When More Transmission Equals Less Disease: Reconciling the Disconnect between Disease Hotspots and Parasite Transmission

The assumed straightforward connection between transmission intensity and disease occurrence impacts surveillance and control efforts along with statistical methodology, including parameter inference and niche modeling. Many infectious disease systems have the potential for this connection to be more complicated–although demonstrating this in any given disease system has remained elusive. Hemorrhagic disease (HD) is one of the most important diseases of white-tailed deer and is caused by viruses in the Orbivirus genus. Like many infectious diseases, the probability or severity of disease increases with age (after loss of maternal antibodies) and the probability of disease is lower upon re-infection compared to first infection (based on cross-immunity between virus strains). These broad criteria generate a prediction that disease occurrence is maximized at intermediate levels of transmission intensity. Using published US field data, we first fit a statistical model to predict disease occurrence as a function of seroprevalence (a proxy for transmission intensity), demonstrating that states with intermediate seroprevalence have the highest level of case reporting. We subsequently introduce an independently parameterized mechanistic model supporting the theory that high case reporting should come from areas with intermediate levels of transmission. This is the first rigorous demonstration of this phenomenon and illustrates that variation in transmission rate (e.g. along an ecologically-controlled transmission gradient) can create cryptic refuges for infectious diseases.     

Alternative (un)stable states in a stochastic predator–prey model

Stochastic models sometimes behave qualitatively differently from their deterministic analogues. We explore the implications of this in ecosystems that shift suddenly from one state to another. This phenomenon is usually studied through deterministic models with multiple stable equilibria under a single set of conditions, with stability defined through linear stability analysis. However, in stochastic systems, some unstable states can trap stochastic dynamics for long intervals, essentially masquerading as additional stable states. Using a predator–prey model, we demonstrate that this effect is sufficient to make a stochastic system with one stable state exhibit the same characteristics as an analogous system with alternative stable states. Although this result is surprising with respect to how stability is defined by standard analyses, we show that it is well-anticipated by an alternative approach based on the system's “quasi-potential.” Broadly, understanding the risk of sudden state shifts will require a more holistic understanding of stability in stochastic systems.     

Catastrophe theory of dopaminergic transmission: a revised dopamine hypothesis of schizophrenia

Mathematical modeling of experimentally observed parameters of dopaminergic neuronal activity suggests the occurrence of multiple equilibrium states in neurons characterized by certain precisely defined properties of the tyrosine hydroxylating system. These equilibria may become unstable under certain conditions and transitions between multiple states are predicted. In addition, modeling of the spatial interactions of dopamine neurons within a neural net leads to domain wall soliton-like solutions of neuronal firing. In the discrete spatial case, these equations are isomorphic to those of the Ising model of phase transitions in lattice spins.The hypothesis is proposed that the occurrence of multiple stable equilibrium states rather than excessive dopaminergic transmission forms the pathophysiological basis of the schizophrenic thought disorder.The model is internally consistent with known clinical effects of drugs such as neuroleptics, reserpine and amphetamine. In agreement with postmortem and other studies, the theory predicts the lack of increased concentrations of dopamine or its major metabolite, homovanillic acid, in brain and cerebrospinal fluid of schizophrenics.The mathematical model is compatible with the theory that postulates an attention deficit as an underlying mechanism of schizophrenic psychosis and allows for a possible genetic heterogeneity of the disease.     

Disease evolution across a range of spatio-temporal scales

Traditional explorations of infectious disease evolution have considered the competition between two cross-reactive strains within the standard framework of disease models. Such techniques predict that diseases should evolve to be highly transmissible, benign to the host and possess a long infectious period: in general, diseases do not conform to this ideal. Here we consider a more holistic approach, suggesting that evolution is a trade-off between adaptive pressures at different scales: within host, between hosts and at the population level. We present a model combining within-host pathogen dynamics and transmission between individuals governed by an explicit contact network, where transmission dynamics between hosts are a function of the interaction between the pathogen and the hosts' immune system, though ultimately constrained by the contacts each infected host possesses. Our results show how each of the scales places constraints on the evolutionary behavior, and that complex dynamics may emerge due to the feedbacks between epidemiological and evolutionary dynamics. In particular, multiple stable states can occur with switching between them stochastically driven.     

