Age × stage-classified demographic analysis: a comprehensive approach.

This paper presents a comprehensive theory for the demographic analysis of populations in which individuals are classified by both age and stage. The earliest demographic models were age classified. Ecologists adopted methods developed by human demographers and used life tables to quantify survivorship and fertility of cohorts and the growth rates and structures of populations. Later, motivated by studies of plants and insects, matrix population models structured by size or stage were developed. The theory of these models has been extended to cover all the aspects of age-classified demography and more. It is a natural development to consider populations classified by both age and stage. A steady trickle of results has appeared since the 1960s, analyzing one or another aspect of age × stage-classified populations, in both ecology and human demography. Here, we use the vec-permutation formulation of multistate matrix population models to incorporate age- and stage-specific vital rates into demographic analysis. We present cohort results for the life table functions (survivorship, mortality, and fertility), the dynamics of intra-cohort selection, the statistics of longevity, the joint distribution of age and stage at death, and the statistics of life disparity. Combining transitions and fertility yields a complete set of population dynamic results, including population growth rates and structures, net reproductive rate, the statistics of lifetime reproduction, and measures of generation time. We present a complete analysis of a hypothetical model species, inspired by poecilogonous marine invertebrates that produce two kinds of larval offspring. Given the joint effects of age and stage, many familiar demographic results become multidimensional, so calculations of marginal and mixture distributions are an important tool. From an age-classified point of view, stage structure is a form of unobserved heterogeneity. From a stage-classified point of view, age structure is unobserved heterogeneity. In an age × stage-classified model, variance in demographic outcomes can be partitioned into contributions from both sources. Because these models are formulated as matrices, they are amenable to a complete sensitivity analysis. As more detailed and longer longitudinal studies are developed, age × stage-classified demography will become more common and more important.

Stochasticity, heterogeneity, and variance in longevity in human populations.

Inter-individual variance in longevity (or any other demographic outcome) may arise from heterogeneity or from individual stochasticity. Heterogeneity refers to differences among individuals in the demographic rates experienced at a given age or stage. Stochasticity refers to variation due to the random outcome of demographic rates applied to individuals with the same properties. The variance due to individual stochasticity can be calculated from a Markov chain description of the life cycle. The variance due to heterogeneity can be calculated from a multistate model that incorporates the heterogeneity. We show how to use this approach to decompose the variance in longevity into contributions from stochasticity and heterogeneous frailty for male and female cohorts from Sweden (1751-1899), France (1816-1903), and Italy (1872-1899), and also for a selection of period data for the same countries. Heterogeneity in mortality is described by the gamma-Gompertz-Makeham model, in which a gamma distributed "frailty" modifies a baseline Gompertz-Makeham mortality schedule. Model parameters were estimated by maximum likelihood for a range of starting ages. The estimates were used to construct an age×frailty-classified matrix model, from which we compute the variance of longevity and its components due to heterogeneous frailty and to individual stochasticity. The estimated fraction of the variance in longevity due to heterogeneous frailty (averaged over time) is less than 10% for all countries and for both sexes. These results suggest that most of the variance in human longevity arises from stochasticity, rather than from heterogeneous frailty.

High Resolution Spatial Analysis of Habitat Preference of Aedes Albopictus (Diptera: Culicidae) in an Urban Environment.

Over the past decades, the Asian tiger mosquito (Aedes albopictus (Skuse, 1895)) has emerged in many countries, and it has colonized new environments, including urban areas. The species is a nuisance and a potential vector of several human pathogens, and a better understanding of the habitat preferences of the species is needed for help in successful prevention and control. So far, the habitat preference in urban environments has not been studied in Southern European cities. In this paper, spatial statistical models were used to evaluate the relationship between egg abundances and land cover types on the campus of Sapienza University in Rome, which is taken as an example of a European urban habitat. Predictor variables included land cover types, classified in detail on a high resolution image, as well as solar radiation and month of capture. The models account for repeated measures in the same trap and are adjusted for meteorological circumstances. Vegetation and solar radiation were found to be positively related to the number of eggs. More specifically, trees were positively related to the number of eggs and the relationship with grass was negative. These findings are consistent with the species' known preference for shaded areas. The unexpected positive relationship with solar radiation is amply discussed in the paper. This study represents a first step toward a better understanding of the spatial distribution of Ae. albopictus in urban environments.

