Cholera forecast for Dhaka, Bangladesh, with the 2015-2016 El Niño: Lessons learned.

A substantial body of work supports a teleconnection between the El Niño-Southern Oscillation (ENSO) and cholera incidence in Bangladesh. In particular, high positive anomalies during the winter (Dec-Feb) in sea surface temperatures (SST) in the tropical Pacific have been shown to exacerbate the seasonal outbreak of cholera following the monsoons from August to November. Climate studies have indicated a role of regional precipitation over Bangladesh in mediating this long-distance effect. Motivated by this previous evidence, we took advantage of the strong 2015-2016 El Niño event to evaluate the predictability of cholera dynamics for the city in recent times based on two transmission models that incorporate SST anomalies and are fitted to the earlier surveillance records starting in 1995. We implemented a mechanistic temporal model that incorporates both epidemiological processes and the effect of ENSO, as well as a previously published statistical model that resolves space at the level of districts (thanas). Prediction accuracy was evaluated with "out-of-fit" data from the same surveillance efforts (post 2008 and 2010 for the two models respectively), by comparing the total number of cholera cases observed for the season to those predicted by model simulations eight to twelve months ahead, starting in January each year. Although forecasts were accurate for the low cholera risk observed for the years preceding the 2015-2016 El Niño, the models also predicted a high probability of observing a large outbreak in fall 2016. Observed cholera cases up to Oct 2016 did not show evidence of an anomalous season. We discuss these predictions in the context of regional and local climate conditions, which show that despite positive regional rainfall anomalies, rainfall and inundation in Dhaka remained low. Possible explanations for these patterns are given together with future implications for cholera dynamics and directions to improve their prediction for the city.

Predictability of epidemic malaria under non-stationary conditions with process-based models combining epidemiological updates and climate variability.

BACKGROUND: Previous studies have demonstrated the feasibility of early-warning systems for epidemic malaria informed by climate variability. Whereas modelling approaches typically assume stationary conditions, epidemiological systems are characterized by changes in intervention measures over time, at scales typically longer than inter-epidemic periods. These trends in control efforts preclude simple application of early-warning systems validated by retrospective surveillance data; their effects are also difficult to distinguish from those of climate variability itself. METHODS: Rainfall-driven transmission models for falciparum and vivax malaria are fitted to long-term retrospective surveillance data from four districts in northwest India. Maximum-likelihood estimates (MLEs) of model parameters are obtained for each district via a recently introduced iterated filtering method for partially observed Markov processes. The resulting MLE model is then used to generate simulated yearly forecasts in two different ways, and these forecasts are compared with more recent (out-of-fit) data. In the first approach, initial conditions for generating the predictions are repeatedly updated on a yearly basis, based on the new epidemiological data and the inference method that naturally lends itself to this purpose, given its time-sequential application. In the second approach, the transmission parameters themselves are also updated by refitting the model over a moving window of time. RESULTS: Application of these two approaches to examine the predictability of epidemic malaria in the different districts reveals differences in the effectiveness of intervention for the two parasites, and illustrates how the 'failure' of predictions can be informative to evaluate and quantify the effect of control efforts in the context of climate variability. The first approach performs adequately, and sometimes even better than the second one, when the climate remains the major driver of malaria dynamics, as found for Plasmodium vivax for which an effective clinical intervention is lacking. The second approach offers more skillful forecasts when the dynamics shift over time, as is the case of Plasmodium falciparum in recent years with declining incidence under improved control. CONCLUSIONS: Predictive systems for infectious diseases such as malaria, based on process-based models and climate variables, can be informative and applicable under non-stationary conditions.

Seasonality in the migration and establishment of H3N2 Influenza lineages with epidemic growth and decline.

