Uncertainties regarding dengue modeling in Rio de Janeiro, Brazil

Dengue fever is currently the most important arthropod-borne viral disease in Brazil. Mathematical modeling of disease dynamics is a very useful tool for the evaluation of control measures. To be used in decision-making, however, a mathematical model must be carefully parameterized and validated with epidemiological and entomological data. In this work, we developed a simple dengue model to answer three questions: (i) which parameters are worth pursuing in the field in order to develop a dengue transmission model for Brazilian cities; (ii) how vector density spatial heterogeneity influences control efforts; (iii) with a degree of uncertainty, what is the invasion potential of dengue virus type 4 (DEN-4) in Rio de Janeiro city. Our model consists of an expression for the basic reproductive number (R0) that incorporates vector density spatial heterogeneity. To deal with the uncertainty regarding parameter values, we parameterized the model using a priori probability density functions covering a range of plausible values for each parameter. Using the Latin Hypercube Sampling procedure, values for the parameters were generated. We conclude that, even in the presence of vector spatial heterogeneity, the two most important entomological parameters to be estimated in the field are the mortality rate and the extrinsic incubation period. The spatial heterogeneity of the vector population increases the risk of epidemics and makes the control strategies more complex. At last, we conclude that Rio de Janeiro is at risk of a DEN-4 invasion. Finally, we stress the point that epidemiologists, mathematicians, and entomologists need to interact more to find better approaches to the measuring and interpretation of the transmission dynamics of arthropod-borne diseases.

Dynamics of spatial heterogeneity in a landfill with interacting phase densities:a stochastic analysis

A landfill represents a complex and dynamically evolving structure that can be stochastically perturbed by exogenous factors. Both thermodynamic (equilibrium) and time varying (non-steady state) properties of a landfill are affected by spatially heterogenous and nonlinear subprocesses that combine with constraining initial and boundary conditions arising from the associated surroundings. While multiple approaches have been made to model landfill statistics by incorporating spatially dependent parameters on the one hand (data based approach) and continuum dynamical mass-balance equations on the other (equation based modelling), practically no attempt has been made to amalgamate these two approaches while also incorporating inherent stochastically induced fluctuations affecting the process overall. In this article, we will implement a minimalist scheme of modelling the time evolution of a realistic three dimensional landfill through a reaction-diffusion based approach, focusing on the coupled interactions of four key variables - solid mass density, hydrolysed mass density, acetogenic mass density and methanogenic mass density, that themselves are stochastically affected by fluctuations, coupled with diffusive relaxation of the individual densities, in ambient surroundings. Our results indicate that close to the linearly stable limit, the large time steady state properties, arising out of a series of complex coupled interactions between the stochastically driven variables, are scarcely affected by the biochemical growth-decay statistics. Our results clearly show that an equilibrium landfill structure is primarily determined by the solid and hydrolysed mass densities only rendering the other variables as statistically "irrelevant" in this (large time) asymptotic limit. The other major implication of incorporation of stochasticity in the landfill evolution dynamics is in the hugely reduced production times of the plants that are now approximately 20-30 years instead of the previous deterministic model predictions of 50 years and above. The predictions from this stochastic model are in conformity with available experimental observations.

Spatial heterogeneity of leaf wetness duration in apple trees and its influence on performance of a warning system for sooty blotch and flyspeck

