Floquet theory for seasonal environmental forcing of spatially explicit waterborne epidemics

Tracking the time course of reproduction number and lockdown's effect on human behaviour during SARS-CoV-2 epidemic: nonparametric estimation

Understanding the SARS-CoV-2 dynamics has been subject of intense research in the last months. In particular, accurate modeling of lockdown effects on human behaviour and epidemic evolution is a key issue in order e.g. to inform health-care decisions on emergency management. In this regard, the compartmental and spatial models so far proposed use parametric descriptions of the contact rate, often assuming a time-invariant effect of the lockdown. In this paper we show that these assumptions may lead to erroneous evaluations on the ongoing pandemic. Thus, we develop a new class of nonparametric compartmental models able to describe how the impact of the lockdown varies in time. Our estimation strategy does not require significant Bayes prior information and exploits regularization theory. Hospitalized data are mapped into an infinite-dimensional space, hence obtaining a function which takes into account also how social distancing measures and people's growing awareness of infection's risk evolves as time progresses. This also permits to reconstruct a continuous-time profile of SARS-CoV-2 reproduction number with a resolution never reached before in the literature. When applied to data collected in Lombardy, the most affected Italian region, our model illustrates how people behaviour changed during the restrictions and its importance to contain the epidemic. Results also indicate that, at the end of the lockdown, around [Formula: see text] of people in Lombardy and [Formula: see text] in Italy was affected by SARS-CoV-2, with the fatality rate being 1.14%. Then, we discuss how the situation evolved after the end of the lockdown showing that the reproduction number dangerously increased in the summer, due to holiday relax, reaching values larger than one on August 1, 2020. Finally, we also document how Italy faced the second wave of infection in the last part of 2020. Since several countries still observe a growing epidemic and others could be subject to other waves, the proposed reproduction number tracking methodology can be of great help to health care authorities to prevent SARS-CoV-2 diffusion or to assess the impact of lockdown restrictions on human behaviour to contain the spread.

SARS-COV-2: SIR Model Limitations and Predictive Constraints

Background: The main purpose of this research is to describe the mathematical asymmetric patterns of susceptible, infectious, or recovered (SIR) model equation application in the light of coronavirus disease 2019 (COVID-19) skewness patterns worldwide. Methods: The research modeled severe acute respiratory syndrome coronavirus 2 (SARS-COV-2) spreading and dissemination patterns sensitivity by redesigning time series data extraction of daily new cases in terms of deviation consistency concerning variables that sustain COVID-19 transmission. The approach opened a new scenario where seasonality forcing behavior was introduced to understand SARS-COV-2 non-linear dynamics due to heterogeneity and confounding epidemics scenarios. Results: The main research results are the elucidation of three birth- and death-forced seasonality persistence phases that can explain COVID-19 skew patterns worldwide. They are presented in the following order: (1) the environmental variables (Earth seasons and atmospheric conditions); (2) health policies and adult learning education (HPALE) interventions; (3) urban spaces (local indoor and outdoor spaces for transit and social-cultural interactions, public or private, with natural physical features (river, lake, terrain). Conclusions: Three forced seasonality phases (positive to negative skew) phases were pointed out as a theoretical framework to explain uncertainty found in the predictive SIR model equations that might diverge in outcomes expected to express the disease’s behaviour.

