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, ℛk(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 ℛk(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.

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.

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.

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.

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.

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.

Range of reproduction number estimates for COVID-19 spread.

To monitor local and global COVID-19 outbreaks, and to plan containment measures, accessible and comprehensible decision-making tools need to be based on the growth rates of new confirmed infections, hospitalization or case fatality rates. Growth rates of new cases form the empirical basis for estimates of a variety of reproduction numbers, dimensionless numbers whose value, when larger than unity, describes surging infections and generally worsening epidemiological conditions. Typically, these determinations rely on noisy or incomplete data gained over limited periods of time, and on many parameters to estimate. This paper examines how estimates from data and models of time-evolving reproduction numbers of national COVID-19 infection spread change by using different techniques and assumptions. Given the importance acquired by reproduction numbers as diagnostic tools, assessing their range of possible variations obtainable from the same epidemiological data is relevant. We compute control reproduction numbers from Swiss and Italian COVID-19 time series adopting both data convolution (renewal equation) and a SEIR-type model. Within these two paradigms we run a comparative analysis of the possible inferences obtained through approximations of the distributions typically used to describe serial intervals, generation, latency and incubation times, and the delays between onset of symptoms and notification. Our results suggest that estimates of reproduction numbers under these different assumptions may show significant temporal differences, while the actual variability range of computed values is rather small.

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.

Integrated field, laboratory, and theoretical study of PKD spread in a Swiss prealpine river.

Proliferative kidney disease (PKD) is a major threat to wild and farmed salmonid populations because of its lethal effect at high water temperatures. Its causative agent, the myxozoan Tetracapsuloides bryosalmonae, has a complex lifecycle exploiting freshwater bryozoans as primary hosts and salmonids as secondary hosts. We carried out an integrated study of PKD in a prealpine Swiss river (the Wigger). During a 3-year period, data on fish abundance, disease prevalence, concentration of primary hosts' DNA in environmental samples [environmental DNA (eDNA)], hydrological variables, and water temperatures gathered at various locations within the catchment were integrated into a newly developed metacommunity model, which includes ecological and epidemiological dynamics of fish and bryozoans, connectivity effects, and hydrothermal drivers. Infection dynamics were captured well by the epidemiological model, especially with regard to the spatial prevalence patterns. PKD prevalence in the sampled sites for both young-of-the-year (YOY) and adult brown trout attained 100% at the end of summer, while seasonal population decay was higher in YOY than in adults. We introduce a method based on decay distance of eDNA signal predicting local species' density, accounting for variation in environmental drivers (such as morphology and geology). The model provides a whole-network overview of the disease prevalence. In this study, we show how spatial and environmental characteristics of river networks can be used to study epidemiology and disease dynamics of waterborne diseases.

Hydrology and density feedbacks control the ecology of intermediate hosts of schistosomiasis across habitats in seasonal climates.

We report about field and theoretical studies on the ecology of the aquatic snails (Bulinus spp. and Biomphalaria pfeifferi) that serve as obligate intermediate hosts in the complex life cycle of the parasites causing human schistosomiasis. Snail abundance fosters disease transmission, and thus the dynamics of snail populations are critically important for schistosomiasis modeling and control. Here, we single out hydrological drivers and density dependence (or lack of it) of ecological growth rates of local snail populations by contrasting novel ecological and environmental data with various models of host demography. Specifically, we study various natural and man-made habitats across Burkina Faso's highly seasonal climatic zones. Demographic models are ranked through formal model comparison and structural risk minimization. The latter allows us to evaluate the suitability of population models while clarifying the relevant covariates that explain empirical observations of snail abundance under the actual climatic forcings experienced by the various field sites. Our results link quantitatively hydrological drivers to distinct population dynamics through specific density feedbacks, and show that statistical methods based on model averaging provide reliable snail abundance projections. The consistency of our ranking results suggests the use of ad hoc models of snail demography depending on habitat type (e.g., natural vs. man-made) and hydrological characteristics (e.g., ephemeral vs. permanent). Implications for risk mapping and space-time allocation of control measures in schistosomiasis-endemic contexts are discussed.

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.

River networks as ecological corridors: A coherent ecohydrological perspective.

This paper draws together several lines of argument to suggest that an ecohydrological framework, i.e. laboratory, field and theoretical approaches focused on hydrologic controls on biota, has contributed substantially to our understanding of the function of river networks as ecological corridors. Such function proves relevant to: the spatial ecology of species; population dynamics and biological invasions; the spread of waterborne disease. As examples, we describe metacommunity predictions of fish diversity patterns in the Mississippi-Missouri basin, geomorphic controls imposed by the fluvial landscape on elevational gradients of species' richness, the zebra mussel invasion of the same Mississippi-Missouri river system, and the spread of proliferative kidney disease in salmonid fish. We conclude that spatial descriptions of ecological processes in the fluvial landscape, constrained by their specific hydrologic and ecological dynamics and by the ecosystem matrix for interactions, i.e. the directional dispersal embedded in fluvial and host/pathogen mobility networks, have already produced a remarkably broad range of significant results. Notable scientific and practical perspectives are thus open, in the authors' view, to future developments in ecohydrologic research.

Heterogeneity in schistosomiasis transmission dynamics.

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.

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.

Body size and meta-community structure: the allometric scaling of parasitic worm communities in their mammalian hosts.

