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. The synthetic outbreak tested in Figure 2 was generated with the parameters b ¼ 9 Â 10 À3 , I 0 ¼ 2 Â 10 À3 and C 0 ¼ 7:5 Â 10 À2 . To mimic actual observational error variance, we assumed an observational error variance (OEV) of s 2 t;o ¼ 10 þ ð0:1 Â o simulate ðtÞÞ 2 , which is a baseline uncertainty plus a term related to the simulated incidence o simulate ðtÞ. In reality, because we have only one data point at each observation time point, the variance of observed incidence is unknown. As such, we have to use a heuristic OEV in the inference algorithm. The above form of OEV has been successfully used in real-time influenza forecast (Shaman and Karspeck, 2012; Pei et al., 2018a; Kandula et al., 2018) , and also produces satisfactory performance in the following synthetic tests. The observation used in the inference was drawn from a Gaussian distribution oðtÞ~N ðo simulate ðtÞ; s 2 t;o Þ. The initial system state z 0 was drawn from the following ranges b 2 ½0; 0:001, I 0 2 ½0; 0:003 and C 0 2 ½0; 0:1, using Latin Hypercube Sampling (LHS) (Tang, 1993) . For simplicity, the initial covariance matrix was assumed to be diagonal S ¼ diagððz max À z min Þ 2 =16Þ, where z max and z min are the vectors of the upper and lower bounds of parameters b, I 0 and C 0 . In each iteration, the covariance matrix was contracted by a factor of a 2 (equivalent to a reduction of the standard deviation by a factor of a). We used a discount factor of a ¼ 0:9 and terminated the algorithm at L ¼ 20 iterations. For the EAKF, n ¼ 300 ensemble members were used.