Modelling the potential spatial distribution of mosquito species using three different techniques.

BACKGROUND: Models for the spatial distribution of vector species are important tools in the assessment of the risk of establishment and subsequent spread of vector-borne diseases. The aims of this study are to define the environmental conditions suitable for several mosquito species through species distribution modelling techniques, and to compare the results produced with the different techniques. METHODS: Three different modelling techniques, i.e., non-linear discriminant analysis, random forest and generalised linear model, were used to investigate the environmental suitability in the Netherlands for three indigenous mosquito species (Culiseta annulata, Anopheles claviger and Ochlerotatus punctor). Results obtained with the three statistical models were compared with regard to: (i) environmental suitability maps, (ii) environmental variables associated with occurrence, (iii) model evaluation. RESULTS: The models indicated that precipitation, temperature and population density were associated with the occurrence of Cs. annulata and An. claviger, whereas land surface temperature and vegetation indices were associated with the presence of Oc. punctor. The maps produced with the three different modelling techniques showed consistent spatial patterns for each species, but differences in the ranges of the predictions. Non-linear discriminant analysis had lower predictions than other methods. The model with the best classification skills for all the species was the random forest model, with specificity values ranging from 0.89 to 0.91, and sensitivity values ranging from 0.64 to 0.95. CONCLUSIONS: We mapped the environmental suitability for three mosquito species with three different modelling techniques. For each species, the maps showed consistent spatial patterns, but the level of predicted environmental suitability differed; NLDA gave lower predicted probabilities of presence than the other two methods. The variables selected as important in the models were in agreement with the existing knowledge about these species. All model predictions had a satisfactory to excellent accuracy; best accuracy was obtained with random forest. The insights obtained can be used to gain more knowledge on vector and non-vector mosquito species. The output of this type of distribution modelling methods can, for example, be used as input for epidemiological models of vector-borne diseases.

Exploring the influence of host community composition on the outbreak potential of Anaplasma phagocytophilum and Borrelia burgdorferi s.l.

In large parts of the northern hemisphere, multiple deer species coexist, and management actions can strongly influence wild deer communities. Such changes may also indirectly influence other species in the community, such as small mammals and birds, because deer can have strong effects on their habitats and resources. Deer, small mammals and birds play an important role in the dynamics of tick-borne zoonotic diseases. It is, however, relatively underexplored how the abundance and composition of vertebrate communities may affect the outbreak potential, maintenance and circulation of tick-borne pathogens. In this study we focus on the outbreak potential by exploring how the basic reproduction number R0 for different tick-borne pathogens depends on host community composition. We used published data on co-varying roe deer (Capreolus capreolus) and fallow deer (Dama dama) densities following a hunting ban, and different small mammal and bird densities, to investigate how the change in host community influences the R0 of four tick-borne pathogens: one non-zoonotic, namely Anaplasma phagocytophilum ecotype 2, and three zoonotic, namely A. phagocytophilum ecotype 1, Borrelia afzelii and Borrelia garinii. We calculated R0 using a next generation matrix approach, and used elasticities to quantify the contributions to R0 of the different groups of host species. The value of R0 for A. phagocytophilum ecotype 1 was higher with high fallow deer density and low roe deer density, while it was the other way round for A. phagocytophilum ecotype 2. For B. afzelii, R0 was mostly related to the density of small mammals and for B. garinii it was mostly determined by bird density. Our results show that the effect of species composition is substantial in the outbreak potential of tick-borne pathogens. This implies that also management actions that change this composition, can (indirectly and unintentionally) affect the outbreak potential of tick-borne diseases.

