Helminth ecological requirements shape the impact of climate change on the hazard of infection

Outbreaks and spread of infectious diseases are often associated with seasonality and environmental changes, including global warming. Free-living stages of soil-transmitted helminths are highly susceptible to climatic drivers; however, how multiple climatic variables affect helminth species, and the long-term consequences of these interactions, is poorly understood. We used experiments on nine trichostrongylid species of herbivores to develop a temperature- and humidity-dependent model of infection hazard, which was then implemented at the European scale under climate change scenarios. Intestinal and stomach helminths exhibited contrasting climatic responses, with the former group strongly affected by temperature while the latter primarily impacted by humidity. Among the demographic traits, larval survival heavily modulated the infection hazard. According to the specific climatic responses of the two groups, climate change is expected to generate differences in the seasonal and spatial shifts of the infection hazard and group co-circulation. In the future, an intensification of these trends could create new opportunities for species range expansion and co-occurrence at European central-northern latitudes.

Spatially explicit effective reproduction numbers from incidence and mobility data

Current methods for near real-time estimation of effective reproduction numbers from surveillance data overlook mobility fluxes of infectors and susceptible individuals within a spatially connected network (the metapopulation). Exchanges of infections among different communities may thus be misrepresented unless explicitly measured and accounted for in the renewal equations. Here, we first derive the equations that include spatially explicit effective reproduction numbers, ℛ_k(t), in an arbitrary community k. These equations embed a suitable connection matrix blending mobility among connected communities and mobility-related containment measures. Then, we propose a tool to estimate, in a Bayesian framework involving particle filtering, the values of ℛ_k(t) maximizing a suitable likelihood function reproducing observed patterns of infections in space and time. We validate our tools against synthetic data and apply them to real COVID-19 epidemiological records in a severely affected and carefully monitored Italian region. Differences arising between connected and disconnected reproduction numbers (the latter being calculated with existing methods, to which our formulation reduces by setting mobility to zero) suggest that current standards may be improved in their estimation of disease transmission over time.

Modeling the contribution of antibody attack rates to single and dual helminth infections in a natural system

Within-host models of infection can provide important insights into the processes that affect parasite spread and persistence in host populations. However, modeling can be limited by the availability of empirical data, a problem commonly encountered in natural systems. Here, we used six years of immune-infection observations of two gastrointestinal helminths (Trichostrongylus retortaeformis and Graphidium strigosum) from a population of European rabbits (Oryctolagus cuniculus) to develop an age-dependent, mathematical model that explicitly included species-specific and cross-reacting antibody (IgA and IgG) responses to each helminth in hosts with single or dual infections. Different models of single infection were formally compared to test alternative mechanisms of parasite regulation. The two models that best described single infections of each helminth species were then coupled through antibody cross-immunity to examine how the presence of one species could alter the host immune response to, and the within-host dynamics of, the other species. For both single infections, model selection suggested that either IgA or IgG responses could equally explain the observed parasite intensities by host age. However, the antibody attack rate and affinity level changed between the two helminths, it was stronger against T. retortaeformis than against G. strigosum and caused contrasting age-intensity profiles. When the two helminths coinfect the same host, we found variation of the species-specific antibody response to both species together with an asymmetric cross-immune response driven by IgG. Lower attack rate and affinity of antibodies in dual than single infections contributed to the significant increase of both helminth intensities. By combining mathematical modeling with immuno-infection data, our work provides a tractable model framework for disentangling some of the complexities generated by host-parasite and parasite-parasite interactions in natural systems.

Reframing Optimal Control Problems for Infectious Disease Management in Low-Income Countries

Optimal control theory can be a useful tool to identify the best strategies for the management of infectious diseases. In most of the applications to disease control with ordinary differential equations, the objective functional to be optimized is formulated in monetary terms as the sum of intervention costs and the cost associated with the burden of disease. We present alternate formulations that express epidemiological outcomes via health metrics and reframe the problem to include features such as budget constraints and epidemiological targets. These alternate formulations are illustrated with a compartmental cholera model. The alternate formulations permit us to better explore the sensitivity of the optimal control solutions to changes in available budget or the desired epidemiological target. We also discuss some limitations of comprehensive cost assessment in epidemiology.

The enemy of my enemy is my friend: Immune-mediated facilitation contributes to fitness of co-infecting helminths

The conceptual understanding of immune-mediated interactions between parasites is rooted in the theory of community ecology. One of the limitations of this approach is that most of the theory and empirical evidence has focused on resource or immune-mediated competition between parasites and yet there is ample evidence of positive interactions that could be generated by immune-mediated facilitation. We developed an immuno-epidemiological model and applied it to long-term data of two gastrointestinal helminths in two rabbit populations to investigate, through model testing, how immune-mediated mechanisms of parasite regulation could explain the higher intensities of both helminths in rabbits with dual than single infections. The model framework was selected and calibrated on rabbit population A and then validated on the nearby rabbit population B to confirm the consistency of the findings and the generality of the mechanisms. Simulations suggested that the higher intensities in rabbits with dual infections could be explained by a weakened or low species-specific IgA response and an asymmetric IgA cross-reaction. Simulations also indicated that rabbits with dual infections shed more free-living stages that survived for longer in the environment, implying greater transmission than stages from hosts with single infections. Temperature and humidity selectively affected the free-living stages of the two helminths. These patterns were comparable in the two rabbit populations and support the hypothesis that immune-mediated facilitation can contribute to greater parasite fitness and local persistence.

Across the deserts and sea: inter-individual variation in migration routes of south-central European barn swallows (Hirundo rustica)

BACKGROUND

The spatiotemporal organization of migratory routes of long-distance migrants results from trade-offs between minimizing the journey length and en route risk of migration-related mortality, which may be reduced by avoiding crossing inhospitable ecological barriers. Despite flourishing avian migration research in recent decades, little is still known about inter-individual variability in migratory routes, as well as the carry-over effects of spatial and temporal features of migration on subsequent migration stages.

