We are interested in investigating whether one can estimate the magnitude of an outbreak
of a non-communicable or communicable disease based on a very incomplete observation of
the outbreak. The most relevant application is in the problem of bioterrorism
(recall the Anthrax attacks of 2001), but one may also consider outbreaks of
emergent diseases
(e.g.
the epidemic of Ebola in gorillas (NY Times, Science section, December 8, 2006) .
One of the findings of the "Dark Winter" exercise
("Shining Light on Dark Winter", O'Toole, Mair and Inglesby, Clinical
Infectious Diseases, 2002;34:972-983) was that getting a "handle" on the
magnitude of the number of people infected in such an outbreak would have been helpful.
In these cases, all one has to go upon is the set of patients that show
symptoms over time. If the magnitude of an outbreak could be estimated from a few (2-4)
days of observations, it could inform a better medical response.
Outbreaks of non-contagious diseases: A case in point is the accidental release of anthrax on April 2nd, 1979 ("The Sverdlovsk Anthrax Outbreak of 1979", Meselson et al., Science 266, 1202-1208, 1994). The picture on the right (from Meselson's paper) shows the plume spreading out over Sverdlovsk and the locations of the 64 people who died over the next 42 days. First symptoms were manifest on April 4th, and anthrax was diagnosed on April 9th. The prophylatic and vaccination measures which were put into effect during the middle of April in Chkalovskiy rayon affected about 59,000 people. Being able to estimate the magnitude of the outbreak early could have enabled a more measured (and quicker!) response.
Using a time-series of patients showing symptoms, we formulated a Bayesian inverse problem for the size and time of the outbreak. These estimates were developed as probability density functions. By April 7th, the date of the release (April 2nd) was easily identified, and by April 14th (before vaccinations started) one could estimate that the outbreak very probably affected less than 100 people (see SAND2006-7568 below).
Some preliminary results on the efficacy of this method for Variola major is in SAND2006-1491 below.
Outbreaks of contagious diseases: Contagious diseases pose a special complication when attempting to estimate their threat - they spread and grow. The growth rate depends on the intrinsic transmissibility of the pathogen and the mixing patterns of the society. Thus epidemics of contagious diseases, recorded in remote places/societies (Ebola in equitorial Africa, smallpox in the Indian sub-continent in '60s and '70s etc) may provide an incomplete picture of how such an epidemic might behave in contemporary society. NIH, under the MIDAS project releases models of social mixing; obtaining the intrinsic transmissibility of a pathogen then becomes the missing link in accomplishing realistic epidemiological simulations in contemporary society. This is best done records of historical outbreaks. However, since these records do not document mixing patterns, both the transmissibility and the social connections in the observed outbreak have to be inferred from the data at hand. Since the data is often sparse, only simple models of the society can be inferred. One common model of the mixing in a society is a social network.
We developed a method where we form a Bayesian inverse problem using a model of epidemic spread over a static social network. We use data from the Abakaliki smallpox outbreak, Nigeria, 1971 (Transmission potential of smallpox, Eicher and Dietz, Am. J. Epidemiol, 158(2):110-117, 2003.). The population was structured and was modeled a set of binomial graphs of unknown link probabilities. The links of the social network supported a Poisson-process transmission, with an unknown rate. Using the observations (the days 30 people showed symptoms of smallpox, in a population of 74), we were able to infer values for link probabilities and the transmission rate. A simple random-walk MCMC method was used to solve the inverse problem. This also allowed a probabilistic inference of the chain of transmission in that outbreak. Click here to see a plot of it.
Some details are in our JSM 2008 and Chem-Bio conference paper below (SAND2008-6579C and SAND2008-5049C, respectively).
Detailed simulations of emergent infectious diseases in contemporary societies: While inferring pathogenic transmissibilies from historical outbreaks is helpful in planning for their outbreaks in contemporary society, it does require to be married to an actual model of social mixing in a modern society, so that the mechanisms of spread may be reproduced faithfully. As mentioned above, MIDAS project releases models of social mixing; one needs to actually implement the model that realizes the marriage. This can be done using individual-based models (Eubank et al., Nature, Nature, 429(6998), 2004:180-184). These models use data of social mixing - actual observations (or synthetic data which can be quickly validated against actual observations) of a population going through various locations in a city in its day-to-day life - without further processing or approximations, and hence their allure (and potential) for accuracy. The models are computationally intensive, and invaraibly require supercomputers to solve. It would be helpful if the individual-based models, whose interactions are akin to dynamic social networks, could be "boiled-down" into a static network, which nevertheless preserved the epidemiological dynamics one observes in the individual-based models. These would be significantly inexpensive (computationally) and could be easily used in predictive purposes, especially during planning and investigating "what-if" scenarios. We have constructed individual-based models to investigate the spread of diseases, using MIDAS data. We have also explored the "boiling" process, whereby equivalent static network models of mixing may be derived from dynamic (MIDAS) data and are exploring its use in "calibrating" simpler models which are typically used for planning purposes. See our publications in Reference 6 and 7 below (SAND2008-6044 and SAND2008-6170C).
Created by Jaideep Ray