BACKGROUND: Influenza A/H3N2 has been circulating in humans since 1968, causing considerable morbidity and mortality. Although H3N2 incidence is highly seasonal, how such seasonality contributes to global phylogeographic migration dynamics has not yet been established. In this study, we incorporate time-varying migration rates in a Bayesian MCMC framework. We focus on migration within China, and to and from North-America as case studies, then expand the analysis to global communities. RESULTS: Incorporating seasonally varying migration rates improves the modeling of migration in our regional case studies, and also in a global context. In our global model, windows of increased immigration map to the seasonal timing of epidemic spread, while windows of increased emigration map to epidemic decline. Seasonal patterns also correlate with the probability that local lineages go extinct and fail to contribute to long term viral evolution, as measured through the trunk of the phylogeny. However, the fraction of the trunk in each community was found to be better determined by its overall human population size. CONCLUSIONS: Seasonal migration and rapid turnover within regions is sustained by the invasion of 'fertile epidemic grounds' at the end of older epidemics. Thus, the current emphasis on connectivity, including air-travel, should be complemented with a better understanding of the conditions and timing required for successful establishment. Models which account for migration seasonality will improve our understanding of the seasonal drivers of influenza, enhance epidemiological predictions, and ameliorate vaccine updating by identifying strains that not only escape immunity but also have the seasonal opportunity to establish and spread. Further work is also needed on additional conditions that contribute to the persistence and long term evolution of influenza within the human population, such as spatial heterogeneity with respect to climate and seasonality.

Epidemic cholera spreads like wildfire.

Cholera is on the rise globally, especially epidemic cholera which is characterized by intermittent and unpredictable outbreaks that punctuate periods of regional disease fade-out. These epidemic dynamics remain however poorly understood. Here we examine records for epidemic cholera over both contemporary and historical timelines, from Africa (1990-2006) and former British India (1882-1939). We find that the frequency distribution of outbreak size is fat-tailed, scaling approximately as a power-law. This pattern which shows strong parallels with wildfires is incompatible with existing cholera models developed for endemic regions, as it implies a fundamental role for stochastic transmission and local depletion of susceptible hosts. Application of a recently developed forest-fire model indicates that epidemic cholera dynamics are located above a critical phase transition and propagate in similar ways to aggressive wildfires. These findings have implications for the effectiveness of control measures and the mechanisms that ultimately limit the size of outbreaks.

The potential elimination of Plasmodium vivax malaria by relapse treatment: insights from a transmission model and surveillance data from NW India.

BACKGROUND: With over a hundred million annual infections and rising morbidity and mortality, Plasmodium vivax malaria remains largely a neglected disease. In particular, the dependence of this malaria species on relapses and the potential significance of the dormant stage as a therapeutic target, are poorly understood. METHODOLOGY/PRINCIPAL FINDINGS: To quantify relapse parameters and assess the population-wide consequences of anti-relapse treatment, we formulated a transmission model for P. vivax suitable for parameter inference with a recently developed statistical method based on routine surveillance data. A low-endemic region in NW India, whose strong seasonality demarcates the transmission season, provides an opportunity to apply this modeling approach. Our model gives maximum likelihood estimates of 7.1 months for the mean latency and 31% for the relapse rate, in close agreement with regression estimates and clinical evaluation studies in the area. With a baseline of prevailing treatment practices, the model predicts that an effective anti-relapse treatment of 65% of those infected would result in elimination within a decade, and that periodic mass treatment would dramatically reduce the burden of the disease in a few years. CONCLUSION/SIGNIFICANCE: The striking dependence of P. vivax on relapses for survival reinforces the urgency to develop more effective anti-relapse treatments to replace Primaquine (PQ), the only available drug for the last fifty years. Our methods can provide alternative and simple means to estimate latency times and relapse frequency using routine epidemiological data, and to evaluate the population-wide impact of relapse treatment in areas similar to our study area.

Simple models for complex systems: exploiting the relationship between local and global densities.

Simple temporal models that ignore the spatial nature of interactions and track only changes in mean quantities, such as global densities, are typically used under the unrealistic assumption that individuals are well mixed. These so-called mean-field models are often considered overly simplified, given the ample evidence for distributed interactions and spatial heterogeneity over broad ranges of scales. Here, we present one reason why such simple population models may work even when mass-action assumptions do not hold: spatial structure is present but it relates to global densities in a special way. With an individual-based predator-prey model that is spatial and stochastic, and whose mean-field counterpart is the classic Lotka-Volterra model, we show that the global densities and densities of pairs (or spatial covariances) establish a bi-power law at the stationary state and also in their transient approach to this state. This relationship implies that the dynamics of global densities can be written simply as a function of those densities alone without invoking pairs (or higher order moments). The exponents of the bi-power law for the predation rate exhibit a remarkable robustness to changes in model parameters. Evidence is presented for a connection of our findings to the existence of a critical phase transition in the dynamics of the spatial system. We discuss the application of similar modified mean-field equations to other ecological systems for which similar transitions have been described, both in models and empirical data.Electronic supplementary material The online version of this article (doi:10.1007/s12080-011-0116-2) contains supplementary material, which is available to authorized users.