METHODS

We reconstructed post- and pre-breeding migration routes, barrier crossing behaviour and non-breeding movements of the largest sample (N = 85) analysed to date of individual barn swallows breeding in south-central Europe, which were tracked using light-level geolocators.

RESULTS

Most birds spent their non-breeding period in the Congo basin in a single stationary area, but a small fraction of itinerant individuals reaching South Africa was also observed. Birds generally followed a 'clockwise loop migration pattern', moving through the central Mediterranean and the Sahara Desert during post-breeding (north to south) migration yet switching to a more western route, along the Atlantic coast of Africa, Iberia and western Mediterranean during the pre-breeding (south to north) migration. Southward migration was straighter and less variable, while northward migration was significantly faster despite the broader detour along the Atlantic coast and Iberia. These patterns showed limited sex-related variability. The timing of different circannual events was tightly linked with previous migration stages, considerably affecting migration route and speed of subsequent movements. Indeed, individuals departing late from Africa performed straighter and faster pre-breeding migrations, partly compensating for the initial departure delays, but likely at the cost of performing riskier movements across ecological barriers.

CONCLUSIONS

Different spatiotemporal migration strategies during post- and pre-breeding migration suggest that conditions en route may differ seasonally and allow for more efficient travelling along different migration corridors in either season. While highlighting patterns of inter-individual variability, our results support increasing evidence for widespread loop migration patterns among Afro-Palearctic avian migrants. Also, they suggest that carry-over effects acting across different phases of the annual cycle of migratory species can have major impacts on evolutionary processes.

Optimal control of the spatial allocation of COVID-19 vaccines: Italy as a case study

While campaigns of vaccination against SARS-CoV-2 are underway across the world, communities face the challenge of a fair and effective distribution of a limited supply of doses. Current vaccine allocation strategies are based on criteria such as age or risk. In the light of strong spatial heterogeneities in disease history and transmission, we explore spatial allocation strategies as a complement to existing approaches. Given the practical constraints and complex epidemiological dynamics, designing effective vaccination strategies at a country scale is an intricate task. We propose a novel optimal control framework to derive the best possible vaccine allocation for given disease transmission projections and constraints on vaccine supply and distribution logistics. As a proof-of-concept, we couple our framework with an existing spatially explicit compartmental COVID-19 model tailored to the Italian geographic and epidemiological context. We optimize the vaccine allocation on scenarios of unfolding disease transmission across the 107 provinces of Italy, from January to April 2021. For each scenario, the optimal solution significantly outperforms alternative strategies that prioritize provinces based on incidence, population distribution, or prevalence of susceptibles. Our results suggest that the complex interplay between the mobility network and the spatial heterogeneities implies highly non-trivial prioritization strategies for effective vaccination campaigns. Our work demonstrates the potential of optimal control for complex and heterogeneous epidemiological landscapes at country, and possibly global, scales.

Data-driven analysis of amino acid change dynamics timely reveals SARS-CoV-2 variant emergence

Since its emergence in late 2019, the diffusion of SARS-CoV-2 is associated with the evolution of its viral genome. The co-occurrence of specific amino acid changes, collectively named ‘virus variant’, requires scrutiny (as variants may hugely impact the agent’s transmission, pathogenesis, or antigenicity); variant evolution is studied using phylogenetics. Yet, never has this problem been tackled by digging into data with ad hoc analysis techniques. Here we show that the emergence of variants can in fact be traced through data-driven methods, further capitalizing on the value of large collections of SARS-CoV-2 sequences. For all countries with sufficient data, we compute weekly counts of amino acid changes, unveil time-varying clusters of changes with similar—rapidly growing—dynamics, and then follow their evolution. Our method succeeds in timely associating clusters to variants of interest/concern, provided their change composition is well characterized. This allows us to detect variants’ emergence, rise, peak, and eventual decline under competitive pressure of another variant. Our early warning system, exclusively relying on deposited sequences, shows the power of big data in this context, and concurs to calling for the wide spreading of public SARS-CoV-2 genome sequencing for improved surveillance and control of the COVID-19 pandemic.

A parsimonious mechanistic model of reproductive and vegetative growth in fruit trees predicts consequences of fruit thinning and branch pruning

Productivity of fruit tree crops depends on the interaction between plant physiology, environmental conditions and agricultural practices. We develop a mechanistic model of fruit tree crops that reliable simulates the dynamics of variables of interest for growers and consequences of agricultural practices while relying on a minimal number of inputs and parameters. The temporal dynamics of carbon content in the different organs (i.e., shoots-S, roots-R and fruits-F) are the result of photosynthesis by S, nutrient supply by R, respiration by S, R and F, competition among different organs, photoperiod and initial system conditions partially controlled by cultural practices. We calibrate model parameters and evaluate model predictions using unpublished data from a peach (Prunus persica) experimental orchard with trees subjected to different levels of branch pruning and fruit thinning. Fiinally, we evaluate the consequences of different combinations of pruning and thinning intensities within a multi-criteria analysis. The predictions are in good agreement with the experimental measurements and for the different conditions (pruning and thinning). Our simulations indicate that thinning and pruning practices actually used by growers provide the best compromise between total shoot production, which impacts next year's abundance of shoots and fruits, and current year's fruit production in terms of quantity (yield) and quality (average fruit size). This suggests that growers are not only interested in maximizing current year's yield but also in its quality and its durability. The present work provides for modelers a system of equations based on acknowledged principles of plant science easily modifiable for different purposes. For horticulturists, it gives insights on the potentialities of pruning and thinning. For ecologists, it provides a transparent quantitative framework that can be coupled with biotic and abiotic stressors.

