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.

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.

Earth and field observations underpin metapopulation dynamics in complex landscapes: Near-term study on carabids.

Understanding risks to biodiversity requires predictions of the spatial distribution of species adapting to changing ecosystems and, to that end, Earth observations integrating field surveys prove essential as they provide key numbers for assessing landscape-wide biodiversity scenarios. Here, we develop, and apply to a relevant case study, a method suited to merge Earth/field observations with spatially explicit stochastic metapopulation models to study the near-term ecological dynamics of target species in complex terrains. Our framework incorporates the use of species distribution models for a reasoned estimation of the initial presence of the target species and accounts for imperfect and incomplete detection of the species presence in the study area. It also uses a metapopulation fitness function derived from Earth observation data subsuming the ecological niche of the target species. This framework is applied to contrast occupancy of two species of carabids (Pterostichus flavofemoratus, Carabus depressus) observed in the context of a large ecological monitoring program carried out within the Gran Paradiso National Park (GPNP, Italy). Results suggest that the proposed framework may indeed exploit the hallmarks of spatially explicit ecological approaches and of remote Earth observations. The model reproduces well the observed in situ data. Moreover, it projects in the near term the two species' presence both in space and in time, highlighting the features of the metapopulation dynamics of colonization and extinction, and their expected trends within verifiable timeframes.

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.

Near real-time forecasting for cholera decision making in Haiti after Hurricane Matthew.

Computational models of cholera transmission can provide objective insights into the course of an ongoing epidemic and aid decision making on allocation of health care resources. However, models are typically designed, calibrated and interpreted post-hoc. Here, we report the efforts of a team from academia, field research and humanitarian organizations to model in near real-time the Haitian cholera outbreak after Hurricane Matthew in October 2016, to assess risk and to quantitatively estimate the efficacy of a then ongoing vaccination campaign. A rainfall-driven, spatially-explicit meta-community model of cholera transmission was coupled to a data assimilation scheme for computing short-term projections of the epidemic in near real-time. The model was used to forecast cholera incidence for the months after the passage of the hurricane (October-December 2016) and to predict the impact of a planned oral cholera vaccination campaign. Our first projection, from October 29 to December 31, predicted the highest incidence in the departments of Grande Anse and Sud, accounting for about 45% of the total cases in Haiti. The projection included a second peak in cholera incidence in early December largely driven by heavy rainfall forecasts, confirming the urgency for rapid intervention. A second projection (from November 12 to December 31) used updated rainfall forecasts to estimate that 835 cases would be averted by vaccinations in Grande Anse (90% Prediction Interval [PI] 476-1284) and 995 in Sud (90% PI 508-2043). The experience gained by this modeling effort shows that state-of-the-art computational modeling and data-assimilation methods can produce informative near real-time projections of cholera incidence. Collaboration among modelers and field epidemiologists is indispensable to gain fast access to field data and to translate model results into operational recommendations for emergency management during an outbreak. Future efforts should thus draw together multi-disciplinary teams to ensure model outputs are appropriately based, interpreted and communicated.

A stratified compartmental model for the transmission of Sparicotyle chrysophrii (Platyhelminthes: Monogenea) in gilthead seabream (Sparus aurata) fish farms†.

The rapid development of intensive fish farming has been associated with the spreading of infectious diseases, pathogens and parasites. One such parasite is Sparicotyle chrysophrii (Platyhelminthes: Monogenea), which commonly infects cultured gilthead seabream (Sparus aurata)-a vital species in Mediterranean aquaculture. The parasite attaches to fish gills and can cause epizootics in sea cages with relevant consequences for fish health and associated economic losses for fish farmers. In this study, a novel stratified compartmental epidemiological model of S. chrysophrii transmission was developed and analysed. The model accounts for the temporal progression of the number of juvenile and adult parasites attached to each fish, as well as the abundance of eggs and oncomiracidia. We applied the model to data collected in a seabream farm, where the fish population and the number of adult parasites attached to fish gills were closely monitored in six different cages for 10 months. The model successfully replicated the temporal dynamics of the distribution of the parasite abundance within fish hosts and simulated the effects of environmental factors, such as water temperature, on the transmission dynamics. The findings highlight the potential of modelling tools for farming management, aiding in the prevention and control of S. chrysophrii infections in Mediterranean aquaculture.

Epidemicity of cholera spread and the fate of infection control measures.

The fate of ongoing infectious disease outbreaks is predicted through reproduction numbers, defining the long-term establishment of the infection, and epidemicity indices, tackling the reactivity of the infectious pool to new contagions. Prognostic metrics of unfolding outbreaks are of particular importance when designing adaptive emergency interventions facing real-time assimilation of epidemiological evidence. Our aim here is twofold. First, we propose a novel form of the epidemicity index for the characterization of cholera epidemics in spatial models of disease spread. Second, we examine in hindsight the survey of infections, treatments and containment measures carried out for the now extinct 2010-2019 Haiti cholera outbreak, to suggest that magnitude and timing of non-pharmaceutical and vaccination interventions imply epidemiological responses recapped by the evolution of epidemicity indices. Achieving negative epidemicity greatly accelerates fading of infections and thus proves a worthwhile target of containment measures. We also show that, in our model, effective reproduction numbers and epidemicity indices are explicitly related. Therefore, providing an upper bound to the effective reproduction number (significantly lower than the unit threshold) warrants negative epidemicity and, in turn, a rapidly fading outbreak preventing coalescence of sparse local sub-threshold flare-ups.