Robust scaling in ecosystems and the meltdown of patch size distributions before extinction.

Robust critical systems are characterized by power laws which occur over a broad range of conditions. Their robust behaviour has been explained by local interactions. While such systems could be widespread in nature, their properties are not well understood. Here, we study three robust critical ecosystem models and a null model that lacks spatial interactions. In all these models, individuals aggregate in patches whose size distributions follow power laws which melt down under increasing external stress. We propose that this power-law decay associated with the connectivity of the system can be used to evaluate the level of stress exerted on the ecosystem. We identify several indicators along the transition to extinction. These indicators give us a relative measure of the distance to extinction, and have therefore potential application to conservation biology, especially for ecosystems with self-organization and critical transitions.

Trophic garnishes: cat-rat interactions in an urban environment.

BACKGROUND: Community interactions can produce complex dynamics with counterintuitive responses. Synanthropic community members are of increasing practical interest for their effects on biodiversity and public health. Most studies incorporating introduced species have been performed on islands where they may pose a risk to the native fauna. Few have examined their interactions in urban environments where they represent the majority of species. We characterized house cat (Felis catus) predation on wild Norway rats (Rattus norvegicus), and its population effects in an urban area as a model system. Three aspects of predation likely to influence population dynamics were examined; the stratum of the prey population killed by predators, the intensity of the predation, and the size of the predator population. METHODOLOGY/PRINCIPAL FINDINGS: Predation pressure was estimated from the sizes of the rat and cat populations, and the characteristics of rats killed in 20 alleys. Short and long term responses of rat population to perturbations were examined by removal trapping. Perturbations removed an average of 56% of the rats/alley but had no negative long-term impact on the size of the rat population (49.6+/-12.5 rats/alley and 123.8+/-42.2 rats/alley over two years). The sizes of the cat population during two years (3.5 animals/alley and 2.7 animals/alley) also were unaffected by rat population perturbations. Predation by cats occurred in 9/20 alleys. Predated rats were predominantly juveniles and significantly smaller (144.6 g+/-17.8 g) than the trapped rats (385.0 g+/-135.6 g). Cats rarely preyed on the larger, older portion of the rat population. CONCLUSIONS/SIGNIFICANCE: The rat population appears resilient to perturbation from even substantial population reduction using targeted removal. In this area there is a relatively low population density of cats and they only occasionally prey on the rat population. This occasional predation primarily removes the juvenile proportion of the rat population. The top predator in this urban ecosystem appears to have little impact on the size of the prey population, and similarly, reduction in rat populations doesn't impact the size of the cat population. However, the selected targeting of small rats may locally influence the size structure of the population which may have consequences for patterns of pathogen transmission.

Generalizing Levins metapopulation model in explicit space: models of intermediate complexity.

A recent study [Harding and McNamara, 2002. A unifying framework for metapopulation dynamics. Am. Nat. 160, 173-185] presented a unifying framework for the classic Levins metapopulation model by incorporating several realistic biological processes, such as the Allee effect, the Rescue effect and the Anti-rescue effect, via appropriate modifications of the two basic functions of colonization and extinction rates. Here we embed these model extensions on a spatially explicit framework. We consider population dynamics on a regular grid, each site of which represents a patch that is either occupied or empty, and with spatial coupling by neighborhood dispersal. While broad qualitative similarities exist between the spatially explicit models and their spatially implicit (mean-field) counterparts, there are also important differences that result from the details of local processes. Because of localized dispersal, spatial correlation develops among the dynamics of neighboring populations that decays with distance between patches. The extent of this correlation at equilibrium differs among the metapopulation types, depending on which processes prevail in the colonization and extinction dynamics. These differences among dynamical processes become manifest in the spatial pattern and distribution of "clusters" of occupied patches. Moreover, metapopulation dynamics along a smooth gradient of habitat availability show significant differences in the spatial pattern at the range limit. The relevance of these results to the dynamics of disease spread in metapopulations is discussed.

Effects of predation on host-pathogen dynamics in SIR models.

