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ISDS 2012 Conference Abstracts

Sequential Bayesian Inference for Detection and
Response to Seasonal Epidemics
Michael Ludkovski* and Junjing Lin

Statistics and Applied Probability, UC Santa Barbara, Santa Barbara, CA, USA

Objective
Development of a sequential Bayesian methodology for inference

and detection of seasonal infectious disease epidemics.

Introduction
Detection and response to seasonal outbreaks of endemic diseases

provides an excellent testbed for quantitative bio-surveillance. As a
case study we focus on annual influenza outbreaks. To incorporate
observed year-over-year variation in flu incidence cases and timing
of outbreaks, we analyze a stochastic compartmental SIS model that
includes seasonal forcing by a latent Markovian factor. Epidemic de-
tection then consists in identifying the presence of the environmen-
tal factor (“high” flu season), as well as estimation of the epidemic
parameters, such as contact and recovery rates.

Methods
Anticipating policy-making applications, we consider sequential

Bayesian inference. To focus on intrinsic model uncertainty, we as-
sume full observation of all individual status changes, but unobserved
seasonal factor M underscore “t” and unknown reaction rates. Using
theory of nonlinear filtering of point processes, we derive analytic
expressions for conditional likelihoods of latent factor trajectories.
We then utilize a Sequential Monte Carlo approach based on Particle
Learning (PL) [1] to infer the epidemic parameters in conjunction
with online filtering of M underscore “t.” These tools extend the PL
method to continuous-time jump-Markov models and are widely ap-
plicable in generic stochastic chemical kinetic models.

Using the developed inference methods, we then investigate cost-
efficient sequential policy making. We analyze and compare several
heuristic counter-measure strategies that work by modifying the du-
ration/frequency of the high epidemic season.

Results
The proposed algorithm was implemented in R and extensively

tested on simulated data [2]. We find that the PL method is able to ef-
ficiently carry out joint inference. We also find that counter-measures
incorporating sequential learning are generally more efficient that
other inference-free policies.

Conclusions
We developed a new Bayesian approach to joint inference of pa-

rameters and latent factors in continuous-time stochastic compart-
mental models. There is ongoing work [3] to adjust our methods for
more realistic observation schemes.

Fig: Response strategy based on the Bayesian posterior probability
$\Pi^2_t$ (use math notation) of high flu season $\{ M_t = 1\}$. Counter-
measures begin when prob > 95% and end when prob <5%.

Keywords
Bayesian inference; stochastic compartmental models; seasonal epi-
demics; hidden Markov models

Acknowledgments

We thank Jarad Niemi for useful discussions.

References

[1] Carvalho, C. M.; Johannes, M.; Lopes, H. F. and Polson, N. Particle
learning for sequential Bayesian computation. Bayesian Statistics,
2011, 9, 317-360.

[2] Lin J, and Ludkovski M., Sequential Bayesian Inference in Hidden
Markov Stochastic Kinetic Models with Application to Detection and
Response to Seasonal Epidemics, Submitted, 2012.

[3] Ludkovski M, Niemi J. Optimal disease outbreak decisions using sto-
chastic simulation. In: Proceedings of the 2011 Winter Simulation
Conference. Jain S, et al eds.

*Michael Ludkovski
E-mail: ludkovski@pstat.ucsb.edu

Online Journal of Public Health Informatics * ISSN 1947-2579 * http://ojphi.org * 5(1):e7, 2013