Calculation of Disease Dynamics in a Population of Households

Early mathematical representations of infectious disease dynamics assumed a single, large, homogeneously mixing population. Over the past decade there has been growing interest in models consisting of multiple smaller subpopulations (households, workplaces, schools, communities), with the natural assumption of strong homogeneous mixing within each subpopulation, and weaker transmission between subpopulations. Here we consider a model of SIRS (susceptible-infectious-recovered-susceptible) infection dynamics in a very large (assumed infinite) population of households, with the simplifying assumption that each household is of the same size (although all methods may be extended to a population with a heterogeneous distribution of household sizes). For this households model we present efficient methods for studying several quantities of epidemiological interest: (i) the threshold for invasion; (ii) the early growth rate; (iii) the household offspring distribution; (iv) the endemic prevalence of infection; and (v) the transient dynamics of the process. We utilize these methods to explore a wide region of parameter space appropriate for human infectious diseases. We then extend these results to consider the effects of more realistic gamma-distributed infectious periods. We discuss how all these results differ from standard homogeneous-mixing models and assess the implications for the invasion, transmission and persistence of infection. The computational efficiency of the methodology presented here will hopefully aid in the parameterisation of structured models and in the evaluation of appropriate responses for future disease outbreaks.     

From bistability to oscillations in a model for the isocitrate dehydrogenase reaction

Considered is a bienzymatic system consisting of isocitrate dehydrogenase (IDH, EC 1.1.1.42), which transforms NADP(+) into NADPH, and of diaphorase (DIA, EC 1.8.1.4), which catalyzes the reverse reaction. Experimental evidence as well as a theoretical model show the possibility of a coexistence between two stable steady states in this reaction system. The phenomenon originates from the regulatory properties of IDH. We extend the analysis of a theoretical model proposed for the IDH-DIA bienzymatic system and investigate the occurrence of different modes of bistability, with or without hysteresis, i.e. in the presence of two or only one limit point bounding the domain of multiple steady states. The analysis indicates that the two types of bistability may sometimes be observed sequentially as a given control parameter is progressively increased. We further obtain conditions in which sustained oscillations develop in the model. These results establish the isocitrate dehydrogenase reaction coupled to diaphorase as a suitable candidate for further experimental and theoretical studies of bistability and oscillations in biochemical systems.     

Multiplicity of stable states in freshwater systems

It is shown with the use of minimal models that several ecological relationships in freshwater systems potentially give rise to the existence of alternative equilibria over a certain range of nutrient values. The existence of alternative stable states has some implications for the management of such systems. An important consequence is that signs of eutrophication are only apparent after the occurrence of changes that are very difficult to reverse. Reduction of the nutrient level as a measure to restore such systems gives poor results, but biomanipulation as an additional measure can have significant effects, provided that the nutrient level has been reduced enough to allow the existence of a stable alternative clear water equilibrium.     

Animal models for the study of lymphatic insufficiency

Lymphedema is the term commonly employed to describe the spectrum of pathological states that arise as a consequence of functional lymphatic insufficiency. These human disease entities currently lack an effective cure. Satisfactory therapeutic strategies for both primary and secondary lymphedema will require additional insight into the complex cellular mechanisms and responses that comprise both normal lymphatic function and its regional derangement in states of pathologic dysfunction. Such insights must, initially, be derived from suitable animal models of the chronic human disease process. Historically, efforts to replicate the untreated disease of human lymphedema in animals, through surgery, irradiation, and toxicology, have been fraught with difficulty. The major impediments to the creation of satisfactory animal models have included an inability to reproduce the chronic disease in a stable, reproducible format. Recently, with the promise of potentially successful growth factor-mediated therapeutic lymphangiogenesis, and with the enhanced availability of investigative tools to assess therapeutic responses to molecular therapies, there has been a resurgence of interest in the development of viable animal models of lymphatic insufficiency. Current research has led to the development of genetic and postsurgical models of lymphedema that closely simulate the human conditions of primary and secondary lymphatic insufficiency, respectively. Such models will help to refine the assessment of various therapeutic approaches and their potential applicability to human disease interventions.     

Modelling the Contributions of Malaria,HIV, Malnutrition and Rainfall to the Decline in Paediatric Invasive Non-typhoidal Salmonella Disease in Malawi

Introduction

Nontyphoidal Salmonellae (NTS) are responsible for a huge burden of bloodstream infection in Sub-Saharan African children. Recent reports of a decline in invasive NTS (iNTS) disease from Kenya and The Gambia have emphasised an association with malaria control. Following a similar decline in iNTS disease in Malawi, we have used 9 years of continuous longitudinal data to model the interrelationships between iNTS disease, malaria, HIV and malnutrition.

