David Gurarie

Connectivity sustains disease transmission in environments with low potential for endemicity: modelling schistosomiasis with hydrologic and social connectivities.

Social interaction and physical interconnections between populations can influence the spread of parasites. The role that these pathways play in sustaining the transmission of parasitic diseases is unclear, although increasingly realistic metapopulation models are being used to study how diseases persist in connected environments. We use a mathematical model of schistosomiasis transmission for a distributed set of heterogeneous villages to show that the transport of parasites via social (host movement) and environmental (parasite larvae movement) pathways has consequences for parasite control, spread and persistence. We find that transmission can be sustained regionally throughout a group of connected villages even when individual village conditions appear not to support endemicity. Optimum transmission is determined by an interplay between different transport pathways, and not necessarily by those that are the most dispersive (e.g. disperse social contacts may not be optimal for transmission). We show that the traditional targeting of villages with high infection, without regard to village interconnections, may not lead to optimum control. These findings have major implications for effective disease control, which needs to go beyond considering local variations in disease intensity, to also consider the degree to which populations are interconnected.

A Sub-Microscopic Gametocyte Reservoir Can Sustain Malaria Transmission

Background Novel diagnostic tools, including PCR and high field gradient magnetic fractionation (HFGMF), have improved detection of asexual Plasmodium falciparum parasites and especially infectious gametocytes in human blood. These techniques indicate a significant number of people carry gametocyte densities that fall below the conventional threshold of detection achieved by standard light microscopy (LM). Methodology/Principal Findings To determine how low-level gametocytemia may affect transmission in present large-scale efforts for P. falciparum control in endemic areas, we developed a refinement of the classical Ross-Macdonald model of malaria transmission by introducing multiple infective compartments to model the potential impact of highly prevalent, low gametocytaemic reservoirs in the population. Models were calibrated using field-based data and several numerical experiments were conducted to assess the effect of high and low gametocytemia on P. falciparum transmission and control. Special consideration was given to the impact of long-lasting insecticide-treated bed nets (LLIN), presently considered the most efficient way to prevent transmission, and particularly LLIN coverage similar to goals targeted by the Roll Back Malaria and Global Fund malaria control campaigns. Our analyses indicate that models which include only moderate-to-high gametocytemia (detectable by LM) predict finite eradication times after LLIN introduction. Models that include a low gametocytemia reservoir (requiring PCR or HFGMF detection) predict much more stable, persistent transmission. Our modeled outcomes result in significantly different estimates for the level and duration of control needed to achieve malaria elimination if submicroscopic gametocytes are included. Conclusions/Significance It will be very important to complement current methods of surveillance with enhanced diagnostic techniques to detect asexual parasites and gametocytes to more accurately plan, monitor and guide malaria control programs aimed at eliminating malaria.

Quantitative analyses and modelling to support achievement of the 2020 goals for nine neglected tropical diseases

Quantitative analysis and mathematical models are useful tools in informing strategies to control or eliminate disease. Currently, there is an urgent need to develop these tools to inform policy to achieve the 2020 goals for neglected tropical diseases (NTDs). In this paper we give an overview of a collection of novel model-based analyses which aim to address key questions on the dynamics of transmission and control of nine NTDs: Chagas disease, visceral leishmaniasis, human African trypanosomiasis, leprosy, soil-transmitted helminths, schistosomiasis, lymphatic filariasis, onchocerciasis and trachoma. Several common themes resonate throughout these analyses, including: the importance of epidemiological setting on the success of interventions; targeting groups who are at highest risk of infection or re-infection; and reaching populations who are not accessing interventions and may act as a reservoir for infection,. The results also highlight the challenge of maintaining elimination ‘as a public health problem’ when true elimination is not reached. The models elucidate the factors that may be contributing most to persistence of disease and discuss the requirements for eventually achieving true elimination, if that is possible. Overall this collection presents new analyses to inform current control initiatives. These papers form a base from which further development of the models and more rigorous validation against a variety of datasets can help to give more detailed advice. At the moment, the models’ predictions are being considered as the world prepares for a final push towards control or elimination of neglected tropical diseases by 2020.