Using mechanistic models to highlight research priorities for tick-borne zoonotic diseases: Improving our understanding of the ecology and maintenance of Kyasanur Forest Disease in India.

The risk of spillover of zoonotic diseases to humans is changing in response to multiple environmental and societal drivers, particularly in tropical regions where the burden of neglected zoonotic diseases is highest and land use change and forest conversion is occurring most rapidly. Neglected zoonotic diseases can have significant impacts on poor and marginalised populations in low-resource settings but ultimately receive less attention and funding for research and interventions. As such, effective control measures and interventions are often hindered by a limited ecological evidence base, which results in a limited understanding of epidemiologically relevant hosts or vectors and the processes that contribute to the maintenance of pathogens and spillover to humans. Here, we develop a generalisable next generation matrix modelling framework to better understand the transmission processes and hosts that have the greatest contribution to the maintenance of tick-borne diseases with the aim of improving the ecological evidence base and framing future research priorities for tick-borne diseases. Using this model we explore the relative contribution of different host groups and transmission routes to the maintenance of a neglected zoonotic tick-borne disease, Kyasanur Forest Disease Virus (KFD), in multiple habitat types. The results highlight the potential importance of transovarial transmission and small mammals and birds in maintaining this disease. This contradicts previous hypotheses that primates play an important role influencing the distribution of infected ticks. There is also a suggestion that risk could vary across different habitat types but currently more research is needed to evaluate this relationship. In light of these results, we outline the key knowledge gaps for this system and future research priorities that could inform effective interventions and control measures.

Inferring bovine tuberculosis transmission between cattle and badgers via the environment and risk mapping.

Bovine tuberculosis (bTB), caused by Mycobacterium bovis, is one of the most challenging and persistent health issues in many countries worldwide. In several countries, bTB control is complicated due to the presence of wildlife reservoirs of infection, i.e. European badger (Meles meles) in Ireland and the UK, which can transmit infection to cattle. However, a quantitative understanding of the role of cattle and badgers in bTB transmission is elusive, especially where there is spatial variation in relative density between badgers and cattle. Moreover, as these two species have infrequent direct contact, environmental transmission is likely to play a role, but the quantitative importance of the environment has not been assessed. Therefore, the objective of this study is to better understand bTB transmission between cattle and badgers via the environment in a spatially explicit context and to identify high-risk areas. We developed an environmental transmission model that incorporates both within-herd/territory transmission and between-species transmission, with the latter facilitated by badger territories overlapping with herd areas. Model parameters such as transmission rate parameters and the decay rate parameter of M. bovis were estimated by maximum likelihood estimation using infection data from badgers and cattle collected during a 4-year badger vaccination trial. Our estimation showed that the environment can play an important role in the transmission of bTB, with a half-life of M. bovis in the environment of around 177 days. Based on the estimated transmission rate parameters, we calculate the basic reproduction ratio (R) within a herd, which reveals how relative badger density dictates transmission. In addition, we simulated transmission in each small local area to generate a first between-herd R map that identifies high-risk areas.

Seasonal patterns and spatial variation of Borrelia burgdorferi (sensu lato) infections in Ixodes ricinus in the Netherlands.

