How to make epidemiological training infectious

Abstract

Modern infectious disease epidemiology builds on two independently developed fields: classical epidemiology and dynamical epidemiology. Over the past decade, integration of the two fields has increased in research practice, but training options within the fields remain distinct with few opportunities for integration in the classroom. The annual Clinic on the Meaningful Modeling of Epidemiological Data (MMED) at the African Institute for Mathematical Sciences has begun to address this gap. MMED offers participants exposure to a broad range of concepts and techniques from both epidemiological traditions. During MMED 2010 we developed a pedagogical approach that bridges the traditional distinction between classical and dynamical epidemiology and can be used at multiple educational levels, from high school to graduate level courses. The approach is hands-on, consisting of a real-time simulation of a stochastic outbreak in course participants, including realistic data reporting, followed by a variety of mathematical and statistical analyses, stemming from both epidemiological traditions. During the exercise, dynamical epidemiologists developed empirical skills such as study design and learned concepts of bias while classical epidemiologists were trained in systems thinking and began to understand epidemics as dynamic nonlinear processes. We believe this type of integrated educational tool will prove extremely valuable in the training of future infectious disease epidemiologists. We also believe that such interdisciplinary training will be critical for local capacity building in analytical epidemiology as Africa continues to produce new cohorts of well-trained mathematicians, statisticians, and scientists. And because the lessons draw on skills and concepts from many fields in biology--from pathogen biology, evolutionary dynamics of host--pathogen interactions, and the ecology of infectious disease to bioinformatics, computational biology, and statistics--this exercise can be incorporated into a broad array of life sciences courses.

Figure 1. Muizenberg Mathematical Fever epidemic time series.

Epidemic time series for the outbreaks at the 2010 (A) and 2011 (B) outbreaks. The former and latter outbreaks differ by their different basic reproductive numbers (defined as the average number of people an infectious individual infects if the rest of the population is susceptible; R ₀ = 1.23 and 1.82, respectively), the initial number of infectious individuals in the population (2 and 4, respectively), and the number of individuals immune at the start of the outbreak (0 and 14, respectively). (C and D) demonstrate how the effective reproductive number (R _eff; average number of individuals each infected person infects) changes during the course of the outbreak as the number of susceptibles decreases and that the epidemic begins to burn out when R _eff decreases below 1 and infectious individuals no longer replace themselves with new infections. The script for production of and further detail on this figure are given in Text S3.

Figure 2. Demonstration of information and confounding bias with simulated outbreak data.

(A) Muizenberg Mathematical Fever 2011 outbreak data to illustrate how using a case definition with imperfect sensitivity (symptomatic disease) can cause nondifferential misclassification bias (the category of information bias where exposed and unexposed individuals are equally likely to be misclassified). Nondifferential misclassification biases the association between a risk factor and a disease outcome towards the null hypothesis of no association (odds ratio = 1). While attendance at the prior year's clinic was actually protective (black square and 95% CI), this bias was sufficient to cause the confidence interval for the odds ratio of this very protective variable to overlap (gray). (B) illustrates how a risk factor (arrival a day or more early to the clinic) that has no real association to a disease outcome can appear associated through confounding. Individuals who had attended the clinic in prior years were less likely to come to the clinic early and were also protected (i.e., A). Consequently, early attendance appeared associated with a higher risk of disease in a univariate analysis (gray) though the CI contains the null hypothesis of no association in a multivariate analysis that adjusts for prior attendance (black). The script for production of and further detail on this figure are given in Text S3.

Figure 3. Utility of stochastic simulation to study the effect of vaccination on future outbreaks.

(A) Five stochastic simulations of Muizenberg Mathematical Fever outbreaks using transmission parameters fit from the 2011 outbreak data but with only one infected individual initiating the outbreak (instead of four) but the same proportion initially immune (25%). In comparison to Figure 1A, the outbreak would appear less likely to take off (with four simulated outbreaks burning out by Wednesday) if only one infected individual initiated the outbreak. (B) shows the distribution of outbreak size (total number infected before burnout) among simulated outbreaks in populations with different immune proportions at the outbreak initiation. The black line shows the median outbreak size among 1,000 stochastic simulations for each immune proportion and the gray regions show 10% quantiles of outbreak size. Only small levels of immunity are necessary to make outbreaks rare (with a fifth of the population immune 50% of simulated outbreaks never exceed more than two secondary cases), but just by chance larger outbreaks still occur. The script for production of and further detail on this figure are given in Text S3.