Water Supply Interruptions and Suspected Cholera Incidence: A Time-Series Regression in the Democratic Republic of the Congo

Data that underpins a publication on water supply interruptions and suspected Cholera incidenc

Evolutionary Game Theory and Social Learning Can Determine How Vaccine Scares Unfold

Immunization programs have often been impeded by vaccine scares, as evidenced by the measles-mumps-rubella (MMR) autism vaccine scare in Britain. A “free rider” effect may be partly responsible: vaccine-generated herd immunity can reduce disease incidence to such low levels that real or imagined vaccine risks appear large in comparison, causing individuals to cease vaccinating. This implies a feedback loop between disease prevalence and strategic individual vaccinating behavior. Here, we analyze a model based on evolutionary game theory that captures this feedback in the context of vaccine scares, and that also includes social learning. Vaccine risk perception evolves over time according to an exogenously imposed curve. We test the model against vaccine coverage data and disease incidence data from two vaccine scares in England & Wales: the whole cell pertussis vaccine scare and the MMR vaccine scare. The model fits vaccine coverage data from both vaccine scares relatively well. Moreover, the model can explain the vaccine coverage data more parsimoniously than most competing models without social learning and/or feedback (hence, adding social learning and feedback to a vaccine scare model improves model fit with little or no parsimony penalty). Under some circumstances, the model can predict future vaccine coverage and disease incidence—up to 10 years in advance in the case of pertussis—including specific qualitative features of the dynamics, such as future incidence peaks and undulations in vaccine coverage due to the population's response to changing disease incidence. Vaccine scares could become more common as eradication goals are approached for more vaccine-preventable diseases. Such models could help us predict how vaccine scares might unfold and assist mitigation efforts

The Role of Environmental Transmission in Recurrent Avian Influenza Epidemics

Avian influenza virus (AIV) persists in North American wild waterfowl, exhibiting major outbreaks every 2–4 years. Attempts to explain the patterns of periodicity and persistence using simple direct transmission models are unsuccessful. Motivated by empirical evidence, we examine the contribution of an overlooked AIV transmission mode: environmental transmission. It is known that infectious birds shed large concentrations of virions in the environment, where virions may persist for a long time. We thus propose that, in addition to direct fecal/oral transmission, birds may become infected by ingesting virions that have long persisted in the environment. We design a new host–pathogen model that combines within-season transmission dynamics, between-season migration and reproduction, and environmental variation. Analysis of the model yields three major results. First, environmental transmission provides a persistence mechanism within small communities where epidemics cannot be sustained by direct transmission only (i.e., communities smaller than the critical community size). Second, environmental transmission offers a parsimonious explanation of the 2–4 year periodicity of avian influenza epidemics. Third, very low levels of environmental transmission (i.e., few cases per year) are sufficient for avian influenza to persist in populations where it would otherwise vanish

Modeling Transmission Dynamics and Control of Vector-Borne Neglected Tropical Diseases

Neglected tropical diseases affect more than one billion people worldwide. The populations most impacted by such diseases are typically the most resource-limited. Mathematical modeling of disease transmission and cost-effectiveness analyses can play a central role in maximizing the utility of limited resources for neglected tropical diseases. We review the contributions that mathematical modeling has made to optimizing intervention strategies of vector-borne neglected diseases. We propose directions forward in the modeling of these diseases, including integrating new knowledge of vector and pathogen ecology, incorporating evolutionary responses to interventions, and expanding the scope of sensitivity analysis in order to achieve robust results

A Simple Stochastic Model with Environmental Transmission Explains Multi-Year Periodicity in Outbreaks of Avian Flu

Avian influenza virus reveals persistent and recurrent outbreaks in North American wild waterfowl, and exhibits major outbreaks at 2–8 years intervals in duck populations. The standard susceptible-infected- recovered (SIR) framework, which includes seasonal migration and reproduction, but lacks environmental transmission, is unable to reproduce the multi-periodic patterns of avian influenza epidemics. In this paper, we argue that a fully stochastic theory based on environmental transmission provides a simple, plausible explanation for the phenomenon of multi-year periodic outbreaks of avian flu. Our theory predicts complex fluctuations with a dominant period of 2 to 8 years which essentially depends on the intensity of environmental transmission. A wavelet analysis of the observed data supports this prediction. Furthermore, using master equations and van Kampen system-size expansion techniques, we provide an analytical expression for the spectrum of stochastic fluctuations, revealing how the outbreak period varies with the environmental transmission