The dynamics of microplastics and associated contaminants: Data-driven Lagrangian and Eulerian modelling approaches in the Mediterranean Sea

Plastic pollution is widespread in the global oceans, but at the same time several other types of hydrophobic pollutants contaminate the marine environment. As more and more evidence highlights, microplastics and polluting chemicals are intertwined via adsorption/desorption processes. A thorough assessment of their total impact on marine ecosystems thus requires that these two kinds of pollution are not considered separately. Here we compare the outcomes of two complementary, data-driven modelling approaches for microplastic dispersal and for Plastic-Related Organic Pollutants (PROPs) in the marine environment. Focusing on the Mediterranean Sea, we simulate two years of Lagrangian particle tracking to map microplastic dispersion from the most impacting sources of pollution (i.e. coastal areas, the watersheds of major rivers, and fishing activities). Our particle sources are data-informed by national census data, hydrological regimes, and vessel tracking data to account for spatial and temporal variability of mismanaged plastic waste generation. These particle-based simulations are complemented with a simulation of the dynamics of primary pollutants in the sea, obtained via an advection-diffusion Eulerian model. While providing further understanding of the spatiotemporal distribution of microplastics and the dynamics of PROPs at a Mediterranean-wide scale, our results call for the development of novel integrated modelling approaches aimed at coupling the dynamics of microplastics with the chemical exchanges occurring through them, thus promoting a holistic description of marine plastic pollution.

The epidemicity index of recurrent SARS-CoV-2 infections

Several indices can predict the long-term fate of emerging infectious diseases and the effect of their containment measures, including a variety of reproduction numbers (e.g. [Formula: see text]). Other indices evaluate the potential for transient increases of epidemics eventually doomed to disappearance, based on generalized reactivity analysis. They identify conditions for perturbations to a stable disease-free equilibrium ([Formula: see text]) to grow, possibly causing significant damage. Here, we introduce the epidemicity index e0, a threshold-type indicator: if e0 > 0, initial foci may cause infection peaks even if [Formula: see text]. Therefore, effective containment measures should achieve a negative epidemicity index. We use spatially explicit models to rank containment measures for projected evolutions of the ongoing pandemic in Italy. There, we show that, while the effective reproduction number was below one for a sizable timespan, epidemicity remained positive, allowing recurrent infection flare-ups well before the major epidemic rebounding observed in the fall.

Within-host mechanisms of immune regulation explain the contrasting dynamics of two helminth species in both single and dual infections

Variation in the intensity and duration of infections is often driven by variation in the network and strength of host immune responses. While many of the immune mechanisms and components are known for parasitic helminths, how these relationships change from single to multiple infections and impact helminth dynamics remains largely unclear. Here, we used laboratory data from a rabbit-helminth system and developed a within-host model of infection to investigate different scenarios of immune regulation in rabbits infected with one or two helminth species. Model selection suggests that the immunological pathways activated against Trichostrongylus retortaeformis and Graphidium strigosum are similar. However, differences in the strength of these immune signals lead to the contrasting dynamics of infections, where the first parasite is rapidly cleared and the latter persists with high intensities. In addition to the reactions identified in single infections, rabbits with both helminths also activate new pathways that asymmetrically affect the dynamics of the two species. These new signals alter the intensities but not the general trend of the infections. The type of interactions described can be expected in many other host-helminth systems. Our immune framework is flexible enough to capture different mechanisms and their complexity, and provides essential insights to the understanding of multi-helminth infections.

The geography of COVID-19 spread in Italy and implications for the relaxation of confinement measures

The pressing need to restart socioeconomic activities locked-down to control the spread of SARS-CoV-2 in Italy must be coupled with effective methodologies to selectively relax containment measures. Here we employ a spatially explicit model, properly attentive to the role of inapparent infections, capable of: estimating the expected unfolding of the outbreak under continuous lockdown (baseline trajectory); assessing deviations from the baseline, should lockdown relaxations result in increased disease transmission; calculating the isolation effort required to prevent a resurgence of the outbreak. A 40% increase in effective transmission would yield a rebound of infections. A control effort capable of isolating daily  ~5.5% of the exposed and highly infectious individuals proves necessary to maintain the epidemic curve onto the decreasing baseline trajectory. We finally provide an ex-post assessment based on the epidemiological data that became available after the initial analysis and estimate the actual disease transmission that occurred after weakening the lockdown.

Modelled effects of prawn aquaculture on poverty alleviation and schistosomiasis control

Recent evidence suggests that snail predators may aid efforts to control the human parasitic disease schistosomiasis by eating aquatic snail species that serve as intermediate hosts of the parasite. Potential synergies between schistosomiasis control and aquaculture of giant prawns are evaluated using an integrated bio-economic-epidemiologic model. Combinations of stocking density and aquaculture cycle length that maximize cumulative, discounted profit are identified for two prawn species in sub-Saharan Africa: the endemic, non-domesticated Macrobrachium vollenhovenii, and the non-native, domesticated Macrobrachium rosenbergii. At profit maximizing densities, both M. rosenbergii and M. vollenhovenii may substantially reduce intermediate host snail populations and aid schistosomiasis control efforts. Control strategies drawing on both prawn aquaculture to reduce intermediate host snail populations and mass drug administration to treat infected individuals are found to be superior to either strategy alone. Integrated aquaculture-based interventions can be a win-win strategy in terms of health and sustainable development in schistosomiasis endemic regions of the world.

Spread and dynamics of the COVID-19 epidemic in Italy: Effects of emergency containment measures

The spread of coronavirus disease 2019 (COVID-19) in Italy prompted drastic measures for transmission containment. We examine the effects of these interventions, based on modeling of the unfolding epidemic. We test modeling options of the spatially explicit type, suggested by the wave of infections spreading from the initial foci to the rest of Italy. We estimate parameters of a metacommunity Susceptible-Exposed-Infected-Recovered (SEIR)-like transmission model that includes a network of 107 provinces connected by mobility at high resolution, and the critical contribution of presymptomatic and asymptomatic transmission. We estimate a generalized reproduction number ([Formula: see text] = 3.60 [3.49 to 3.84]), the spectral radius of a suitable next-generation matrix that measures the potential spread in the absence of containment interventions. The model includes the implementation of progressive restrictions after the first case confirmed in Italy (February 21, 2020) and runs until March 25, 2020. We account for uncertainty in epidemiological reporting, and time dependence of human mobility matrices and awareness-dependent exposure probabilities. We draw scenarios of different containment measures and their impact. Results suggest that the sequence of restrictions posed to mobility and human-to-human interactions have reduced transmission by 45% (42 to 49%). Averted hospitalizations are measured by running scenarios obtained by selectively relaxing the imposed restrictions and total about 200,000 individuals (as of March 25, 2020). Although a number of assumptions need to be reexamined, like age structure in social mixing patterns and in the distribution of mobility, hospitalization, and fatality, we conclude that verifiable evidence exists to support the planning of emergency measures.

