Emerging Themes in Epidemiology

Great progress has been made in mathematical models of cholera transmission dynamics in recent years. However, little impact, if any, has been made by models upon public health decision-making and day-to-day routine of epidemiologists. This paper provides a brief introduction to the basics of ordinary differential equation models of cholera transmission dynamics. We discuss a basic model adapted from Codeço (2001), and how it can be modified to incorporate different hypotheses, including the importance of asymptomatic or inapparent infections, and hyperinfectious V. cholerae and human-to-human transmission. We highlight three important challenges of cholera models: (1) model misspecification and parameter uncertainty, (2) modeling the impact of water, sanitation and hygiene interventions and (3) model structure. We use published models, especially those related to the 2010 Haitian outbreak as examples. We emphasize that the choice of models should be dictated by the research questions in mind. More collaboration is needed between policy-makers, epidemiologists and modelers in public health. Introduction Since the 19th century, humans have experienced seven cholera pandemics. The seventh pandemic started in Indonesia in 1961 and continues to threaten vulnerable populations globally [1]. The cholera outbreak that began in October 2010 in Haiti, where cholera had been absent for a century, reminds us the importance of timely cholera prevention, treatment and control and the critical importance of water and sanitation infrastructure that has eliminated cholera from much of the developed world [2]. To better understand cholera epidemiology retrospectively and to predict the impact of interventions in the future, many researchers have begun using mathematical models as tools complementary to field epidemiology and statistical analysis. Mathematical models help us conceptualize the transmission dynamics in a quantitative way and allow us to test different hypotheses and understand their relative importance in silico. Important epidemiological observations and hypotheses for cholera Correspondence: [email protected] Department of Epidemiology, Jiann-Ping Hsu College of Public Health, Georgia Southern University, Statesboro, GA, USA Health Economics and Modeling Unit, Scientific and Program Services Branch, Division of Preparedness and Emerging Infections, National Center for Emerging and Zoonotic Infectious Diseases, Centers for Disease Control and Prevention, Atlanta, GA, USA © 2014 Fung; licensee BioMed Central Ltd. Th Attribution License (http://creativecommons.o reproduction in any medium, provided the or have been modeled; examples include estimation of the basic reproduction number (R0) [3,4], seasonal variation in cholera incidence [5], inapparent cholera infections [6], hyperinfectivity of V. cholerae [7], human-to-human transmission [8], and the role of human mobility and river networks in transmission [5,9]. Mathematical models also allow us to prospectively estimate the impact of various interventions, from treatment (oral rehydration therapy and antibiotics) to prevention (oral cholera vaccine (OCV), and water, sanitation and hygiene (WASH) interventions (e.g. [9-12])). The purpose of this paper is to introduce cholera dynamic transmission models to public health practitioners, with an educational emphasis of conveying modeling concepts to students of these models. Models are simple, but not simplistic representations of the real world. They are used to capture the “essence” of a complex phenomenon. Models may help us better understand the relationship between different parts of the system. Some models may shed light on past epidemics while some may help us forecast the future. Here we define dynamic transmission models as models that explicitly simulate the transmission dynamics of infectious diseases in time. This paper will focus on the ordinary differential equation (ODE) models (population-based continuous-time models as contrast to population-based discrete-time models using difference is is an open access article distributed under the terms of the Creative Commons rg/licenses/by/2.0), which permits unrestricted use, distribution, and iginal work is properly cited. Fung Emerging Themes in Epidemiology 2014, 11:1 Page 2 of 11 http://www.ete-online.com/content/11/1/1 equations), while we will mention relevant agent-based models where appropriate (e.g. [9]). Through a basic model, we will explain the major parameters and how interventions may change them. We will discuss how different assumptions and hypotheses can be accommodated by making changes to the model’s structure. Focus is given to the way different research questions dictate the model structure. Published models were chosen as illustrations and the list is not meant to be exhaustive. Priority is given to papers that model specifically the 2010 Haiti cholera epidemic. Instead of being a systematic review of all existing cholera models, my aim is to highlight three current major challenges of modeling efforts of cholera transmission dynamics: (1) parameter uncertainty and model misspecification; (2) interventions (especially, water, sanitation and hygiene); and (3) model structure. Spatial and climatic elements are also important features but they are beyond the scope of this paper (they are briefly discussed in the Additional file 1). For a detailed review of the recent cholera modeling literature, please refer to ref. [13].