BACKGROUND: The incidence of Lyme borreliosis varies over time and space through as yet incompletely understood mechanisms. In Europe, Lyme borreliosis is caused by infection with a Borrelia burgdorferi (s.l.) genospecies, which is primarily transmitted by a bite of Ixodes ricinus nymphs. The aim of this study was to investigate the spatial and temporal variation in nymphal infection prevalence of B. burgdorferi (s.l.) (NIP), density of questing nymphs (DON) and the resulting density of infected nymphs (DIN). METHODS: We investigated the infection rates in I. ricinus nymphs that were collected monthly between 2009 and 2016 in 12 locations in the Netherlands. Using generalized linear mixed models, we explored how the NIP, DON and DIN varied during the seasons, between years and between locations. We also determined the genospecies of the Borrelia infections and investigated whether the genospecies composition differed between locations. RESULTS: The overall NIP was 14.7%. A seasonal pattern in infection prevalence was observed, with higher estimated prevalences in the summer than in the spring and autumn. This, combined with higher nymphal densities in summer, resulted in a pronounced summer peak in the estimated DIN. Over the 7.5-year study period, a significant decrease in infection prevalence was found, as well as a significant increase in nymphal density. These two effects appear to cancel each other out; the density of infected nymphs, which is the product of NIP × DON, showed no significant trend over years. Mean infection prevalence (NIP, averaged over all years and all months) varied considerably between locations, ranging from 5 to 26%. Borrelia genospecies composition differed between locations: in some locations almost all infections consisted of B. afzelii, whereas other locations had more diverse genospecies compositions. CONCLUSION: In the Netherlands, the summer peak in DIN is a result of peaks in both NIP and DON. No significant trend in DIN was observed over the years of the study, and variations in DIN between locations were mostly a result of the variation in DON. There were considerable differences in acarological risk between areas in terms of infection prevalence and densities of ticks as well as in Borrelia genospecies composition.

Why Hantavirus Prevalence Does Not Always Increase With Host Density: Modeling the Role of Host Spatial Behavior and Maternal Antibodies.

For wildlife diseases, one often relies on host density to predict host infection prevalence and the subsequent force of infection to humans in the case of zoonoses. Indeed, if transmission is mainly indirect, i.e., by way of the environment, the force of infection is expected to increase with host density, yet the laborious field data supporting this theoretical claim are often absent. Hantaviruses are among those zoonoses that have been studied extensively over the past decades, as they pose a significant threat to humans. In Europe, the most widespread hantavirus is the Puumala virus (PUUV), which is carried by the bank vole and causes nephropathia epidemica (NE) in humans. Extensive field campaigns have been carried out in Central Finland to shed light on this supposed relationship between bank vole density and PUUV prevalence and to identify other drivers for the infection dynamics. This resulted in the surprising observation that the relationship between bank vole density and PUUV prevalence is not purely monotonic on an annual basis, contrary to what previous models predicted: a higher vole density does not necessary result in a higher infection prevalence, nor in an increased number of humans reported having NE. Here, we advance a novel individual-based spatially-explicit model which takes into account the immunity provided by maternal antibodies and which simulates the spatial behavior of the host, both possible causes for this discrepancy that were not accounted for in previous models. We show that the reduced prevalence in peak years can be attributed to transient immunity, and that the density-dependent spatial vole behavior, i.e., the fact that home ranges are smaller in high density years, plays only a minor role. The applicability of the model is not limited to the study and prediction of PUUV (and NE) occurrence in Europe, as it could be easily adapted to model other rodent-borne diseases, either with indirect or direct transmission.

Elasticity analysis in epidemiology: an application to tick-borne infections.

The application of projection matrices in population biology to plant and animal populations has a parallel in infectious disease ecology when next-generation matrices (NGMs) are used to characterize growth in numbers of infected hosts (R(0)). The NGM is appropriate for multi-host pathogens, where each matrix element represents the number of cases of one type of host arising from a single infected individual of another type. For projection matrices, calculations of the sensitivity and elasticity of the population growth rate to changes in the matrix elements has generated insight into plant and animal populations. These same perturbation analyses can be used for infectious disease systems. To illustrate this in detail we parameterized an NGM for seven tick-borne zoonoses and compared them in terms of the contributions to R(0) from three different routes of transmission between ticks, and between ticks and vertebrate hosts. The definition of host type may be the species of the host or the route of infection, or, as was the case for the set of tick-borne pathogens, a combination of species and the life stage at infection. This freedom means that there is a broad range of disease systems and questions for which the methodology is appropriate.

Temporal-Spatial Variation in Questing Tick Activity in the Netherlands: The Effect of Climatic and Habitat Factors.