Protection reveals density-dependent dynamics in fish populations: A case study in the central Mediterranean

Casting light on how the interaction between protection and density dependence affects fish population dynamics is critical for understanding the effectiveness of marine protected areas (MPAs). We developed a framework based on nonparametric statistics, model selection and multi-model inference to contrast alternative hypotheses about the effect of density dependence on demographic dynamics under protected and unprotected conditions. We trialed it using a 12-year long time series of white seabream (Diplodus sargus sargus) population density within the no-take zone of Torre Guaceto MPA (Italy) and at two nearby unprotected locations. Then, we showed how the demographic models obtained can be used to assess the consequences of protection on population viability. Population dynamics were significantly influenced by fish density within the MPA and at one of the unprotected locations, where demography is possibly driven by directional recruitment subsidy from the MPA. The comparison of population growth rates within and outside the MPA suggests that in unprotected conditions the fishery may remove a fraction between 40 and 70% of the population each year. The population viability analysis pointed out that, while the probability that the population becomes depleted (i.e. undergoes a local, temporary quasi-extinction) is high in unprotected locations, it is negligible within the no-take zone of the MPA.

When resolution does matter: Modelling indirect contacts in dairy farms at different levels of detail

Animal exchanges are considered the major pathway for between-farm transmission of many livestock infectious diseases. Yet, vehicles and operators visiting several farms during routine activities can also contribute to disease spread. Indeed, if contaminated, they can act as mechanical vectors of fomites, generating indirect contacts between visited farms. While data on animal exchanges is often available in national databases, information about the daily itineraries of trucks and operators is rare because difficult to obtain. Thus, some unavoidable approximations have been frequently introduced in the description of indirect contacts in epidemic models. Here, we showed that the level of detail in such description can significantly affect the predictions on disease dynamics. Our analyses focused on the potential spread of a disease in a dairy farm system subject of a comprehensive data collection campaign on calf transportations. We developed two temporal multilayer networks to model between-farm contacts generated by either animal exchanges (direct contacts) and connections operated by trucks moving calves (indirect contacts). The complete model used the full knowledge of the daily trucks' itineraries, while the partial informed one used only a subset of such available information. To account for various conditions of pathogen survival ability and effectiveness of cleaning operations, we performed a sensitivity analysis on trucks' contamination period. An accurate description of indirect contacts was crucial both to correctly predict the final size of epidemics and to identify the seed farms responsible for generating the most severe outbreaks. The importance of detailed information emerged even more clearly in the case of short contamination periods. Our conclusions could be extended to between-farm contacts generated by other vehicles and operators. Overcoming these information gaps would be decisive for a deeper understanding of epidemic spread in livestock and to develop effective control plans.

Reconstruction of long-distance bird migration routes using advanced machine learning techniques on geolocator data

Geolocators are a well-established technology to reconstruct migration routes of animals that are too small to carry satellite tags (e.g. passerine birds). These devices record environmental light-level data that enable the reconstruction of daily positions from the time of twilight. However, all current methods for analysing geolocator data require manual pre-processing of raw records to eliminate twilight events showing unnatural variation in light levels, a step that is time-consuming and must be accomplished by a trained expert. Here, we propose and implement advanced machine learning techniques to automate this procedure and we apply them to 108 migration tracks of barn swallows ( Hirundo rustica). We show that routes reconstructed from the automated pre-processing are comparable to those obtained from manual selection accomplished by a human expert. This raises the possibility of fully automating light-level geolocator data analysis and possibly analysing the large amount of data already collected on several species.

Conditions for transient epidemics of waterborne disease in spatially explicit systems

Waterborne diseases are a diverse family of infections transmitted through ingestion of-or contact with-water infested with pathogens. Outbreaks of waterborne infections often show well-defined spatial signatures that are typically linked to local eco-epidemiological conditions, water-mediated pathogen transport and human mobility. In this work, we apply a spatially explicit network model describing the transmission cycle of waterborne pathogens to determine invasion conditions in metacommunities endowed with a realistic spatial structure. Specifically, we aim to define conditions under which pathogens can temporarily colonize a set of human communities, thus triggering a transient epidemic outbreak. To that end, we apply generalized reactivity analysis, a recently developed methodological framework for the study of transient dynamics in ecological systems subject to external perturbations. The study of pathogen invasion is complemented by the detection of the spatial signatures associated with the perturbations to a disease-free system that are expected to be amplified the most over different time scales. Understanding the drivers of waterborne disease dynamics over time scales that are relevant to epidemic and/or endemic transmission is a crucial, cross-disciplinary challenge, as large portions of the developing world still struggle to cope with the burden of these infections.

Barn swallows long-distance migration occurs between significantly temperature-correlated areas

Organisms are routinely confronted with crucial decisions on the best time and place to perform fundamental activities. However, unpredictable spatio-temporal variation in ecological factors makes life-history optimization difficult particularly for long-distance migrants, which are putatively blind of conditions thousands of kilometers and weeks ahead along their journey. Here we challenge, on a hierarchy of geographical scales, the common wisdom that migratory birds have no clue to ecological conditions at destination. Using ringing data of the inter-continental migrating barn swallow (Hirundo rustica), we show that temperatures at breeding sites and at times of arrival from migration are more correlated with those at actual wintering sites and at times of departure than with those at other sites and at periods before/after departure. Hence, individual swallows have clues to adjust timing of spring migration based on expected conditions at destination, and they apparently choose wintering sites to increase availability of such information.

