Marisa C. Eisenberg

What Factors Might Have Led to the Emergence of Ebola in West Africa

An Ebola outbreak of unprecedented scope emerged in West Africa in December 2013 and presently continues unabated in the countries of Guinea, Sierra Leone, and Liberia. Ebola is not new to Africa, and outbreaks have been confirmed as far back as 1976. The current West African Ebola outbreak is the largest ever recorded and differs dramatically from prior outbreaks in its duration, number of people affected, and geographic extent. The emergence of this deadly disease in West Africa invites many questions, foremost among these: why now, and why in West Africa? Here, we review the sociological, ecological, and environmental drivers that might have influenced the emergence of Ebola in this region of Africa and its spread throughout the region. Containment of the West African Ebola outbreak is the most pressing, immediate need. A comprehensive assessment of the drivers of Ebola emergence and sustained human-to-human transmission is also needed in order to prepare other countries for importation or emergence of this disease. Such assessment includes identification of country-level protocols and interagency policies for outbreak detection and rapid response, increased understanding of cultural and traditional risk factors within and between nations, delivery of culturally embedded public health education, and regional coordination and collaboration, particularly with governments and health ministries throughout Africa. Public health education is also urgently needed in countries outside of Africa in order to ensure that risk is properly understood and public concerns do not escalate unnecessarily. To prevent future outbreaks, coordinated, multiscale, early warning systems should be developed that make full use of these integrated assessments, partner with local communities in high-risk areas, and provide clearly defined response recommendations specific to the needs of each community.

Mechanistic modeling of the effects of myoferlin on tumor cell invasion

Myoferlin (MYOF) is a member of the evolutionarily conserved ferlin family of proteins, noted for their role in a variety of membrane processes, including endocytosis, repair, and vesicular transport. Notably, ferlins are implicated in Caenorhabditis elegans sperm motility (Fer-1), mammalian skeletal muscle development and repair (MYOF and dysferlin), and presynaptic transmission in the auditory system (otoferlin). In this paper, we demonstrate that MYOF plays a previously unrecognized role in cancer cell invasion, using a combination of mathematical modeling and in vitro experiments. Using a real-time impedance-based invasion assay (xCELLigence), we have shown that lentiviral-based knockdown of MYOF significantly reduced invasion of MDA-MB-231 breast cancer cells in Matrigel bioassays. Based on these experimental data, we developed a partial differential equation model of MYOF effects on cancer cell invasion, which we used to generate mechanistic hypotheses. The mathematical model predictions revealed that matrix metalloproteinases (MMPs) may play a key role in modulating this invasive property, which was supported by experimental data using quantitative RT-PCR screens. These results suggest that MYOF may be a promising target for biomarkers or drug target for metastatic cancer diagnosis and therapy, perhaps mediated through MMPs.

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.

Extensions, Validation, and Clinical Applications of a Feedback Control System Simulator of the Hypothalamo-Pituitary-Thyroid Axis

BACKGROUND We upgraded our recent feedback control system (FBCS) simulation model of human thyroid hormone (TH) regulation to include explicit representation of hypothalamic and pituitary dynamics, and updated TH distribution and elimination (D&E) parameters. This new model greatly expands the range of clinical and basic science scenarios explorable by computer simulation. METHODS We quantified the model from pharmacokinetic (PK) and physiological human data and validated it comparatively against several independent clinical data sets. We then explored three contemporary clinical issues with the new model: combined triiodothyronine (T(3))/thyroxine (T(4)) versus T(4)-only treatment, parenteral levothyroxine (L-T(4)) administration, and central hypothyroidism. RESULTS Combined T(3)/T(4) therapy--In thyroidectomized patients, the L-T(4)-only replacement doses needed to normalize plasma T(3) or average tissue T(3) were 145 microg L-T(4)/day or 165 microg L-T(4)/day, respectively. The combined T(4) + T(3) dosing needed to normalize both plasma and tissue T(3) levels was 105 microg L-T(4) + 9 microg T(3) per day. For all three regimens, simulated mean steady-state plasma thyroid-stimulating hormone (TSH), T(3), and T(4) was within normal ranges (TSH: 0.5-5 mU/L; T(4): 5-12 microg/dL; T(3): 0.8-1.9 ng/mL). Parenteral T(4) administration--800 microg weekly or 400 microg twice weekly normalized average tissue T(3) levels both for subcutaneous (SC) and intramuscular (IM) routes of administration. TSH, T(3), and T(4) levels were maintained within normal ranges for all four of these dosing schemes (1x vs. 2x weekly, SC vs. IM). Central hypothyroidism--We simulated steady-state plasma T(3), T(4), and TSH concentrations in response to varying degrees of central hypothyroidism, reducing TSH secretion from 50% down to 0.1% of normal. Surprisingly, TSH, T(3), and T(4) plasma concentrations remained within normal ranges for TSH secretion as low as 25% of normal. CONCLUSIONS Combined T(3)/T(4) treatment--Simulated standard L-T(4)-only therapy was sufficient to renormalize average tissue T(3) levels and maintain normal TSH, T(3), and T(4) plasma levels, supporting adequacy of standard L-T(4)-only treatment. Parenteral T(4) administration-TSH, T(3), and T(4) levels were maintained within normal ranges for all four of these dosing schemes (1x vs. 2x weekly, SC vs. IM), supporting these therapeutic alternatives for patients with compromised L-T(4) gut absorption. Central hypothyroidism--These results highlight how highly nonlinear feedback in the hypothalamic-pituitary-thyroid axis acts to maintain normal hormone levels, even with severely reduced TSH secretion.