To determine the effect of sensor placement on the performance of a disease-warning system for sooty blotch and flyspeck (SBFS), we measured leaf wetness duration (LWD) at 12 canopy positions in apple trees, then simulated operation of the disease-warning system using LWD measurements from different parts of the canopy. LWD sensors were placed in four trees within one Iowa orchard during two growing seasons, and in one tree in each of four orchards during a single growing season. The LWD measurements revealed substantial heterogeneity among sensor locations. In all data sets, the upper, eastern portion of the canopy had the longest mean daily LWD, and was the first site to form dew and the last to dry. The lower, western portion of the canopy averaged about 3 It less LWD per day than the top of the canopy, and was the last zone where dew formed and the first to dry off. On about 25% of nights when dew occurred in the top of the canopy, no dew formed in the lower, western canopy. Intracanopy variability of LWD was more pronounced when dew was the sole source of wetness than on days when rainfall occurred. Daily LWD in the upper, eastern portion of the canopy was slightly less than reference measurements made at a 0.7-m height over turfgrass located near the orchard. When LWD measurements from several canopy positions were input to the SBFS warning system, timing of occurrence of a fungicide-spray threshold varied by as much as 30 days among canopy positions. Under Iowa conditions, placement of an LWD sensor at an unobstructed site over turfgrass was a fairly accurate surrogate for the wettest part of the canopy. Therefore, such an extra-canopy LWD sensor might be substituted for a within-canopy sensor to enhance operational reliability of the SBFS warning system.

Analysis of sandflies (Diptera: Psychodidae) in Barra do Garças, State of Mato Grosso, Brazil, and the influence of environmental variables on the vector density of Lutzomyia longipalpis (Lutz & Neiva, 1912)

INTRODUCTION: Leishmaniasis is an infectious and parasitic zoonotic, non-contagious, vector-borne disease caused by protozoa of the genus Leishmania. In Brazil, the major vector of Leishmania (Leishmania) infantum chagasi (Cunha & Chagas, 1934) is Lutzomyia longipalpis. Barra do Garças, State of Mato Grosso, was designated as a priority area by the Brazilian Ministry of Health for american visceral leishmaniasis, and it is important to identify the vector species present in this municipality. Our objective was to raise sandflies and study the influence of environmental variables on the vector density of Lutzomyia longipalpis. METHODS: We performed entomological monitoring in 3 districts using Centers for Disease Control and Prevention (CDC) light traps and recorded human cases of american visceral leishmaniasis in the city. We calculated the relative frequency and richness of sandflies and applied a transfer function model to the vector density correlate with relative humidity. RESULTS: The sandfly population was composed of 2 genera and 27 species, totaling 8,097 individuals. Monitoring identified Lutzomyia longipalpis (44%), followed by Lutzomyia lenti (18.9%), Lutzomyia whitmani (13.9%), Lutzomyia carmelinoi (9.1%), Lutzomyia evandroi (5.1%), Lutzomyia termitophila (3.3%), Lutzomyia sordellii (1.9%), and 20 other species (<4%). The male:female ratio was 3.5:1. We observed high species diversity (Dα = 6.65). Lutzomyia longipalpis showed occurrence peaks during the rainy season; there was a temporal correlation with humidity, but not with frequency or temperature. CONCLUSIONS: The presence of Lutzomyia longipalpis in the urban area of Barra do Garças underscores the changing disease profile, which was previously restricted to the wild environment.

Vector density and the control of kala-azar in Bihar, India

Bihar, India has been in the grip of kala-azar for many years. Its rampant and severe spread has made life miserable in most parts of the state. Such conditions require a comprehensive understanding of this affliction. The numbers coming out of the districts prone to the disease in the north and south Ganges have provided us with several startling revelations, as there are striking uniformities on both sides, including similar vegetation, water storage facilities, house construction and little change in risk factors. The northern areas have been regularly sprayed with DDT since 1977, but eradication of the disease appears to be a distant dream. In 2007 alone, there were as many as 37,738 cases in that region. In contrast, the southern districts of Patna and Nalanda have never had the disease in its epidemic form and endemic disease has been present in only some pockets of the two districts. In those cases, two rounds of spraying with DDT had very positive results, with successful control and no new established foci. In addition, an eleven-year longitudinal study of the man hour density and house index for the vector Phlebotomus argentipes demonstrated that they were quite high in Patna and Nalanda and quite low in north Bihar. Given these facts, an attempt has been made to unravel the role of P. argentipes saliva (salivary gland) in the epidemiology of kala-azar. It was determined that patchy DDT spraying should be avoided for effective control of kala-azar.