Epidemicity thresholds for water-borne and water-related diseases

Determining the conditions that favor pathogen establishment in a host community is key to disease control and eradication. However, focusing on long-term dynamics alone may lead to an underestimation of the threats imposed by outbreaks triggered by short-term transient phenomena. Achieving an effective epidemiological response thus requires to look at different timescales, each of which may be endowed with specific management objectives. In this work we aim to determine epidemicity thresholds for some prototypical examples of water-borne and water-related diseases, a diverse family of infections transmitted either directly through water infested with pathogens or by vectors whose lifecycles are closely associated with water. From a technical perspective, while conditions for endemicity are determined via stability analysis, epidemicity thresholds are defined through generalized reactivity analysis, a recently proposed method that allows the study of the short-term instability properties of ecological systems. Understanding the drivers of water-borne and water-related disease dynamics over timescales that may be relevant to epidemic and/or endemic transmission is a challenge of the utmost importance, as large portions of the developing world are still struggling with the burden imposed by these infections.

The spatial spread of schistosomiasis: A multidimensional network model applied to Saint-Louis region, Senegal

Schistosomiasis is a parasitic, water-related disease that is prevalent in tropical and subtropical areas of the world, causing severe and chronic consequences especially among children. Here we study the spatial spread of this disease within a network of connected villages in the endemic region of the Lower Basin of the Senegal River, in Senegal. The analysis is performed by means of a spatially explicit metapopulation model that couples local-scale eco-epidemiological dynamics with spatial mechanisms related to human mobility (estimated from anonymized mobile phone records), snail dispersal and hydrological transport of schistosome larvae along the main water bodies of the region. Results show that the model produces epidemiological patterns consistent with field observations, and point out the key role of spatial connectivity on the spread of the disease. These findings underline the importance of considering different transport pathways in order to elaborate disease control strategies that can be effective within a network of connected populations.

Heterogeneity in schistosomiasis transmission dynamics

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Transmission dynamics of schistosomiasis presents multiple heterogeneity sources.

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A comprehensive framework for heterogeneous disease transmission is proposed.

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Heterogeneous multigroup communities can be more prone to parasite transmission.

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Presence of multiple water sources can hinder parasite transmission.

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Spatial and temporal heterogeneities can have nontrivial implications for endemicity.

Simple models of disease propagation often disregard the effects of transmission heterogeneity on the ecological and epidemiological dynamics associated with host-parasite interactions. However, for some diseases like schistosomiasis, a widespread parasitic infection caused by Schistosoma worms, accounting for heterogeneity is crucial to both characterize long-term dynamics and evaluate opportunities for disease control. Elaborating on the classic Macdonald model for macroparasite transmission, we analyze families of models including explicit descriptions of heterogeneity related to differential transmission risk within a community, water contact patterns, the distribution of the snail host population, human mobility, and the seasonal fluctuations of the environment. Through simple numerical examples, we show that heterogeneous multigroup communities may be more prone to schistosomiasis than homogeneous ones, that the availability of multiple water sources can hinder parasite transmission, and that both spatial and temporal heterogeneities may have nontrivial implications for disease endemicity. Finally, we discuss the implications of heterogeneity for disease control. Although focused on schistosomiasis, results from this study may apply as well to other parasitic infections with complex transmission cycles, such as cysticercosis, dracunculiasis and fasciolosis.

Understanding large-scale, long-term larval connectivity patterns: The case of the Northern Line Islands in the Central Pacific Ocean

Protecting key hotspots of marine biodiversity is essential to maintain ecosystem services at large spatial scales. Protected areas serve not only as sources of propagules colonizing other habitats, but also as receptors, thus acting as protected nurseries. To quantify the geographical extent and the temporal persistence of ecological benefits resulting from protection, we investigate larval connectivity within a remote archipelago, characterized by a strong spatial gradient of human impact from pristine to heavily exploited: the Northern Line Islands (NLIs), including part of the Pacific Remote Islands Marine National Monument (PRI-MNM). Larvae are described as passive Lagrangian particles transported by oceanic currents obtained from a oceanographic reanalysis. We compare different simulation schemes and compute connectivity measures (larval exchange probabilities and minimum/average larval dispersal distances from target islands). To explore the role of PRI-MNM in protecting marine organisms with pelagic larval stages, we drive millions of individual-based simulations for various Pelagic Larval Durations (PLDs), in all release seasons, and over a two-decades time horizon (1991-2010). We find that connectivity in the NLIs is spatially asymmetric and displays significant intra- and inter-annual variations. The islands belonging to PRI-MNM act more as sinks than sources of larvae, and connectivity is higher during the winter-spring period. In multi-annual analyses, yearly averaged southward connectivity significantly and negatively correlates with climatological anomalies (El Niño). This points out a possible system fragility and susceptibility to global warming. Quantitative assessments of large-scale, long-term marine connectivity patterns help understand region-specific, ecologically relevant interactions between islands. This is fundamental for devising scientifically-based protection strategies, which must be space- and time-varying to cope with the challenges posed by the concurrent pressures of human exploitation and global climate change.