Longitudinal studies are fundamental in the assessment of the effect of environmental factors on tick population dynamics. In this study, we use data from a 10-year study in 11 different locations in the Netherlands to gauge the effects of climatic and habitat factors on the temporal and spatial variation in questing tick activity. Marked differences in the total number of ticks were found between locations and between years. We investigated which climatic and habitat factors might explain this variation. No effects of climatic factors on the total number of ticks per year were observed, but we found a clear effect of temperature on the onset of tick activity. In addition, we found positive associations between (1) humus layer thickness and densities of all three stages, (2) moss and blackberry abundance and larval densities, and (3) blueberry abundance and densities of larva and nymphs. We conclude that climatic variables do not have a straightforward association with tick density in the Netherlands, but that winter and spring temperatures influence the onset of tick activity. Habitats with apparently similar vegetation types can still differ in tick population densities, indicating that local composition of vegetation and especially of wildlife is likely to contribute considerably to the spatial variation in tick densities.

Variance in animal longevity: contributions of heterogeneity and stochasticity.

Variance in longevity among individuals may arise as an effect of heterogeneity (differences in mortality rates experienced at the same age or stage) or as an effect of individual stochasticity (the outcome of random demographic events during the life cycle). Decomposing the variance into components due to heterogeneity and stochasticity is crucial for evolutionary analyses.In this study, we analyze longevity from ten studies of invertebrates in the laboratory, and use the results to partition the variance in longevity into its components. To do so, we fit finite mixtures of Weibull survival functions to each data set by maximum likelihood, using the EM algorithm. We used the Bayesian Information Criterion to select the most well supported model. The results of the mixture analysis were used to construct an age × stage-classified matrix model, with heterogeneity groups as stages, from which we calculated the variance in longevity and its components. Almost all data sets revealed evidence of some degree of heterogeneity. The median contribution of unobserved heterogeneity to the total variance was 35%, with the remaining 65% due to stochasticity. The differences among groups in mean longevity were typically on the order of 30% of the overall life expectancy. There was considerable variation among data sets in both the magnitude of heterogeneity and the proportion of variance due to heterogeneity, but no clear patterns were apparent in relation to sex, taxon, or environmental conditions.

Modelling West Nile virus transmission risk in Europe: effect of temperature and mosquito biotypes on the basic reproduction number.

West Nile virus (WNV) is a mosquito-borne flavivirus which has caused repeated outbreaks in humans in southern and central Europe, but thus far not in northern Europe. The main mosquito vector for WNV, Culex pipiens, consists of two behaviourally distinct biotypes, pipiens and molestus, which can form hybrids. Differences between biotypes, such as vector competence and host preference, could be important in determining the risk of WNV outbreaks. Risks for WNV establishment can be modelled with basic reproduction number (R 0) models. However, existing R 0 models have not differentiated between biotypes. The aim of this study was, therefore, to explore the role of temperature-dependent and biotype-specific effects on the risk of WNV establishment in Europe. We developed an R 0 model with temperature-dependent and biotype-specific parameters, and calculated R 0 values using the next-generation matrix for several scenarios relevant for Europe. In addition, elasticity analysis was done to investigate the contribution of each biotype to R 0. Global warming and increased mosquito-to-host ratios can possibly result in more intense WNV circulation in birds and spill-over to humans in northern Europe. Different contributions of the Cx. pipiens biotypes to R 0 shows the importance of including biotype-specific parameters in models for reliable WNV risk assessments.

Acarological Risk of Borrelia burgdorferi Sensu Lato Infections Across Space and Time in The Netherlands.

A longitudinal investigation on tick populations and their Borrelia infections in the Netherlands was undertaken between 2006 and 2011 with the aim to assess spatial and temporal patterns of the acarological risk in forested sites across the country and to assess variations in Borrelia genospecies diversity. Ticks were collected monthly in 11 sites and nymphs were examined for Borrelia infections. Tick populations expressed strong seasonal variations, with consistent and significant differences in mean tick densities between sites. Borrelia infections were present in all study sites, with a site-specific mean prevalence per month ranging from 7% to 26%. Prevalence was location-dependent and was not associated with tick densities. Mean Borrelia prevalence was lowest in January (4%), gradually increasing to reach a maximum (24%) in August. Borrelia afzelii represented 70% of all infections, with Borrelia burgdorferi sensu stricto, Borrelia garinii, and Borrelia valaisiana represented with 4%, 8%, and 10%, respectively. The density of infected nymphs and the proportional distribution of the four Borrelia genospecies, were significantly different between sites. The results show a consistent and significant spatial and temporal difference in acarological risk across the Netherlands.

