Joseph H. Tien

Second-pandemic strain of Vibrio cholerae from the Philadelphia cholera outbreak of 1849.

In the 19th century, there were several major cholera pandemics in the Indian subcontinent, Europe, and North America. The causes of these outbreaks and the genomic strain identities remain a mystery. We used targeted high-throughput sequencing to reconstruct the Vibrio cholerae genome from the preserved intestine of a victim of the 1849 cholera outbreak in Philadelphia, part of the second cholera pandemic. This O1 biotype strain has 95 to 97% similarity with the classical O395 genome, differing by 203 single-nucleotide polymorphisms (SNPs), lacking three genomic islands, and probably having one or more tandem cholera toxin prophage (CTX) arrays, which potentially affected its virulence. This result highlights archived medical remains as a potential resource for investigations into the genomic origins of past pandemics.

Examining rainfall and cholera dynamics in Haiti using statistical and dynamic modeling approaches.

Haiti has been in the midst of a cholera epidemic since October 2010. Rainfall is thought to be associated with cholera here, but this relationship has only begun to be quantitatively examined. In this paper, we quantitatively examine the link between rainfall and cholera in Haiti for several different settings (including urban, rural, and displaced person camps) and spatial scales, using a combination of statistical and dynamic models. Statistical analysis of the lagged relationship between rainfall and cholera incidence was conducted using case crossover analysis and distributed lag nonlinear models. Dynamic models consisted of compartmental differential equation models including direct (fast) and indirect (delayed) disease transmission, where indirect transmission was forced by empirical rainfall data. Data sources include cholera case and hospitalization time series from the Haitian Ministry of Public Health, the United Nations Water, Sanitation and Health Cluster, International Organization for Migration, and Hôpital Albert Schweitzer. Rainfall data was obtained from rain gauges from the U.S. Geological Survey and Haiti Regeneration Initiative, and remote sensing rainfall data from the National Aeronautics and Space Administration Tropical Rainfall Measuring Mission. A strong relationship between rainfall and cholera was found for all spatial scales and locations examined. Increased rainfall was significantly correlated with increased cholera incidence 4-7 days later. Forcing the dynamic models with rainfall data resulted in good fits to the cholera case data, and rainfall-based predictions from the dynamic models closely matched observed cholera cases. These models provide a tool for planning and managing the epidemic as it continues.

Identifiability and estimation of multiple transmission pathways in cholera and waterborne disease.

Cholera and many waterborne diseases exhibit multiple characteristic timescales or pathways of infection, which can be modeled as direct and indirect transmission. A major public health issue for waterborne diseases involves understanding the modes of transmission in order to improve control and prevention strategies. An important epidemiological question is: given data for an outbreak, can we determine the role and relative importance of direct vs. environmental/waterborne routes of transmission? We examine whether parameters for a differential equation model of waterborne disease transmission dynamics can be identified, both in the ideal setting of noise-free data (structural identifiability) and in the more realistic setting in the presence of noise (practical identifiability). We used a differential algebra approach together with several numerical approaches, with a particular emphasis on identifiability of the transmission rates. To examine these issues in a practical public health context, we apply the model to a recent cholera outbreak in Angola (2006). Our results show that the model parameters-including both water and person-to-person transmission routes-are globally structurally identifiable, although they become unidentifiable when the environmental transmission timescale is fast. Even for water dynamics within the identifiable range, when noisy data are considered, only a combination of the water transmission parameters can practically be estimated. This makes the waterborne transmission parameters difficult to estimate, leading to inaccurate estimates of important epidemiological parameters such as the basic reproduction number (R0). However, measurements of pathogen persistence time in environmental water sources or measurements of pathogen concentration in the water can improve model identifiability and allow for more accurate estimation of waterborne transmission pathway parameters as well as R0. Parameter estimates for the Angola outbreak suggest that both transmission pathways are needed to explain the observed cholera dynamics. These results highlight the importance of incorporating environmental data when examining waterborne disease.

A cholera model in a patchy environment with water and human movement.

A mathematical model for cholera is formulated that incorporates direct and indirect transmission, patch structure, and both water and human movement. The basic reproduction number R0 is defined and shown to give a sharp threshold that determines whether or not the disease dies out. Kirchhoffs Matrix Tree Theorem from graph theory is used to investigate the dependence of R0 on the connectivity and movement of water, and to prove the global stability of the endemic equilibrium when R0>1. The type/target reproduction numbers are derived to measure the control strategies that are required to eradicate cholera from all patches.

Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive of R0. We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more general n-patch setting.

Parameter estimation for bursting neural models.

This paper presents work on parameter estimation methods for bursting neural models. In our approach we use both geometrical features specific to bursting, as well as general features such as periodic orbits and their bifurcations. We use the geometry underlying bursting to introduce defining equations for burst initiation and termination, and restrict the estimation algorithms to the space of bursting periodic orbits when trying to fit periodic burst data. These geometrical ideas are combined with automatic differentiation to accurately compute parameter sensitivities for the burst timing and period. In addition to being of inherent interest, these sensitivities are used in standard gradient-based optimization algorithms to fit model burst duration and period to data. As an application, we fit Butera et al.’s (Journal of Neurophysiology 81, 382–397, 1999) model of preBötzinger complex neurons to empirical data both in control conditions and when the neuromodulator norepinephrine is added (Viemari and Ramirez, Journal of Neurophysiology 95, 2070–2082, 2006). The results suggest possible modulatory mechanisms in the preBötzinger complex, including modulation of the persistent sodium current.

Cholera Models with Hyperinfectivity and Temporary Immunity

A mathematical model for cholera is formulated that incorporates hyperinfectivity and temporary immunity using distributed delays. The basic reproduction number

BIFURCATIONS IN THE FAST DYNAMICS OF NEURONS: IMPLICATIONS FOR BURSTING

\mathcal{R}_{0}

Herald waves of cholera in nineteenth century London

is defined and proved to give a sharp threshold that determines whether or not the disease dies out. The case of constant temporary immunity is further considered with two different infectivity kernels. Numerical simulations are carried out to show that when

Pituitary network connectivity as a mechanism for the luteinising hormone surge.

\mathcal{R}_{0}>1