Population genomics meet Lagrangian simulations: Oceanographic patterns and long larval duration ensure connectivity among Paracentrotus lividus populations in the Adriatic and Ionian seas

Connectivity between populations influences both their dynamics and the genetic structuring of species. In this study, we explored connectivity patterns of a marine species with long-distance dispersal, the edible common sea urchin Paracentrotus lividus, focusing mainly on the Adriatic-Ionian basins (Central Mediterranean). We applied a multidisciplinary approach integrating population genomics, based on 1,122 single nucleotide polymorphisms (SNPs) obtained from 2b-RAD in 275 samples, with Lagrangian simulations performed with a biophysical model of larval dispersal. We detected genetic homogeneity among eight population samples collected in the focal Adriatic-Ionian area, whereas weak but significant differentiation was found with respect to two samples from the Western Mediterranean (France and Tunisia). This result was not affected by the few putative outlier loci identified in our dataset. Lagrangian simulations found a significant potential for larval exchange among the eight Adriatic-Ionian locations, supporting the hypothesis of connectivity of P. lividus populations in this area. A peculiar pattern emerged from the comparison of our results with those obtained from published P. lividus cytochrome b (cytb) sequences, the latter revealing genetic differentiation in the same geographic area despite a smaller sample size and a lower power to detect differences. The comparison with studies conducted using nuclear markers on other species with similar pelagic larval durations in the same Adriatic-Ionian locations indicates species-specific differences in genetic connectivity patterns and warns against generalizing single-species results to the entire community of rocky shore habitats.

A Theoretical Analysis of the Geography of Schistosomiasis in Burkina Faso Highlights the Roles of Human Mobility and Water Resources Development in Disease Transmission

We study the geography of schistosomiasis across Burkina Faso by means of a spatially explicit model of water-based disease dynamics. The model quantitatively addresses the geographic stratification of disease burden in a novel framework by explicitly accounting for drivers and controls of the disease, including spatial information on the distributions of population and infrastructure, jointly with a general description of human mobility and climatic/ecological drivers. Spatial patterns of disease are analysed by the extraction and the mapping of suitable eigenvectors of the Jacobian matrix subsuming the stability of the disease-free equilibrium. The relevance of the work lies in the novel mapping of disease burden, a byproduct of the parametrization induced by regional upscaling, by model-guided field validations and in the predictive scenarios allowed by exploiting the range of possible parameters and processes. Human mobility is found to be a primary control at regional scales both for pathogen invasion success and the overall distribution of disease burden. The effects of water resources development highlighted by systematic reviews are accounted for by the average distances of human settlements from water bodies that are habitats for the parasite’s intermediate host. Our results confirm the empirical findings about the role of water resources development on disease spread into regions previously nearly disease-free also by inspection of empirical prevalence patterns. We conclude that while the model still needs refinements based on field and epidemiological evidence, the proposed framework provides a powerful tool for large-scale public health planning and schistosomiasis management.

Dynamical models of schistosomiasis infections, even spatially explicit ones, have so far only addressed spatial scales encompassing at best a few villages and the disease transmission impacts of related short-range human mobility. Here, we build from existing models of disease dynamics and spread, including a proxy of the ecology of the intermediate host of the parasite, and from generalized reproduction numbers of SIR-type systems developed for epidemics of waterborne disease, to set up large-scale projections of spatial patterns of the disease at whole country level. We ground our study in Burkina Faso in sub-Saharan Africa, and its model of social and economic development including the infrastructure built to exploit water resources, especially irrigation schemes, which have been empirically linked to enhanced disease burden. We make extensive use of remotely sensed and field data, and capitalize on ecohydrological insight. We suggest that reliable nationwide patterns of disease burden can be projected in relation to the key roles of human mobility and water resources development subsuming exposure, and claim that the case at hand provides an insightful example towards the integration of development and environmental thinking not confined to ad-hoc indicators of human development.

On the predictive ability of mechanistic models for the Haitian cholera epidemic

Predictive models of epidemic cholera need to resolve at suitable aggregation levels spatial data pertaining to local communities, epidemiological records, hydrologic drivers, waterways, patterns of human mobility and proxies of exposure rates. We address the above issue in a formal model comparison framework and provide a quantitative assessment of the explanatory and predictive abilities of various model settings with different spatial aggregation levels and coupling mechanisms. Reference is made to records of the recent Haiti cholera epidemics. Our intensive computations and objective model comparisons show that spatially explicit models accounting for spatial connections have better explanatory power than spatially disconnected ones for short-to-intermediate calibration windows, while parsimonious, spatially disconnected models perform better with long training sets. On average, spatially connected models show better predictive ability than disconnected ones. We suggest limits and validity of the various approaches and discuss the pathway towards the development of case-specific predictive tools in the context of emergency management.

The temporal patterns of disease severity and prevalence in schistosomiasis

Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra- and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility.

Connectivity interplays with age in shaping contagion over networks with vital dynamics

The effects of network topology on the emergence and persistence of infectious diseases have been broadly explored in recent years. However, the influence of the vital dynamics of the hosts (i.e., birth-death processes) on the network structure, and their effects on the pattern of epidemics, have received less attention in the scientific community. Here, we study Susceptible-Infected-Recovered(-Susceptible) [SIR(S)] contact processes in standard networks (of Erdös-Rényi and Barabási-Albert type) that are subject to host demography. Accounting for the vital dynamics of hosts is far from trivial, and it causes the scale-free networks to lose their characteristic fat-tailed degree distribution. We introduce a broad class of models that integrate the birth and death of individuals (nodes) with the simplest mechanisms of infection and recovery, thus generating age-degree structured networks of hosts that interact in a complex manner. In our models, the epidemiological state of each individual may depend both on the number of contacts (which changes through time because of the birth-death process) and on its age, paving the way for a possible age-dependent description of contagion and recovery processes. We study how the proportion of infected individuals scales with the number of contacts among them. Rather unexpectedly, we discover that the result of highly connected individuals at the highest risk of infection is not as general as commonly believed. In infections that confer permanent immunity to individuals of vital populations (SIR processes), the nodes that are most likely to be infected are those with intermediate degrees. Our age-degree structured models allow such findings to be deeply analyzed and interpreted, and they may aid in the development of effective prevention policies.