R0 for vector-borne diseases: impact of the assumption for the duration of the extrinsic incubation period.

Mathematical modeling and notably the basic reproduction number R0 have become popular tools for the description of vector-borne disease dynamics. We compare two widely used methods to calculate the probability of a vector to survive the extrinsic incubation period. The two methods are based on different assumptions for the duration of the extrinsic incubation period; one method assumes a fixed period and the other method assumes a fixed daily rate of becoming infectious. We conclude that the outcomes differ substantially between the methods when the average life span of the vector is short compared to the extrinsic incubation period.

Towards a resource-based habitat approach for spatial modelling of vector-borne disease risks.

Given the veterinary and public health impact of vector-borne diseases, there is a clear need to assess the suitability of landscapes for the emergence and spread of these diseases. Current approaches for predicting disease risks neglect key features of the landscape as components of the functional habitat of vectors or hosts, and hence of the pathogen. Empirical-statistical methods do not explicitly incorporate biological mechanisms, whereas current mechanistic models are rarely spatially explicit; both methods ignore the way animals use the landscape (i.e. movement ecology). We argue that applying a functional concept for habitat, i.e. the resource-based habitat concept (RBHC), can solve these issues. The RBHC offers a framework to identify systematically the different ecological resources that are necessary for the completion of the transmission cycle and to relate these resources to (combinations of) landscape features and other environmental factors. The potential of the RBHC as a framework for identifying suitable habitats for vector-borne pathogens is explored and illustrated with the case of bluetongue virus, a midge-transmitted virus affecting ruminants. The concept facilitates the study of functional habitats of the interacting species (vectors as well as hosts) and provides new insight into spatial and temporal variation in transmission opportunities and exposure that ultimately determine disease risks. It may help to identify knowledge gaps and control options arising from changes in the spatial configuration of key resources across the landscape. The RBHC framework may act as a bridge between existing mechanistic and statistical modelling approaches.

Consequences of landscape fragmentation on Lyme disease risk: a cellular automata approach.

The abundance of infected Ixodid ticks is an important component of human risk of Lyme disease, and various empirical studies have shown that this is associated, at least in part, to landscape fragmentation. In this study, we aimed at exploring how varying woodland fragmentation patterns affect the risk of Lyme disease, through infected tick abundance. A cellular automata model was developed, incorporating a heterogeneous landscape with three interactive components: an age-structured tick population, a classical disease transmission function, and hosts. A set of simplifying assumptions were adopted with respect to the study objective and field data limitations. In the model, the landscape influences both tick survival and host movement. The validation of the model was performed with an empirical study. Scenarios of various landscape configurations (focusing on woodland fragmentation) were simulated and compared. Lyme disease risk indices (density and infection prevalence of nymphs) differed considerably between scenarios: (i) the risk could be higher in highly fragmented woodlands, which is supported by a number of recently published empirical studies, and (ii) grassland could reduce the risk in adjacent woodland, which suggests landscape fragmentation studies of zoonotic diseases should not focus on the patch-level woodland patterns only, but also on landscape-level adjacent land cover patterns. Further analysis of the simulation results indicated strong correlations between Lyme disease risk indices and the density, shape and aggregation level of woodland patches. These findings highlight the strong effect of the spatial patterns of local host population and movement on the spatial dynamics of Lyme disease risks, which can be shaped by woodland fragmentation. In conclusion, using a cellular automata approach is beneficial for modelling complex zoonotic transmission systems as it can be combined with either real world landscapes for exploring direct spatial effects or artificial representations for outlining possible empirical investigations.

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

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