Methods

Trends in monthly numbers of childhood iNTS disease presenting at Queen’s Hospital, Blantyre, Malawi from 2002 to 2010 were reviewed in the context of longitudinal monthly data describing malaria slide-positivity among paediatric febrile admissions, paediatric HIV prevalence, nutritional rehabilitation unit admissions and monthly rainfall over the same 9 years, using structural equation models (SEM).

Results

Analysis of 3,105 iNTS episodes identified from 49,093 blood cultures, showed an 11.8% annual decline in iNTS (p < 0.001). SEM analysis produced a stable model with good fit, revealing direct and statistically significant seasonal effects of malaria and malnutrition on the prevalence of iNTS disease. When these data were smoothed to eliminate seasonal cyclic changes, these associations remained strong and there were additional significant effects of HIV prevalence.

Conclusions

These data suggest that the overall decline in iNTS disease observed in Malawi is attributable to multiple public health interventions leading to reductions in malaria, HIV and acute malnutrition. Understanding the impacts of public health programmes on iNTS disease is essential to plan and evaluate interventions.     

Effect of Biodiversity Changes in Disease Risk: Exploring Disease Emergence in a Plant-Virus System

The effect of biodiversity on the ability of parasites to infect their host and cause disease (i.e. disease risk) is a major question in pathology, which is central to understand the emergence of infectious diseases, and to develop strategies for their management. Two hypotheses, which can be considered as extremes of a continuum, relate biodiversity to disease risk: One states that biodiversity is positively correlated with disease risk (Amplification Effect), and the second predicts a negative correlation between biodiversity and disease risk (Dilution Effect). Which of them applies better to different host-parasite systems is still a source of debate, due to limited experimental or empirical data. This is especially the case for viral diseases of plants. To address this subject, we have monitored for three years the prevalence of several viruses, and virus-associated symptoms, in populations of wild pepper (chiltepin) under different levels of human management. For each population, we also measured the habitat species diversity, host plant genetic diversity and host plant density. Results indicate that disease and infection risk increased with the level of human management, which was associated with decreased species diversity and host genetic diversity, and with increased host plant density. Importantly, species diversity of the habitat was the primary predictor of disease risk for wild chiltepin populations. This changed in managed populations where host genetic diversity was the primary predictor. Host density was generally a poorer predictor of disease and infection risk. These results support the dilution effect hypothesis, and underline the relevance of different ecological factors in determining disease/infection risk in host plant populations under different levels of anthropic influence. These results are relevant for managing plant diseases and for establishing conservation policies for endangered plant species.     

Inheritance of epigenetic chromatin silencing

Maintenance of alternative chromatin states through cell divisions pose some fundamental constraints on the dynamics of histone modifications. In this paper, we study the systems biology of epigenetic inheritance by defining and analyzing general classes of mathematical models. We discuss how the number of modification states involved plays an essential role in the stability of epigenetic states. In addition, DNA duplication and the consequent dilution of marked histones act as a large perturbation for a stable state of histone modifications. The requirement that this large perturbation falls into the basin of attraction of the original state sometimes leads to additional constraints on effective models. Two such models, inspired by two different biological systems, are compared in their fulfilling the requirements of multistability and of recovery after DNA duplication. We conclude that in the presence of multiple histone modifications that characterize alternative epigenetic stable states, these requirements are more easily fulfilled.     

Influence of Consumption of Cadmium-Polluted Rice or Jinzu River Water on Occurrence of Renal Tubular Dysfunction and/or Itai-itai Disease

The aim of this study was to clarify whether consumption of cadmium (Cd)-polluted rice or Jinzu River water exerted any influence on the occurrence of renal tubular dysfunction and/or Itai-itai disease. From the participants of health examinations conducted in 1967 and 1968, 3,078 subjects who had resided for >30 years in the present hamlet and were aged >50 years were selected as the target population and were divided according to their residence in 55 hamlets. In a multiple regression analysis, the regression coefficients between rice-Cd concentration and prevalence of abnormal urinary findings (proteinuria, glucosuria, or proteinuria with glucosuria) or patients with Itai-itai disease were statistically significant between both sexes. The correlation between the prevalence of users of Jinzu River water and the occurrence of glucosuria in men as well as abnormal urinary findings in women was not statistically significant. We surmise that eating Cd-polluted rice and drinking and/or cooking with Jinzu River water influenced the occurrence of Itai-itai disease. The occurrence of renal tubular dysfunction is likely to have also been influenced by both factors, with eating Cd-polluted rice having a greater impact on the occurrence of renal tubular dysfunction as compared to drinking and/or cooking with Jinzu River water.     