Metapopulation persistence and species spread in river networks

River networks define ecological corridors characterised by unidirectional streamflow, which may impose downstream drift to aquatic organisms or affect their movement. Animals and plants manage to persist in riverine ecosystems, though, which in fact harbour high biological diversity. Here, we study metapopulation persistence in river networks analysing stage-structured populations that exploit different dispersal pathways, both along-stream and overland. Using stability analysis, we derive a novel criterion for metapopulation persistence in arbitrarily complex landscapes described as spatial networks. We show how dendritic geometry and overland dispersal can promote population persistence, and that their synergism provides an explanation of the so-called `drift paradox'. We also study the geography of the initial spread of a species and place it in the context of biological invasions. Applications concerning the persistence of stream salamanders in the Shenandoah river, and the spread of two invasive species in the Mississippi-Missouri are also discussed.

Spatially explicit conditions for waterborne pathogen invasion

Waterborne pathogens cause many possibly lethal human diseases. We derive the condition for pathogen invasion and subsequent disease outbreak in a territory with specific, space-inhomogeneous characteristics (hydrological, ecological, demographic, and epidemiological). The criterion relies on a spatially explicit model accounting for the density of susceptible and infected individuals and the pathogen concentration in a network of communities linked by human mobility and the water system. Pathogen invasion requires that a dimensionless parameter, the dominant eigenvalue of a generalized reproductive matrix J0, be larger than unity. Conditions for invasion are studied while crucial parameters (population density distribution, contact and water contamination rates, pathogen growth rates) and the characteristics of the networks (connectivity, directional transport, water retention times, mobility patterns) are varied. We analyze both simple, prototypical test cases and realistic landscapes, in which optimal channel networks mimic the water systems and gravitational models describe human mobility. Also, we show that the dominant eigenvector of J0 effectively portrays the geography of epidemic outbreaks, that is, the areas of the studied territory that will be initially affected by an epidemic. This is important for planning an efficient spatial allocation of interventions (e.g., improving sanitation and providing emergency aid and medicines).

Modelling cholera epidemics: the role of waterways, human mobility and sanitation

We investigate the role of human mobility as a driver for long-range spreading of cholera infections, which primarily propagate through hydrologically controlled ecological corridors. Our aim is to build a spatially explicit model of a disease epidemic, which is relevant to both social and scientific issues. We present a two-layer network model that accounts for the interplay between epidemiological dynamics, hydrological transport and long-distance dissemination of the pathogen Vibrio cholerae owing to host movement, described here by means of a gravity-model approach. We test our model against epidemiological data recorded during the extensive cholera outbreak occurred in the KwaZulu-Natal province of South Africa during 2000-2001. We show that long-range human movement is fundamental in quantifying otherwise unexplained inter-catchment transport of V. cholerae, thus playing a key role in the formation of regional patterns of cholera epidemics. We also show quantitatively how heterogeneously distributed drinking water supplies and sanitation conditions may affect large-scale cholera transmission, and analyse the effects of different sanitation policies.

Central-place seed foraging and vegetation patterns

We investigate how central-place seed foragers with a nest in the proximity of one or more seed sources determine the formation of different vegetation patterns. In particular, we discuss the ecological conditions that lead to the formation of hump-shaped (Janzen-Connell) patterns in a two-dimensional landscape. Our analysis shows that central-place predation can generate Janzen-Connell patterns even if predators' movement strategies are exclusively based on resource abundance, both in the single-plant/single-nest case and in a forest with several seed sources. We also show that social foraging may either promote or work against the formation of Janzen-Connell patterns, depending upon the way foragers take advantage of social interactions.

On spatially explicit models of cholera epidemics

We generalize a recently proposed model for cholera epidemics that accounts for local communities of susceptibles and infectives in a spatially explicit arrangement of nodes linked by networks having different topologies. The vehicle of infection (Vibrio cholerae) is transported through the network links that are thought of as hydrological connections among susceptible communities. The mathematical tools used are borrowed from general schemes of reactive transport on river networks acting as the environmental matrix for the circulation and mixing of waterborne pathogens. Using the diffusion approximation, we analytically derive the speed of propagation for travelling fronts of epidemics on regular lattices (either one-dimensional or two-dimensional) endowed with uniform population density. Power laws are found that relate the propagation speed to the diffusion coefficient and the basic reproduction number. We numerically obtain the related, slower speed of epidemic spreading for more complex, yet realistic river structures such as Peano networks and optimal channel networks. The analysis of the limit case of uniformly distributed population sizes proves instrumental in establishing the overall conditions for the relevance of spatially explicit models. To that extent, the ratio between spreading and disease outbreak time scales proves the crucial parameter. The relevance of our results lies in the major differences potentially arising between the predictions of spatially explicit models and traditional compartmental models of the susceptible-infected-recovered (SIR)-like type. Our results suggest that in many cases of real-life epidemiological interest, time scales of disease dynamics may trigger outbreaks that significantly depart from the predictions of compartmental models.

Local resource competition and the skewness of the sex ratio: a demographic model

Most animal populations are characterized by balanced sex ratios, but there exist several exceptions in which the sex ratio at birth is skewed. An interesting hypothesis proposed by Clark (1978) to explain male-biased sex ratios is the local resource competition theory: the bias may be expected in those species in which males disperse more than females, which are thus more prone to local competition for resources. Here we discuss some of the ideas underlying Clark's theory using a spatially explicit approach. In particular, we focus on the role of spatiotemporal heterogeneity as a possible determinant of biased sex ratios. We model spatially structured semelparous populations where either Ricker density dependence or environmental stochasticity can generate irregular spatiotemporal patterns. The proposed discrete-time model describes both genetic and complex population dynamics assuming that (1) sex ratio is genetically determined, (2) only young males can disperse, and (3) individuals locally compete for resources. The analysis of the model shows that no skewed sex ratios can arise in homogeneous habitats. Temporal asynchronized fluctuations between two distinct patches coupled with dispersal of young males is the minimum requirement for obtaining skewed sex ratios of demographic nature in local adult populations. However, the establishment of a male-biased sex ratio at birth in the long run is possible if dispersal is genetically determined and there is genetic linkage between sex ratio determination and dispersal.

