- V Yohai
- C Wisnivesky-Colli
J. Rabinovich, N. Schweigmann, V. Yohai, C. Wisnivesky-Colli,
Probability of Trypanosoma cruzi transmission by Triatoma infestans
(Hemiptera: Reduviidae) to the opossum Didelphis albiventris
(Marsupialia: Didelphidae), Am. J. Trop. Med. Hyg. 65, 125-130, 2001.