In this paper we derive from first principles the expected body sizes of the parasite communities that can coexist in a mammal of given body size. We use a mixture of mathematical models and known allometric relationships to examine whether host and parasite life histories constrain the diversity of parasite species that can coexist in the population of any host species. The model consists of one differential equation for each parasite species and a single density-dependent nonlinear equation for the affected host under the assumption of exploitation competition. We derive threshold conditions for the coexistence and competitive exclusion of parasite species using invasion criteria and stability analysis of the resulting equilibria. These results are then used to evaluate the range of parasites species that can invade and establish in a target host and identify the 'optimal' size of a parasite species for a host of a given body size; 'optimal' is defined as the body size of a parasite species that cannot be outcompeted by any other parasite species. The expected distributions of parasites body sizes in hosts of different sizes are then compared with those observed in empirical studies. Our analysis predicts the relative abundance of parasites of different size that establish in the host and suggests that increasing the ratio of parasite body size to host body size above a minimum threshold increases the persistence of the parasite population.

A global viability assessment of the European eel.

The global European eel (Anguilla anguilla) stock is critically endangered according to the IUCN, and the European Commission has urged the development of conservation plans aimed to ensure its viability. However, the complex life cycle of this panmictic species, which reproduces in the open ocean but spends most of its prereproductive life in continental waters (thus embracing a huge geographic range and a variety of habitat types), makes it difficult to assess the long-term effectiveness of conservation measures. The interplay between local and global stressors raises intriguing cross-scale conservation challenges that require a comprehensive modelling approach to be addressed. We developed a full life cycle model of the global European eel stock, encompassing both the oceanic and the continental phases of eel's life, and explicitly allowing for spatial heterogeneity in vital rates, availability of suitable habitat and settlement potential via a metapopulation approach. We calibrated the model against a long-term time series of global European eel catches and used it to hindcast the dynamics of the stock in the past and project it over the 21st century under different management scenarios. Although our analysis relies on a number of inevitable simplifying assumptions and on data that may not embrace the whole range of variation in population dynamics at the small spatiotemporal scale, our hindcast is consistent with the general pattern of decline of the stock over recent decades. The results of our projections suggest that (i) habitat loss played a major role in the European eel decline; (ii) the viability of the global stock is at risk if appropriate protection measures are not implemented; (iii) the recovery of spawner escapement requires that fishing mortality is significantly reduced; and (iv) the recovery of recruitment might not be feasible if reproductive output is not enhanced.

Generalized reproduction numbers and the prediction of patterns in waterborne disease.

Understanding, predicting, and controlling outbreaks of waterborne diseases are crucial goals of public health policies, but pose challenging problems because infection patterns are influenced by spatial structure and temporal asynchrony. Although explicit spatial modeling is made possible by widespread data mapping of hydrology, transportation infrastructure, population distribution, and sanitation, the precise condition under which a waterborne disease epidemic can start in a spatially explicit setting is still lacking. Here we show that the requirement that all the local reproduction numbers R0 be larger than unity is neither necessary nor sufficient for outbreaks to occur when local settlements are connected by networks of primary and secondary infection mechanisms. To determine onset conditions, we derive general analytical expressions for a reproduction matrix G0, explicitly accounting for spatial distributions of human settlements and pathogen transmission via hydrological and human mobility networks. At disease onset, a generalized reproduction number Λ0 (the dominant eigenvalue of G0) must be larger than unity. We also show that geographical outbreak patterns in complex environments are linked to the dominant eigenvector and to spectral properties of G0. Tests against data and computations for the 2010 Haiti and 2000 KwaZulu-Natal cholera outbreaks, as well as against computations for metapopulation networks, demonstrate that eigenvectors of G0 provide a synthetic and effective tool for predicting the disease course in space and time. Networked connectivity models, describing the interplay between hydrology, epidemiology, and social behavior sustaining human mobility, thus prove to be key tools for emergency management of waterborne infections.

Reassessment of the 2010-2011 Haiti cholera outbreak and rainfall-driven multiseason projections.

Mathematical models can provide key insights into the course of an ongoing epidemic, potentially aiding real-time emergency management in allocating health care resources and by anticipating the impact of alternative interventions. We study the ex post reliability of predictions of the 2010-2011 Haiti cholera outbreak from four independent modeling studies that appeared almost simultaneously during the unfolding epidemic. We consider the impact of different approaches to the modeling of spatial spread of Vibrio cholerae and mechanisms of cholera transmission, accounting for the dynamics of susceptible and infected individuals within different local human communities. To explain resurgences of the epidemic, we go on to include waning immunity and a mechanism explicitly accounting for rainfall as a driver of enhanced disease transmission. The formal comparative analysis is carried out via the Akaike information criterion (AIC) to measure the added information provided by each process modeled, discounting for the added parameters. A generalized model for Haitian epidemic cholera and the related uncertainty is thus proposed and applied to the year-long dataset of reported cases now available. The model allows us to draw predictions on longer-term epidemic cholera in Haiti from multiseason Monte Carlo runs, carried out up to January 2014 by using suitable rainfall fields forecasts. Lessons learned and open issues are discussed and placed in perspective. We conclude that, despite differences in methods that can be tested through model-guided field validation, mathematical modeling of large-scale outbreaks emerges as an essential component of future cholera epidemic control.

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.

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.