COVID-19 epidemic control using short-term lockdowns for collective gain

While many efforts are currently devoted to vaccines development and administration, social distancing measures, including severe restrictions such as lockdowns, remain fundamental tools to contain the spread of COVID-19. A crucial point for any government is to understand, on the basis of the epidemic curve, the right temporal instant to set up a lockdown and then to remove it. Different strategies are being adopted with distinct shades of intensity. USA and Europe tend to introduce restrictions of considerable temporal length. They vary in time: a severe lockdown may be reached and then gradually relaxed. An interesting alternative is the Australian model where short and sharp responses have repeatedly tackled the virus and allowed people a return to near normalcy. After a few positive cases are detected, a lockdown is immediately set. In this paper we show that the Australian model can be generalized and given a rigorous mathematical analysis, casting strategies of the type short-term pain for collective gain in the context of sliding-mode control, an important branch of nonlinear control theory. This allows us to gain important insights regarding how to implement short-term lockdowns, obtaining a better understanding of their merits and possible limitations. Effects of vaccines administration in improving the control law's effectiveness are also illustrated. Our model predicts the duration of the severe lockdown to be set to maintain e.g. the number of people in intensive care under a certain threshold. After tuning our strategy exploiting data collected in Italy, it turns out that COVID-19 epidemic could be e.g. controlled by alternating one or two weeks of complete lockdown with one or two months of freedom, respectively. Control strategies of this kind, where the lockdown's duration is well circumscribed, could be important also to alleviate coronavirus impact on economy.

Permafrost dynamics and the risk of anthrax transmission: a modelling study

A recent outbreak of anthrax disease, severely affecting reindeer herds in Siberia, has been reportedly associated to the presence of infected carcasses or spores released from the active layer over permafrost, which is thawing and thickening at increasing rates, thus underlying the re-emerging nature of this pathogen in the Arctic region because of warming temperatures. Anthrax is a global zoonotic and epizootic disease, with a high case-fatality ratio in infected animals. Its transmission is mediated by environmental contamination through highly resistant spores which can persist in the soil for several decades. Here we develop and analyze a new epidemiological model for anthrax transmission that is specifically tailored to the Arctic environmental conditions. The model describes transmission dynamics including also herding practices (e.g. seasonal grazing) and the role of the active layer over permafrost acting as a long-term storage of spores that could be viable for disease transmission during thawing periods. Model dynamics are investigated through linear stability analysis, Floquet theory for periodically forced systems, and a series of simulations with realistic forcings. Results show how the temporal variability of grazing and active layer thawing may influence the dynamics of anthrax disease and, specifically, favor sustained pathogen transmission. Particularly warm years, favoring deep active layers, are shown to be associated with an increase risk of anthrax outbreaks, and may also foster infections in the following years. Our results enable preliminary insights into measures (e.g. changes in herding practice) that may be adopted to decrease the risk of infection and lay the basis to possibly establish optimal procedures for preventing transmission; furthermore, they elicit the need of further investigations and observation campaigns focused on anthrax dynamics in the Arctic environment.

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.

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.

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

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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.

Challenges in developing methods for quantifying the effects of weather and climate on water-associated diseases: A systematic review

Infectious diseases attributable to unsafe water supply, sanitation and hygiene (e.g. Cholera, Leptospirosis, Giardiasis) remain an important cause of morbidity and mortality, especially in low-income countries. Climate and weather factors are known to affect the transmission and distribution of infectious diseases and statistical and mathematical modelling are continuously developing to investigate the impact of weather and climate on water-associated diseases. There have been little critical analyses of the methodological approaches. Our objective is to review and summarize statistical and modelling methods used to investigate the effects of weather and climate on infectious diseases associated with water, in order to identify limitations and knowledge gaps in developing of new methods. We conducted a systematic review of English-language papers published from 2000 to 2015. Search terms included concepts related to water-associated diseases, weather and climate, statistical, epidemiological and modelling methods. We found 102 full text papers that met our criteria and were included in the analysis. The most commonly used methods were grouped in two clusters: process-based models (PBM) and time series and spatial epidemiology (TS-SE). In general, PBM methods were employed when the bio-physical mechanism of the pathogen under study was relatively well known (e.g. Vibrio cholerae); TS-SE tended to be used when the specific environmental mechanisms were unclear (e.g. Campylobacter). Important data and methodological challenges emerged, with implications for surveillance and control of water-associated infections. The most common limitations comprised: non-inclusion of key factors (e.g. biological mechanism, demographic heterogeneity, human behavior), reporting bias, poor data quality, and collinearity in exposures. Furthermore, the methods often did not distinguish among the multiple sources of time-lags (e.g. patient physiology, reporting bias, healthcare access) between environmental drivers/exposures and disease detection. Key areas of future research include: disentangling the complex effects of weather/climate on each exposure-health outcome pathway (e.g. person-to-person vs environment-to-person), and linking weather data to individual cases longitudinally.