Natural,Persistent Oscillations in a Spatial Multi-Strain Disease System with Application to Dengue

Many infectious diseases are not maintained in a state of equilibrium but exhibit significant fluctuations in prevalence over time. For pathogens that consist of multiple antigenic types or strains, such as influenza, malaria or dengue, these fluctuations often take on the form of regular or irregular epidemic outbreaks in addition to oscillatory prevalence levels of the constituent strains. To explain the observed temporal dynamics and structuring in pathogen populations, epidemiological multi-strain models have commonly evoked strong immune interactions between strains as the predominant driver. Here, with specific reference to dengue, we show how spatially explicit, multi-strain systems can exhibit all of the described epidemiological dynamics even in the absence of immune competition. Instead, amplification of natural stochastic differences in disease transmission, can give rise to persistent oscillations comprising semi-regular epidemic outbreaks and sequential dominance of dengue''s four serotypes. Not only can this mechanism explain observed differences in serotype and disease distributions between neighbouring geographical areas, it also has important implications for inferring the nature and epidemiological consequences of immune mediated competition in multi-strain pathogen systems.     

A Novel Statistical Model to Estimate Host Genetic Effects Affecting Disease Transmission

There is increasing recognition that genetic diversity can affect the spread of diseases, potentially affecting plant and livestock disease control as well as the emergence of human disease outbreaks. Nevertheless, even though computational tools can guide the control of infectious diseases, few epidemiological models can simultaneously accommodate the inherent individual heterogeneity in multiple infectious disease traits influencing disease transmission, such as the frequently modeled propensity to become infected and infectivity, which describes the host ability to transmit the infection to susceptible individuals. Furthermore, current quantitative genetic models fail to fully capture the heritable variation in host infectivity, mainly because they cannot accommodate the nonlinear infection dynamics underlying epidemiological data. We present in this article a novel statistical model and an inference method to estimate genetic parameters associated with both host susceptibility and infectivity. Our methodology combines quantitative genetic models of social interactions with stochastic processes to model the random, nonlinear, and dynamic nature of infections and uses adaptive Bayesian computational techniques to estimate the model parameters. Results using simulated epidemic data show that our model can accurately estimate heritabilities and genetic risks not only of susceptibility but also of infectivity, therefore exploring a trait whose heritable variation is currently ignored in disease genetics and can greatly influence the spread of infectious diseases. Our proposed methodology offers potential impacts in areas such as livestock disease control through selective breeding and also in predicting and controlling the emergence of disease outbreaks in human populations.     

Patterns of coral disease across the Hawaiian archipelago: relating disease to environment

In Hawaii, coral reefs occur across a gradient of biological (host abundance), climatic (sea surface temperature anomalies) and anthropogenic conditions from the human-impacted reefs of the main Hawaiian Islands (MHI) to the pristine reefs of the northwestern Hawaiian Islands (NWHI). Coral disease surveys were conducted at 142 sites from across the Archipelago and disease patterns examined. Twelve diseases were recorded from three coral genera (Porites, Montipora, Acropora) with Porites having the highest prevalence. Porites growth anomalies (PorGAs) were significantly more prevalent within and indicative of reefs in the MHI and Porites trematodiasis (PorTrm) was significantly more prevalent within and indicative of reefs in the NWHI. Porites tissue loss syndrome (PorTLS) was also important in driving regional differences but that relationship was less clear. These results highlight the importance of understanding disease ecology when interpreting patterns of disease occurrence. PorTrm is caused by a parasitic flatworm that utilizes multiple hosts during its life cycle (fish, mollusk and coral). All three hosts must be present for the disease to occur and higher host abundance leads to higher disease prevalence. Thus, a high prevalence of PorTrm on Hawaiian reefs would be an indicator of a healthy coral reef ecosystem. In contrast, the high occurrence of PorGAs within the MHI suggests that PorGAs are related, directly or indirectly, to some environmental co-factor associated with increased human population sizes. Focusing on the three indicator diseases (PorGAs, PorTrm, PorTLS) we used statistical modeling to examine the underlying associations between disease prevalence and 14 different predictor variables (biotic and abiotic). All three diseases showed positive associations with host abundance and negative associations with thermal stress. The association with human population density differed among disease states with PorGAs showing a positive and PorTrm showing a negative association, but no significant explanatory power was offered for PorTLS.     