Forest spatial heterogeneity and palm richness, abundance and community composition in Terra Firme forest, Central Amazon

The mechanisms that maintain tree diversity in tropical rain forests are still in debate. Variations in forest structural components produce forest microenvironmental heterogeneity, which in turn may affect plant performance and have been scarcely analyzed in the Amazon. Palms are widespread in the Neotropical rainforests and have relatively well known taxonomy, apart from being ecologically and economically important. The understanding of how palms respond to variation in the forest structural components may help to explain their abundance and richness in a given area. In this study, we describe a palm community and analyze how it is affected by forest microenvironmental heterogeneity. In a pristine "Terra Firme" forest at Reserva Ducke, Manaus, we recorded all adult palm trees in twenty 100 × 10 m plots. In the same plots we recorded the variation in canopy openness, the leaflitter thickness and counted all non-palm forest trees. A total of 713 individuals in 29 palm species were found. The three most abundant species were Astrocaryum sciophilum (Miq.) Pulle, A. gynacanthum Mart. and Attalea attaleoides (Barb. Rodr.) Wess. Boer. The most locally abundant species were also very frequent or occurred in a larger number of plots. There were no significant effects of litter depth, forest canopy openness and forest tree abundance on palm richness. However, in areas where leaf litter was thicker a significant lower number of palm trees occurred. In microsites where proportionally more incident light was reaching the forest understory, due to higher canopy opening, significantly more palm trees were present.

Energy exchange in a dense urban environment Part II: impact of spatial heterogeneity of the surface

The centre of cities, characterised by spatial and temporal complexity, are challenging environments for micrometeorological research. This paper considers the impact of sensor location and heterogeneity of the urban surface on flux observations in the dense city centre of London, UK. Data gathered at two sites in close vicinity, but with different measurement heights, were analysed to investigate the influence of source area characteristics on long-term radiation and turbulent heat fluxes. Combining consideration of diffuse radiation and effects of specular reflections, the non-Lambertian urban surface is found to impact the measurements of surface albedo. Comparisons of observations from the two sites reveal that turbulent heat fluxes are similar under some flow conditions. However, they mostly observe processes at different scales due to their differing measurement heights, highlighting the critical impact of siting sensors in urban areas. A detailed source area analysis is presented to investigate the surface controls influencing the energy exchanges at the different scales

Spatial heterogeneity affecting fish fauna in cascade reservoirs of the Upper Parana Basin, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial heterogeneity of soil nutrients and plant species in herb-dominated communities of contrasting land use

Recent interest in spatial pattern in terrestrial ecosystems has come from an awareness of theintimate relationship between spatial heterogeneity of soil resources and maintenance of plant species diversity. Soil and vegetation can vary spatially inresponse to several state factors of the system. In this study, we examined fine-scale spatial variability of soil nutrients and vascular plant species in contrasting herb-dominated communities (a pasture and an oldfield) to determine degree of spatial dependenceamong soil variables and plant community characteristics within these communities by sampling at 1-m intervals. Each site was divided into 25 1-m 2 plots. Mineral soil was sampled (2-cm diameter, 5-cm depth) from each of four 0.25-m2 quarters and combined into a single composite sample per plot. Soil organic matter was measured as loss-on-ignition. Extractable NH4 and NO3 were determined before and after laboratory incubation to determine potential net N mineralization and nitrification. Cations were analyzed using inductively coupled plasma emission spectrometry. Vegetation was assessed using estimated percent cover. Most soiland plant variables exhibited sharp contrasts betweenpasture and old-field sites, with the old field having significantly higher net N mineralization/nitrification, pH, Ca, Mg, Al, plant cover, and species diversity, richness, and evenness. Multiple regressions revealedthat all plant variables (species diversity, richness,evenness, and cover) were significantly related to soil characteristics (available nitrogen, organic matter,moisture, pH, Ca, and Mg) in the pasture; in the old field only cover was significantly related to soil characteristics (organic matter and moisture). Both sites contrasted sharply with respect to spatial pattern of soil variables, with the old field exhibiting a higher degree of spatial dependence. These results demonstrate that land-use practices can exert profound influence on spatial heterogeneity of both soil properties and vegetation in herb-dominated communities.