Opinion: Mathematical models: A key tool for outbreak response

The 2014 outbreak of Ebola in West Africa is unprecedented in its size and geographic range, and demands swift, effective action from the international community. Understanding the dynamics and spread of Ebola is critical for directing interventions and extinguishing the epidemic; however, observational studies of local conditions have been incomplete and limited by the urgent need to direct resources to patient care.

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.

TSH-Based Protocol, Tablet Instability, and Absorption Effects on L-T4 Bioequivalence

BACKGROUND FDA Guidance for pharmacokinetic (PK) testing of levothyroxine (L-T(4)) for interbrand bioequivalence has evolved recently. Concerns remain about efficacy and safety of the current protocol, based on PK analysis following supraphysiological L-T(4) dosing in euthyroid volunteers, and recent recalls due to intrabrand manufacturing problems also suggest need for further refinement. We examine these interrelated issues quantitatively, using simulated what-if scenarios testing efficacy of a TSH-based protocol and tablet stability and absorption, to enhance precision of L-T(4) bioequivalence methods. METHODS We use an updated simulation model of human thyroid hormone regulation quantified and validated from data that span a wide range of normal and abnormal thyroid system function. Bioequivalence: We explored a TSH-based protocol, using normal replacement dosing in simulated thyroidectomized patients, switching brands after 8 weeks of full replacement dosing. We simulated effects of tablet potency differences and intestinal absorption differences on predicted plasma TSH, T(4), and triiodothyronine (T(3)) dynamics. Stability: We simulated effects of potency decay and lot-by-lot differences in realistic scenarios, using actual tablet potency data spanning 2 years, comparing the recently reduced 95-105% FDA-approved potency range with the original 90-110% range. RESULTS A simulated decrease as small as 10-15% in L-T(4) or its absorption generated TSH concentrations outside the bioequivalence target range (0.5-2.5 mU/L TSH), whereas T(3) and T(4) plasma levels were maintained normal. For a 25% reduction, steady-state TSH changed 300% (from 1.5 to 6 mU/L) compared with <25% for both T(4) and T(3) (both within their reference ranges). Stability: TSH, T(4), and T(3) remained within normal ranges for most potency decay scenarios, but tablets of the same dose strength and brand were not bioequivalent between lots and between fresh and near-expired tablets. CONCLUSIONS A pharmacodynamic TSH-measurement bioequivalence protocol, using normal L-T(4) replacement dosing in athyreotic volunteers, is likely to be more sensitive and safer than current FDA Guidance based on T(4) PK. The tightened 95-105% allowable potency range for L-T(4) tablets is a significant improvement, but otherwise acceptable potency differences (whether due to potency decay or lot-by-lot inconsistencies) may be problematic for some patients, for example, those undergoing high-dose L-T(4) therapy for cancer.

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.

Determining identifiable parameter combinations using subset profiling

Identifiability is a necessary condition for successful parameter estimation of dynamic system models. A major component of identifiability analysis is determining the identifiable parameter combinations, the functional forms for the dependencies between unidentifiable parameters. Identifiable combinations can help in model reparameterization and also in determining which parameters may be experimentally measured to recover model identifiability. Several numerical approaches to determining identifiability of differential equation models have been developed, however the question of determining identifiable combinations remains incompletely addressed. In this paper, we present a new approach which uses parameter subset selection methods based on the Fisher Information Matrix, together with the profile likelihood, to effectively estimate identifiable combinations. We demonstrate this approach on several example models in pharmacokinetics, cellular biology, and physiology.