Modeling Key Drivers of Cholera Transmission Dynamics Provides New Perspectives for Parasitology

Hydroclimatological and anthropogenic factors are key drivers of waterborne disease transmission. Information on human settlements and host mobility on waterways along which pathogens and hosts disperse, and relevant hydroclimatological processes, can be acquired remotely and included in spatially explicit mathematical models of disease transmission. In the case of epidemic cholera, such models allowed the description of complex disease patterns and provided insight into the course of ongoing epidemics. The inclusion of spatial information in models of disease transmission can aid in emergency management and the assessment of alternative interventions. Here, we review the study of drivers of transmission via spatially explicit approaches and argue that, because many parasitic waterborne diseases share the same drivers as cholera, similar principles may apply.

Big-data-driven modeling unveils country-wide drivers of endemic schistosomiasis

Schistosomiasis is a parasitic infection that is widespread in sub-Saharan Africa, where it represents a major health problem. We study the drivers of its geographical distribution in Senegal via a spatially explicit network model accounting for epidemiological dynamics driven by local socioeconomic and environmental conditions, and human mobility. The model is parameterized by tapping several available geodatabases and a large dataset of mobile phone traces. It reliably reproduces the observed spatial patterns of regional schistosomiasis prevalence throughout the country, provided that spatial heterogeneity and human mobility are suitably accounted for. Specifically, a fine-grained description of the socioeconomic and environmental heterogeneities involved in local disease transmission is crucial to capturing the spatial variability of disease prevalence, while the inclusion of human mobility significantly improves the explanatory power of the model. Concerning human movement, we find that moderate mobility may reduce disease prevalence, whereas either high or low mobility may result in increased prevalence of infection. The effects of control strategies based on exposure and contamination reduction via improved access to safe water or educational campaigns are also analyzed. To our knowledge, this represents the first application of an integrative schistosomiasis transmission model at a whole-country scale.

An epidemiological model for proliferative kidney disease in salmonid populations

Background

Proliferative kidney disease (PKD) affects salmonid populations in European and North-American rivers. It is caused by the endoparasitic myxozoan Tetracapsuloides bryosalmonae, which exploits freshwater bryozoans and salmonids as hosts. Incidence and severity of PKD in brown trout populations have recently increased rapidly, causing a decline in fish catches and local extinctions in many river systems. PKD incidence and fish mortality are known to be enhanced by warmer water temperatures. Therefore, environmental change is feared to increase the severity of PKD outbreaks and extend the disease range to higher latitude and altitude regions. We present the first mathematical model regarding the epidemiology of PKD, including the complex life-cycle of its causative agent across multiple hosts.

Methods

A dynamical model of PKD epidemiology in riverine host populations is developed. The model accounts for local demographic and epidemiological dynamics of bryozoans and fish, explicitly incorporates the role of temperature, and couples intra-seasonal and inter-seasonal dynamics. The former are described in a continuous-time domain, the latter in a discrete-time domain. Stability and sensitivity analyses are performed to investigate the key processes controlling parasite invasion and persistence.

Results

Stability analysis shows that, for realistic parameter ranges, a disease-free system is highly invasible, which implies that the introduction of the parasite in a susceptible community is very likely to trigger a disease outbreak. Sensitivity analysis shows that, when the disease is endemic, the impact of PKD outbreaks is mostly controlled by the rates of disease development in the fish population.

Conclusions

The developed mathematical model helps further our understanding of the modes of transmission of PKD in wild salmonid populations, and provides the basis for the design of interventions or mitigation strategies. It can also be used to project changes in disease severity and prevalence because of temperature regime shifts, and to guide field and laboratory experiments.

Electronic supplementary material

The online version of this article (doi:10.1186/s13071-016-1759-z) contains supplementary material, which is available to authorized users.

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.

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.