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.

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.

Achieving coordinated national immunity and cholera elimination in Haiti through vaccination: a modelling study.

BACKGROUND: Cholera was introduced into Haiti in 2010. Since then, more than 820 000 cases and nearly 10 000 deaths have been reported. Oral cholera vaccine (OCV) is safe and effective, but has not been seen as a primary tool for cholera elimination due to a limited period of protection and constrained supplies. Regionally, epidemic cholera is contained to the island of Hispaniola, and the lowest numbers of cases since the epidemic began were reported in 2019. Hence, Haiti may represent a unique opportunity to eliminate cholera with OCV. METHODS: In this modelling study, we assessed the probability of elimination, time to elimination, and percentage of cases averted with OCV campaign scenarios in Haiti through simulations from four modelling teams. For a 10-year period from January 19, 2019, to Jan 13, 2029, we compared a no vaccination scenario with five OCV campaign scenarios that differed in geographical scope, coverage, and rollout duration. Teams used weekly department-level reports of suspected cholera cases from the Haiti Ministry of Public Health and Population to calibrate the models and used common vaccine-related assumptions, but other model features were determined independently. FINDINGS: Among campaigns with the same vaccination coverage (70% fully vaccinated), the median probability of elimination after 5 years was 0-18% for no vaccination, 0-33% for 2-year campaigns focused in the two departments with the highest historical incidence, 0-72% for three-department campaigns, and 35-100% for nationwide campaigns. Two-department campaigns averted a median of 12-58% of infections, three-department campaigns averted 29-80% of infections, and national campaigns averted 58-95% of infections. Extending the national campaign to a 5-year rollout (compared to a 2-year rollout), reduced the probability of elimination to 0-95% and the proportion of cases averted to 37-86%. INTERPRETATION: Models suggest that the probability of achieving zero transmission of Vibrio cholerae in Haiti with current methods of control is low, and that bolder action is needed to promote elimination of cholera from the region. Large-scale cholera vaccination campaigns in Haiti would offer the opportunity to synchronise nationwide immunity, providing near-term population protection while improvements to water and sanitation promote long-term cholera elimination. FUNDING: Bill & Melinda Gates Foundation, Global Good Fund, Institute for Disease Modeling, Swiss National Science Foundation, and US National Institutes of Health.

A minimalist model of extinction and range dynamics of virtual mountain species driven by warming temperatures.

A longstanding question in ecology concerns the prediction of the fate of mountain species under climate change, where climatic and geomorphic factors but also endogenous species characteristics are jointly expected to control species distributions. A significant step forward would single out reliably landscape effects, given their constraining role and relative ease of theoretical manipulation. Here, we address population dynamics in ecosystems where the substrates for ecological interactions are mountain landscapes subject to climate warming. We use a minimalist model of metapopulation dynamics based on virtual species (i.e. a suitable assemblage of focus species) where dispersal processes interact with the spatial structure of the landscape. Climate warming is subsumed by an upward shift of species habitat altering the metapopulation capacity of the landscape and hence species viability. We find that the landscape structure is a powerful determinant of species survival, owing to the specific role of the predictably evolving connectivity of the various habitats. Range shifts and lags in tracking suitable habitat experienced by virtual species under warming conditions are singled out in different landscapes. The range of parameters is identified for which these virtual species (characterized by comparable viability thus restricting their possible fitnesses and niche widths) prove unable to cope with environmental change. The statistics of the proportion of species bound to survive is identified for each landscape, providing the temporal evolution of species range shifts and the related expected occupation patterns. A baseline dynamic model for predicting species fates in evolving habitats is thus provided.

Rainfall as a driver of epidemic cholera: Comparative model assessments of the effect of intra-seasonal precipitation events.

The correlation between cholera epidemics and climatic drivers, in particular seasonal tropical rainfall, has been studied in a variety of contexts owing to its documented relevance. Several mechanistic models of cholera transmission have included rainfall as a driver by focusing on two possible transmission pathways: either by increasing exposure to contaminated water (e.g. due to worsening sanitary conditions during water excess), or water contamination by freshly excreted bacteria (e.g. due to washout of open-air defecation sites or overflows). Our study assesses the explanatory power of these different modeling structures by formal model comparison using deterministic and stochastic models of the type susceptible-infected-recovered-bacteria (SIRB). The incorporation of rainfall effects is generalized using a nonlinear function that can increase or decrease the relative importance of the large precipitation events. Our modelling framework is tested against the daily epidemiological data collected during the 2015 cholera outbreak within the urban context of Juba, South Sudan. This epidemic is characterized by a particular intra-seasonal double peak on the incidence in apparent relation with particularly strong rainfall events. Our results show that rainfall-based models in both their deterministic and stochastic formulations outperform models that do not account for rainfall. In fact, classical SIRB models are not able to reproduce the second epidemiological peak, thus suggesting that it was rainfall-driven. Moreover we found stronger support across model types for rainfall acting on increased exposure rather than on exacerbated water contamination. Although these results are context-specific, they stress the importance of a systematic and comprehensive appraisal of transmission pathways and their environmental forcings when embarking in the modelling of epidemic cholera.