Inefficient epidemic spreading in scale-free networks

Highly heterogeneous degree distributions yield efficient spreading of simple epidemics through networks, but can be inefficient with more complex epidemiological processes. We study diseases with nonlinear force of infection whose prevalences can abruptly collapse to zero while decreasing the transmission parameters. We find that scale-free networks can be unable to support diseases that, on the contrary, are able to persist at high endemic levels in homogeneous networks with the same average degree.

The SIRC model and influenza A

We develop a simple ordinary differential equation model to study the epidemiological consequences of the drift mechanism for influenza A viruses. Improving over the classical SIR approach, we introduce a fourth class (C) for the cross-immune individuals in the population, i.e., those that recovered after being infected by different strains of the same viral subtype in the past years. The SIRC model predicts that the prevalence of a virus is maximum for an intermediate value of R(0), the basic reproduction number. Via a bifurcation analysis of the model, we discuss the effect of seasonality on the epidemiological regimes. For realistic parameter values, the model exhibits a rich variety of behaviors, including chaos and multi-stable periodic outbreaks. Comparison with empirical evidence shows that the simulated regimes are qualitatively and quantitatively consistent with reality, both for tropical and temperate countries. We find that the basins of attraction of coexisting cycles can be fractal sets, thus predictability can in some cases become problematic even theoretically. In accordance with previous studies, we find that increasing cross-immunity tends to complicate the dynamics of the system.

The intermediate dispersal principle in spatially explicit metapopulations

Aim of this paper is to assess the fate of metapopulations described by spatially explicit models. To this end, we first present an interacting particle system (IPS) where individuals of a single species compete logistically at the local scale and can move among patches according to various dispersal kernels. As the IPS is a complex stochastic system, it is impossible to determine the persistence-extinction boundaries in any relevant parameter space with analytical methods or numerical continuation techniques. We thus resort to a heuristic method that lets us determine the boundaries as space-time percolation thresholds with a relatively modest computational effort. Such boundaries are qualitatively consistent with those we obtained with spatial implicit modelling. In particular, we find that the intermediate dispersal principle, namely that globally persistent metapopulations correspond to dispersal rates that are neither too low nor too high, turns out to be very robust even in this explicit context. However, the quantification of the boundaries strongly depends upon the number of patches, the dispersal kernels and the border conditions. Finally, we show that there exists a scaling law that relates the number of species lost in a fragmented landscape to the number of patches. Thus, the law allows a rough estimation of the cost of destroying a patch.

Traveling waves in a model of influenza A drift

Between major pandemics, the influenza A virus changes its antigenic properties by accumulating point mutations (drift) mainly in the RNA genes that code for the surface proteins hemagglutinin (HA) and neuraminidase (NA). The successful strain (variant) that will cause the next epidemic is selected from a reduced number of progenies that possess relatively high transmissibility and the ability to escape from the immune surveillance of the host. In this paper, we analyse a one-dimensional model of influenza A drift (Z. Angew. Math. Mech. 76 (2) (1996) 421) that generalizes the classical SIR model by including mutation as a diffusion process in a phenotype space of variants. The model exhibits traveling wave solutions with an asymptotic wave speed that matches well those obtained from numerical simulations. As exact solutions for these waves are not available, asymptotic estimates for the amplitudes of infected and recovered classes are provided through an exponential approximation based on the smallness of the diffusion constant. Through this approximation, we find simple scaling properties to several parameters of relevance to the epidemiology of the disease.

A persistence criterion for metapopulations

Simple conditions to evaluate the persistence of populations living in fragmented habitats are of primary importance in ecology. We address this need here using a spatially implicit approach that accounts for discrete individuals in a metapopulation. Demographic stochasticity is incorporated into a Markovian model in a natural way, as local extinction is characterized by the death or the dispersal of the last individual inhabiting a patch. The variables of the model are the probabilities p(i) (i=0, 1, 2...) that a patch be occupied by a finite, integer number i of individuals at a given time. We compare the stationary distributions predicted by the model with field data and discuss the role of dispersal in determining different distributions of local abundances. The analysis of the model leads to a persistence criterion which is equivalent to a condition formerly proved by Chesson (Z. Wahrscheinlichkeitstheor. 66, 97-107, 1984) namely that E(0)>1, where E(0) is the expected number of successful dispersers from a patch begun with one individual and to which immigration is excluded. We provide an analytic way of computing E(0) as a function of the main biological characteristics of the species (natality, mortality and dispersal rates, and colonizing ability). We can thus obtain persistence-extinction boundaries in the space of model parameters.

Habitat destruction, environmental catastrophes, and metapopulation extinction

The extinction process of fragmented populations, characterized by a small number of conspecifics inhabiting each patch, is heavily affected by natural and human disturbance. To evaluate the risk of extinction we consider a network of identical patches connected by passive or active dispersal and hosting a finite, discrete number of individuals. We discuss three types of disturbance affecting the metapopulation: permanent loss of habitat patches, erosion of existing patches, and random catastrophes that wipe out the entire population of a patch. Starting from an infinite-dimensional Markov model that fully accounts for demographic stochasticity, we reduce it to finite dimension via moment closure with negative-binomial approximation. The compact models obtained in this way account for the dynamics of the fraction of empty patches, the average number of individuals in occupied patches, and the variance of their distribution. After comparing the performance of these compact models with that of the infinite-dimensional model in the case of no disturbances, we then proceed to computing persistence-extinction boundaries as bifurcation lines of the compact models in the space of demographic and disturbance parameters. We consider bifurcations with respect to demographic and environmental parameters and contrast our results with those of previous theories. We find out that environmental catastrophes increase the risk of extinction for both frequent and infrequent dispersers, while the random loss of patches has a much larger influence on frequent dispersers. This influence can be counterbalanced by active dispersal. Local erosion of habitat fragments has a larger influence on infrequent than on frequent dispersers. We finally discuss the important synergistic effects of disturbances acting simultaneously.