Modeling the Effect of Chronic Schistosomiasis on Childhood Development and the Potential for Catch-Up Growth with Different Drug Treatment Strategies Promoted for Control of Endemic Schistosomiasis

In areas endemic for schistosomiasis having limited healthcare, targeted drug treatment of school-age children is recommended for control of Schistosoma-associated morbidity. However, optimal timing, number, and frequency of treatments are not established. Because longitudinal studies of long-term impact of treatment are few, for current policy considerations we performed quantitative simulation (based on calibrated modeling of Schistosoma-associated disease formation) to project the impact of different school-age treatment regimens. Using published efficacy data from targeted programs, combined with age-specific risk for growth retardation and reinfection, we examined the likely impact of different strategies for morbidity prevention. Results suggest the need for early, repeated treatment through primary school years to optimally prevent the disabling sequelae of stunting and undernutrition. Dynamics of infection/reinfection during childhood and adolescence, combined with early treatment effects against reversible infection-associated morbidities, create a need for aggressive retreatment of preadolescents to achieve optimal suppression of morbidity where drug-based control is used.

Projecting the Long-Term Impact of School- or Community-Based Mass-Treatment Interventions for Control of Schistosoma Infection

Background Schistosomiasis remains a significant health burden in many areas of the world. Morbidity control, focused on limiting infection intensity through periodic delivery of anti-schistosomal medicines, is the thrust of current World Health Organization guidelines (2006) for reduction of Schistosoma-related disease. A new appreciation of the lifetime impact of repeated Schistosoma infection has directed attention toward strategies for greater suppression of parasite infection per se, with the goal of transmission interruption. Variations in drug schedules involving increased population coverage and/or treatment frequency are now undergoing field trials. However, their relative effectiveness in long-term infection suppression is presently unknown. Methodology/Principal Findings Our study used available field data to calibrate advanced network models of village-level Schistosoma transmission to project outcomes of six different community- or school age-based programs, as compared to the impact of current 2006 W.H.O. recommended control strategies. We then scored the number of years each of 10 typical villages would remain below 10% infection prevalence (a practicable level associated with minimal prevalence of disease). All strategies that included four annual treatments effectively reduced community prevalence to less than 10%, while programs having yearly gaps (‘holidays’) failed to reach this objective in half of the communities. Effective post-program suppression of infection prevalence persisted in half of the 10 villages for 7–10 years, whereas in five high-risk villages, program effects on prevalence lasted zero to four years only. Conclusions/Significance At typical levels of treatment adherence (60 to 70%), current WHO recommendations will likely not achieve effective suppression of Schistosoma prevalence unless implemented for ≥6 years. Following more aggressive 4 year annual intervention, some communities may be able to continue without further intervention for 8–10 years, while in higher-risk communities, annual treatment may prove necessary until eco-social factors fostering transmission are removed. Effective ongoing surveillance and locally targeted annual intervention must then become their mainstays of control.

Radial bounds for perturbations of elliptic operators

Abstract Elliptic operators A = ∑ ¦α¦ ⩽ m b α (x) D α , α a multi-index, with leading term positive and constant coefficient, and with lower order coefficients b α (x) ϵ L r α + L α ( with ( n r α ) + ¦α¦ defined on R n or a quotient space R n R n U α , U α ⊂ R n are considered. It is shown that the Lp-spectrum of A is contained in a “parabolic region” Ω of the complex plane enclosing the positive real axis, uniformly in p. Outside Ω, the kernel of the resolvent of A is shown to be uniformly bounded by an L1 radial convolution kernel. Some consequences are: A can be closed in all Lp (1 ⩽ p ⩽ ∞), and is essentially self-adjoint in L2 if it is symmetric; A generates an analytic semigroup e−tA in the right half plane, strongly Lp and pointwise continuous at t = 0. A priori estimates relating the leading term and remainder are obtained, and summability φ(eA)ƒ→ e → 0 φ(0) ƒ , with φ analytic, is proved for ƒ ϵ L p , with convergence in Lp and on the Lebesgue set of ƒ. More comprehensive summability results are obtained when A has constant coefficients.

Population Biology of Schistosoma Mating, Aggregation, and Transmission Breakpoints: More Reliable Model Analysis for the End-Game in Communities at Risk

Mathematical modeling is widely used for predictive analysis of control options for infectious agents. Challenging problems arise for modeling host-parasite systems having complex life-cycles and transmission environments. Macroparasites, like Schistosoma, inhabit highly fragmented habitats that shape their reproductive success and distribution. Overdispersion and mating success are important factors to consider in modeling control options for such systems. Simpler models based on mean worm burden (MWB) formulations do not take these into account and overestimate transmission. Proposed MWB revisions have employed prescribed distributions and mating factor corrections to derive modified MWB models that have qualitatively different equilibria, including ‘breakpoints’ below which the parasite goes to extinction, suggesting the possibility of elimination via long-term mass-treatment control. Despite common use, no one has attempted to validate the scope and hypotheses underlying such MWB approaches. We conducted a systematic analysis of both the classical MWB and more recent “stratified worm burden” (SWB) modeling that accounts for mating and reproductive hurdles (Allee effect). Our analysis reveals some similarities, including breakpoints, between MWB and SWB, but also significant differences between the two types of model. We show the classic MWB has inherent inconsistencies, and propose SWB as a reliable alternative for projection of long-term control outcomes.