The integration of infectious disease epidemiology with community ecology is an active area of research. Recent studies using SI models without acquired immunity have demonstrated that predation can suppress infectious disease levels. The authors recently showed that incorporating immunity (SIR models) can produce a "hump"-shaped relationship between disease prevalence and predation pressure; thus, low to moderate levels of predation can boost prevalence in hosts with acquired immunity. Here we examine the robustness of this pattern to realistic extensions of a basic SIR model, including density-dependent host regulation, predator saturation, interference, frequency-dependent transmission, predator numerical responses, and explicit resource dynamics. A non-monotonic relationship between disease prevalence and predation pressure holds across all these scenarios. With saturation, there can also be complex responses of mean host abundance to increasing predation, as well as bifurcations leading to unstable cycles (epidemics) and pathogen extinction at larger predator numbers. Firm predictions about the relationship between prevalence and predation thus require one to consider the complex interplay of acquired immunity, host regulation, and foraging behavior of the predator.

Predation can increase the prevalence of infectious disease.

Many host-pathogen interactions are embedded in a web of other interspecific interactions. Recent theoretical studies have suggested that reductions in predator abundance can indirectly lead to upsurges in infectious diseases harbored by prey populations. In this note, we use simple models to show that in some circumstances, predation can actually increase the equilibrial prevalence of infection in a host, where prevalence is defined as the fraction of host population that is infected. Our results show that there is no complete generalization possible about how shifts in predation pressure translate into shifts in infection levels, without some understanding of host population regulation and the role of acquired immunity. Our results further highlight the importance of understanding the dynamics of nonregulatory pathogens in reservoir host populations and the understudied effects of demographic costs incurred by individuals that survive infection and develop acquired immunity.

Temporal autocorrelation can enhance the persistence and abundance of metapopulations comprised of coupled sinks.

In spatially heterogeneous landscapes, some habitats may be persistent sources, providing immigrants to sustain populations in unfavorable sink habitats (where extinction is inevitable without immigration). Recent theoretical and empirical studies of source-sink systems demonstrate that temporally variable local growth rates in sinks can substantially increase average abundance of a persisting population, provided that the variation is positively autocorrelated--in effect, temporal variation inflates average abundance. Here we extend these results to a metapopulation in which all habitat patches are sinks. Using numerical studies of a population with discrete generations (buttressed by analytic results), we show that temporal variation and moderate dispersal can jointly permit indefinite persistence of the metapopulation and that positive autocorrelation both lowers the magnitude of variation required for persistence and increases the average abundance of persisting metapopulations. These effects are weakened--but not destroyed--if variation in local growth rates is spatially synchronized and dispersal is localized. We show that the inflationary effect is robust to a number of extensions of the basic model, including demographic stochasticity and density dependence. Because ecological and environmental processes contributing to temporally variable growth rates in natural populations are typically autocorrelated, these observations may have important implications for species persistence.

Competitive coexistence in a dynamic landscape.

This paper investigates the effect of a dynamic landscape on the persistence of many interacting species. We develop a multi-species community model with an evolving landscape in which the creation and destruction of habitat are dynamic and local in space. Species interactions are also local involving hierarchical competitive trade-offs. We show that dynamic landscapes can reverse the trend of increasing species richness with higher fragmentation observed in static landscapes. The increase in the species-area exponent from a homogeneous to a fragmented landscape does not occur when dynamics are turned on. Thus, temporal aspects of the processes that generate and destroy habitat appear dominant relative to spatial characteristics. We also demonstrate, however, that temporal and spatial aspects interact to influence the persistence time of individual species, and therefore, rank-abundance curves. Specifically, persistence in the model increases in habitats with faster local turnover because of the presence of dynamic corridors.

Cluster size distributions: signatures of self-organization in spatial ecologies.

Three different lattice-based models for antagonistic ecological interactions, both nonlinear and stochastic, exhibit similar power-law scalings in the geometry of clusters. Specifically, cluster size distributions and perimeter-area curves follow power-law scalings. In the coexistence regime, these patterns are robust: their exponents, and therefore the associated Korcak exponent characterizing patchiness, depend only weakly on the parameters of the systems. These distributions, in particular the values of their exponents, are close to those reported in the literature for systems associated with self-organized criticality (SOC) such as forest-fire models; however, the typical assumptions of SOC need not apply. Our results demonstrate that power-law scalings in cluster size distributions are not restricted to systems for antagonistic interactions in which a clear separation of time-scales holds. The patterns are characteristic of processes of growth and inhibition in space, such as those in predator-prey and disturbance-recovery dynamics. Inversions of these patterns, that is, scalings with a positive slope as described for plankton distributions, would therefore require spatial forcing by environmental variability.