Regional-scale climate-variability synchrony of cholera epidemics in West Africa

BACKGROUND: The relationship between cholera and climate was explored in Africa, the continent with the most reported cases, by analyzing monthly 20-year cholera time series for five coastal adjoining West African countries: Côte d'Ivoire, Ghana, Togo, Benin and Nigeria. METHODS: We used wavelet analyses and derived methods because these are useful mathematical tools to provide information on the evolution of the periodic component over time and allow quantification of non-stationary associations between time series. RESULTS: The temporal variability of cholera incidence exhibits an interannual component, and a significant synchrony in cholera epidemics is highlighted at the end of the 1980's. This observed synchrony across countries, even if transient through time, is also coherent with both the local variability of rainfall and the global climate variability quantified by the Indian Oscillation Index. CONCLUSION: Results of this study suggest that large and regional scale climate variability influence both the temporal dynamics and the spatial synchrony of cholera epidemics in human populations in the Gulf of Guinea, as has been described for two other tropical regions of the world, western South America and Bangladesh

Development, environmental degradation, and disease spread in the Brazilian Amazon

The Amazon is Brazil’s greatest natural resource and invaluable to the rest of the world as a buffer against climate change. The recent election of Brazil’s president brought disputes over development plans for the region back into the spotlight. Historically, the development model for the Amazon has focused on exploitation of natural resources, resulting in environmental degradation, particularly deforestation. Although considerable attention has focused on the long-term global cost of “losing the Amazon,” too little attention has focused on the emergence and reemergence of vector-borne diseases that directly impact the local population, with spillover effects to other neighboring areas. We discuss the impact of Amazon development models on human health, with a focus on vector-borne disease risk. We outline policy actions that could mitigate these negative impacts while creating opportunities for environmentally sensitive economic activities

Nonlinear Dynamics Simulations of Microbial Ecological Processes: Model, Diagnostic Parameters of Deterministic Chaos, and Sensitivity Analysis

Modeling of ecological processes is demonstrated using a newly developed nonlinear dynamics model of microbial populations, consisting of a 4-variable system of coupled ordinary differential equations. The system also includes a modified version of the Monod kinetics equation. The model is designed to simulate the temporal behavior of a microbiological system containing a nutrient, two feeding microbes and a microbe predator. Three types of modeling scenarios were numerically simulated to assess the instability caused by (a) variations of the nutrient flux into the system, with fixed initial microbial concentrations and parameters, (b) variations in initial conditions, with fixed other parameters, and (c) variations in selected parameters. A modeling framework, using the high-level statistical computing languages MATLAB and R, was developed to conduct the time series analysis in the time domain and phase space. In the time domain, the Hurst exponent, the information measure–Shannon’s entropy, and the time delay of temporal oscillations of nutrient and microbe concentrations were calculated. In the phase domain, we calculated a set of diagnostic criteria of deterministic chaos: global and local embedding dimensions, correlation dimension, information dimension, and a spectrum of Lyapunov exponents. The time series data are used to plot the phase space attractors to express the dependence between the system’s state parameters, i.e., microbe concentrations, and pseudo-phase space attractors, in which the attractor axes are used to compare the observations from a single time series, which are separated by the time delay. Like classical Lorenz or Rossler systems of equations, which generate a deterministic chaotic behavior for a certain range of input parameters, the developed mathematical model generates a deterministic chaotic behavior for a particular set of input parameters. Even a slight variation of the system’s input data might result in vastly different predictions of the temporal oscillations of the system. As the nutrient influx increases, the system exhibits a sharp transition from a steady state to deterministic chaotic to quasi-periodic and again to steady state behavior. For small changes in initial conditions, resulting attractors are bounded (contrary to that of a random system), i.e., may represent a ‘sustainable state’ (i.e., resilience) of the ecological system