Manojit Roy

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.

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.

On representing network heterogeneities in the incidence rate of simple epidemic models

Abstract Mean-field ecological models ignore space and other forms of contact structure. At the opposite extreme, high-dimensional models that are both individual-based and stochastic incorporate the distributed nature of ecological interactions. In between, moment approximations have been proposed that represent the effect of correlations on the dynamics of mean quantities. As an alternative closer to the typical temporal models used in ecology, we present here results on “modified mean-field equations” for infectious disease dynamics, in which only mean quantities are followed and the effect of heterogeneous mixing is incorporated implicitly. We specifically investigate the previously proposed empirical parameterization of heterogeneous mixing in which the bilinear incidence rate SI is replaced by a nonlinear term kS p I q , for the case of stochastic SIRS dynamics on different contact networks, from a regular lattice to a random structure via small-world configurations. We show that, for two distinct dynamical cases involving a stable equilibrium and a noisy endemic steady state, the modified mean-field model approximates successfully the steady state dynamics as well as the respective short and long transients of decaying cycles. This result demonstrates that early on in the transients an approximate power-law relationship is established between global (mean) quantities and the covariance structure in the network. The approach fails in the more complex case of persistent cycles observed within the narrow range of small-world configurations.

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.

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.

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.

Unstable predator–prey dynamics permits the coexistence of generalist and specialist predators, and the maintenance of partial preferences

Saturating functional responses are a unifying principle in ecology, influencing processes at organizational levels from dietary specialization in individuals, to population instability, to community-level indirect interactions among alternative prey. These effects are interrelated. We explore a predator–prey model and demonstrate that unstable dynamics promote coexistence of specialist and generalist predators, when the specialist attacks only high-quality prey, and the generalist attacks high- and low-quality prey (that alone cannot maintain the predator). Coexisting specialist and generalist predators are vulnerable to invasion and replacement by predators with fixed partial preferences. The evolutionarily stable partial preference increases with increasing dynamic instability, but typically declines with increasing abundance of the low-quality prey. Coexisting specialist and generalist consumers, or partial preferences, typically reduce the potential for poor-quality prey to indirectly benefit high-qu...