Inference and control of the nosocomial transmission of methicillin-resistant Staphylococcus aureus

Pei, Sen; Morone, Flaviano; Liljeros, Fredrik; Makse, Hernán; Shaman, Jeffrey L

To generate synthetic outbreak observations, we used the agent-based model to simulate weekly incidence during a one-year period (52 weeks), and then imposed noise to produce the observations used in inference (See details in Appendix 1). We ran 20 iterations of the EAKF within the IF framework. In Figure 2A , we display the inference results for the three parameters b, I 0 and C 0 at different iterations in one realization of the IF algorithm. The blue horizontal lines mark the target values used to generate the outbreak. The orange boxes show the distribution of posterior parameters (300 ensemble members) after each iteration. The IF algorithm returns the stabilized ensemble mean as the MLEs of parameters. As a result of the stochastic nature of model dynamics and initialization of the inference algorithm, different runs of the IF algorithm usually return slightly different MLEs. To obtain the credible intervals (CIs) for the MLEs, we repeated the inference for 100 times (see Materials and methods). The inferred mean values and 95% CIs for the parameters b, I 0 and C 0 are 9:00; ½8:07; 9:68 Â 10 À3 , 1:91; ½1:38; 2:54 Â 10 À3 and 7:18; ½5:84; 8:70 Â 10 À2 , with the actual values b ¼ 9 Â 10 À3 , I 0 ¼ 2 Â 10 À3 and C 0 ¼ 7:5 Â 10 À2 . The inference system thus accurately estimates b and I 0 from noisy observations, and slightly underestimates C 0 . In its implementation, the performance of the inference system depends on the sensitivity of the observations to each parameter. In the agent-based model used here, observed incidence is less sensitive to C 0 due to the long period of colonization. As a consequence, estimates of C 0 do not always exactly match the actual target and are here biased low. Nevertheless, this slight underestimation does not significantly affect the inferred dynamics. To demonstrate this insensitivity, we ran 1000 simulations using the inferred mean parameters and obtained distributions of weekly incidence from the stochastic agent-based model. The distributions of weekly incidence (blue boxes) are compared with the observed cases (red crosses) in Figure 2B . We also evaluated the agreement between the observed and simulated incidences in Figure 2B We repeated the above analysis for the colonized population ( Figure 2C ) and found that the numbers of unobserved colonized patients can also be well estimated by the inference system. Moreover, the inference system can distinguish the number of infections transmitted in hospital and imported from outside the study hospitals ( Figure 2D