Modeling Relapsing Disease Dynamics in a Host-Vector Community

Vector-borne diseases represent a threat to human and wildlife populations and mathematical models provide a means to understand and control epidemics involved in complex host-vector systems. The disease model studied here is a host-vector system with a relapsing class of host individuals, used to investigate tick-borne relapsing fever (TBRF). Equilibrium analysis is performed for models with increasing numbers of relapses and multiple hosts and the disease reproduction number, R₀, is generalized to establish relationships with parameters that would result in the elimination of the disease. We show that host relapses in a single competent host-vector system is needed to maintain an endemic state. We show that the addition of an incompetent second host with no relapses increases the number of relapses needed for maintaining the pathogen in the first competent host system. Further, coupling of the system with hosts of differing competencies will always reduce R₀, making it more difficult for the system to reach an endemic state.     

Primary Skin Fibroblasts as a Model of Parkinson's Disease

Parkinson's disease is the second most frequent neurodegenerative disorder. While most cases occur sporadic mutations in a growing number of genes including Parkin (PARK2) and PINK1 (PARK6) have been associated with the disease. Different animal models and cell models like patient skin fibroblasts and recombinant cell lines can be used as model systems for Parkinson's disease. Skin fibroblasts present a system with defined mutations and the cumulative cellular damage of the patients. PINK1 and Parkin genes show relevant expression levels in human fibroblasts and since both genes participate in stress response pathways, we believe fibroblasts advantageous in order to assess, e.g. the effect of stressors. Furthermore, since a bioenergetic deficit underlies early stage Parkinson's disease, while atrophy underlies later stages, the use of primary cells seems preferable over the use of tumor cell lines. The new option to use fibroblast-derived induced pluripotent stem cells redifferentiated into dopaminergic neurons is an additional benefit. However, the use of fibroblast has also some drawbacks. We have investigated PARK6 fibroblasts and they mirror closely the respiratory alterations, the expression profiles, the mitochondrial dynamics pathology and the vulnerability to proteasomal stress that has been documented in other model systems. Fibroblasts from patients with PARK2, PARK6, idiopathic Parkinson's disease, Alzheimer's disease, and spinocerebellar ataxia type 2 demonstrated a distinct and unique mRNA expression pattern of key genes in neurodegeneration. Thus, primary skin fibroblasts are a useful Parkinson's disease model, able to serve as a complement to animal mutants, transformed cell lines and patient tissues.     

Drosophila as an In Vivo Model for Human Neurodegenerative Disease

With the increase in the ageing population, neurodegenerative disease is devastating to families and poses a huge burden on society. The brain and spinal cord are extraordinarily complex: they consist of a highly organized network of neuronal and support cells that communicate in a highly specialized manner. One approach to tackling problems of such complexity is to address the scientific questions in simpler, yet analogous, systems. The fruit fly, Drosophila melanogaster, has been proven tremendously valuable as a model organism, enabling many major discoveries in neuroscientific disease research. The plethora of genetic tools available in Drosophila allows for exquisite targeted manipulation of the genome. Due to its relatively short lifespan, complex questions of brain function can be addressed more rapidly than in other model organisms, such as the mouse. Here we discuss features of the fly as a model for human neurodegenerative disease. There are many distinct fly models for a range of neurodegenerative diseases; we focus on select studies from models of polyglutamine disease and amyotrophic lateral sclerosis that illustrate the type and range of insights that can be gleaned. In discussion of these models, we underscore strengths of the fly in providing understanding into mechanisms and pathways, as a foundation for translational and therapeutic research.     

Multiple Scales and the Maintenance of Biodiversity

The problem of multiple scales permeates the study of ecological process and pattern, uniting aspects of space, time, and organizational complexity. In particular, it supports the maintenance of biological diversity, allowing for the magnification of underlying patterns of variation in the physical environment to create many resources from few, through the evolutionary diversification of species' niches and life histories. Specialization to particular stages of a successional gradient facilitates coexistence of multiple types in the presence of uncorrelated local disturbances, such as gap formation, which reinitiate successional sequences. Superimposed upon such successional dynamics are the effects of multiple stable states and multiple successional pathways (Levin 1976), which increase diversity even more. Multiple stable states more generally raise the possibility of sudden flips of systems from one stable configuration to another, and with such changes may come huge changes in the biotic composition. On larger spatial scales and longer time scales, these flips may become correlated, resulting in the transformation of the landscape, or may result in sustained spatiotemporal mosaics of states. Instability at the local level may lead to the maintenance of biodiversity on broader scales. Finally, the ultimate scale mismatch involves that between the dynamics of natural systems and the cultural dynamics of human societies. Our ability to live sustainably in a global commons is dependent upon adjusting normative behavior, and tightening feedback loops more generally, so that individual actions serve the common good. Received 11 November 1999; accepted 18 February 2000