Mathematical Modeling of Malaria Infection with Innate and Adaptive Immunity in Individuals and Agent-Based Communities

Background Agent-based modeling of Plasmodium falciparum infection offers an attractive alternative to the conventional Ross-Macdonald methodology, as it allows simulation of heterogeneous communities subjected to realistic transmission (inoculation patterns). Methodology/Principal Findings We developed a new, agent based model that accounts for the essential in-host processes: parasite replication and its regulation by innate and adaptive immunity. The model also incorporates a simplified version of antigenic variation by Plasmodium falciparum. We calibrated the model using data from malaria-therapy (MT) studies, and developed a novel calibration procedure that accounts for a deterministic and a pseudo-random component in the observed parasite density patterns. Using the parasite density patterns of 122 MT patients, we generated a large number of calibrated parameters. The resulting data set served as a basis for constructing and simulating heterogeneous agent-based (AB) communities of MT-like hosts. We conducted several numerical experiments subjecting AB communities to realistic inoculation patterns reported from previous field studies, and compared the model output to the observed malaria prevalence in the field. There was overall consistency, supporting the potential of this agent-based methodology to represent transmission in realistic communities. Conclusions/Significance Our approach represents a novel, convenient and versatile method to model Plasmodium falciparum infection.

Refined stratified-worm-burden models that incorporate specific biological features of human and snail hosts provide better estimates of Schistosoma diagnosis, transmission, and control

BackgroundSchistosoma parasites sustain a complex transmission process that cycles between a definitive human host, two free-swimming larval stages, and an intermediate snail host. Multiple factors modify their transmission and affect their control, including heterogeneity in host populations and environment, the aggregated distribution of human worm burdens, and features of parasite reproduction and host snail biology. Because these factors serve to enhance local transmission, their inclusion is important in attempting accurate quantitative prediction of the outcomes of schistosomiasis control programs. However, their inclusion raises many mathematical and computational challenges. To address these, we have recently developed a tractable stratified worm burden (SWB) model that occupies an intermediate place between simpler deterministic mean worm burden models and the very computationally-intensive, autonomous agent models.MethodsTo refine the accuracy of model predictions, we modified an earlier version of the SWB by incorporating factors representing essential in-host biology (parasite mating, aggregation, density-dependent fecundity, and random egg-release) into demographically structured host communities. We also revised the snail component of the transmission model to reflect a saturable form of human-to-snail transmission. The new model allowed us to realistically simulate overdispersed egg-test results observed in individual-level field data. We further developed a Bayesian-type calibration methodology that accounted for model and data uncertainties.ResultsThe new model methodology was applied to multi-year, individual-level field data on S. haematobium infections in coastal Kenya. We successfully derived age-specific estimates of worm burden distributions and worm fecundity and crowding functions for children and adults. Estimates from the new SWB model were compared with those from the older, simpler SWB with some substantial differences noted. We validated our new SWB estimates in prediction of drug treatment-based control outcomes for a typical Kenyan community.ConclusionsThe new version of the SWB model provides a better tool to predict the outcomes of ongoing schistosomiasis control programs. It reflects parasite features that augment and perpetuate transmission, while it also readily incorporates differences in diagnostic testing and human sub-population differences in treatment coverage. Once extended to other Schistosoma species and transmission environments, it will provide a useful and efficient tool for planning control and elimination strategies.

Zonal Schrödinger operators on the

We study the Direct and Inverse Spectral Problems for a class of Schrödinger operatorsH=−Δ+V onSn withzonal (axisymmetric) potentials. Spectrum ofH is known to consist of clusters of eigenvalues {λkm=k(k+n-1)+μkm:m≦k}. The main result of the work is to derive asymptotic expansion of spectral shifts {μkm} in powers ofk−1, and to link coefficients of the expansion to certain transforms ofV. As a corollary we solve the Inverse Problem, get explicit formulae for the Weinsteinband-invariants of cluster distribution measures, and establishlocal spectral rigidity for zonal potential. The latter provides a partial answer to a long standing Spectral Rigidity Hypothesis of V. Guillemin.