Spatial heterogeneity and lake morphology affect diffusive greenhouse gas emission estimates of lakes

Most estimates of diffusive flux (F) of methane (CH4) and carbon dioxide (CO2) from lakes are based on single-point flux chamber measurements or on piston velocity (k) modeled from wind speed and single-point measurements of surface water gas concentrations (C-aq). We analyzed spatial variability of F of CH4 and CO2, as well as C-aq and k in 22 European lakes during late summer. F and k were higher in the lake centers, leading to considerable bias when extrapolating single-point chamber measurements to whole-lake estimates. The ratio of our empirical k estimates to wind speed-modeled k was related to lake size and shape, suggesting a lake morphology effect on the relationship between wind speed and k. This indicates that the error inherent to established wind speed models can be reduced by determining k and C-aq at multiple sites on lakes to calibrate wind speed-modeled k to the local system.

The Effects of Density, Spatial Pattern, and Competitive Symmetry on Size Variation in Simulated Plant Populations

Patterns of size inequality in crowded plant populations are often taken to be indicative of the degree of size asymmetry of competition, but recent research suggests that some of the patterns attributed to size‐asymmetric competition could be due to spatial structure. To investigate the theoretical relationships between plant density, spatial pattern, and competitive size asymmetry in determining size variation in crowded plant populations, we developed a spatially explicit, individual‐based plant competition model based on overlapping zones of influence. The zone of influence of each plant is modeled as a circle, growing in two dimensions, and is allometrically related to plant biomass. The area of the circle represents resources potentially available to the plant, and plants compete for resources in areas in which they overlap. The size asymmetry of competition is reflected in the rules for dividing up the overlapping areas. Theoretical plant populations were grown in random and in perfectly uniform spatial patterns at four densities under size‐asymmetric and size‐symmetric competition. Both spatial pattern and size asymmetry contributed to size variation, but their relative importance varied greatly over density and over time. Early in stand development, spatial pattern was more important than the symmetry of competition in determining the degree of size variation within the population, but after plants grew and competition intensified, the size asymmetry of competition became a much more important source of size variation. Size variability was slightly higher at higher densities when competition was symmetric and plants were distributed nonuniformly in space. In a uniform spatial pattern, size variation increased with density only when competition was size asymmetric. Our results suggest that when competition is size asymmetric and intense, it will be more important in generating size variation than is local variation in density. Our results and the available data are consistent with the hypothesis that high levels of size inequality commonly observed within crowded plant populations are largely due to size‐asymmetric competition, not to variation in local density.

Spatial heterogeneity of inhibitory surrounds in the middle temporal visual area.

A recurrent theme in the organization of vertebrate visual cortex is that of receptive fields with an associated "silent" opponency component. In the middle temporal area (area MT), a cortical visual area involved in the analysis of retinal motion in primates, this opponency appears in the form of a region outside the classical receptive field (CRF) that in itself gives no response but suppresses responses to motion evoked within the CRF. This antagonistic motion surround has been described as very large and symmetrically arrayed around the CRF. On the basis of this view, the primary function of the surround has long been thought to consist of simple figure-ground segregation based on movement. We have made use of small stimulus patches to map the form and extent of the surround and find evidence that the surround inhibition of many MT cells is in fact confined to restricted regions on one side or on opposite sides of the CRF. Such regions endow MT cells with the ability to make local-to-local motion comparisons, capable of extracting more complex features from the visual environment, and as such, may be better viewed as intrinsic parts of the receptive field, rather than as separate entities responsible for local-to-global comparisons.