Fig 1.
Graphical representation of transfers in a model comprising two exemplary hospitals.
Direct transfers are represented by solid lines, while indirect transfers are represented by dashed lines. Dotted loops indicate the situations when patients stay for a night in the hospitals/community nodes.
Fig 2.
Examples of the results of the transfer detection algorithm in case of different types of overlaps.
Results are represented by red lines, numbers on the left-hand side indicate the numeric codes for particular units, while # stand for days of stay reported for a given healthcare facility. For the classification of particular types of overlaps see [13].
Fig 3.
Fractions of outgoing direct and indirect transfers per day.
Results are presented for all considered healthcare facilities (164 units), which are ordered by the mean size of the units, the smallest first.
Fig 4.
Hospital and community sizes analysis.
(a) Histogram of estimated hospital sizes, defined as average numbers of patients in the hospitals within the period 2008–2015, calculated for each healthcare facility separately (164 units)—given the fact that AOK Lower Saxony covers 30.52% of the population in Lower Saxony, the number of beds has to be multiplied by about 3 to get the actual sizes; (b) histogram of estimated community sizes, defined as average numbers of patients in the given community within the period 2008-2015, calculated for each healthcare facility separately, as above the populations have to be multiplied; (c) dependence of community-node sizes on corresponding healthcare facilities (164 units).
Fig 5.
Visualization of the transfer probability matrix.
Healthcare facilities are numbered from 1 to n and community-nodes numbered from n + 1 to n + n, n = 164. (a) schema presenting four distinguishable blocks; (b) quantitative representation of obtained probabilities, colour pixels denote the probabilities; for the purpose of visualization, all elements were raised to the power 0.075.
Fig 6.
Degrees of the nodes in the hospital network.
(a) In-degree and out-degree for each hospital node of the network (self-loops not included); (b) out-degree for each community node of the network (self-loops not included), in-degree for all community nodes are equal to 1.
Table 1.
SIS parameters used in simulations.
Fig 7.
MRSA prevalence in the individual healthcare facilities and community-nodes.
MRSA prevalence (over time) expressed as the percentage of infectious individuals per healthcare facility (a,c) and corresponding community-node (b,d). Deep blue corresponds to low infection proportions (lower than 5%); yellow or red to facilities with high infection proportions (higher than 20%). Healthcare facilities are ordered by average size, with the smallest first. The process was started by a single infectious patient located in facility number: (a,b) 1 (the smallest facility); (c,d) 164 (the biggest facility).
Fig 8.
Comparison of average system-wide phase durations and individual phase ends expressed in days in simulations when each healthcare facility was selected as the initial infection point.
(a) Phase durations for hospitals and corresponding community nodes. Phase 1 denotes the beginning of the spread (prevalence lower than 10% of the final prevalence); phase 2 denotes the transition state (prevalence < 99.9% final prevalence). The phase durations correspond to a system-wide prevalence, not to individual facility prevalences. (b) Individual phase ends in healthcare facilities and in corresponding community-nodes. Presented results are averaged-out amid all possible initial infection points. Pathogen spread was initiated by a single infectious patient originating from each facility.
Fig 9.
Comparison of the final percentage of infectious individuals in given hospitals/community-nodes.
Healthcare facilities are ordered by the average size of hospitals, the smallest first. Transmission was started by a single infectious patient originating from a given facility, and the results are averaged out through all initial facilities. However, differences in the final prevalence between initial originating facilities are negligible.
Fig 10.
Effect of the change of SIS parameters on MRSA network-wide prevalence.
(a) Effect of the change of the transmission rate on the percentage of susceptible (blue) and infectious (red) individuals in the healthcare facilities network. (b) Effect of the change of the recovery rate on the percentage of susceptible (blue) and infectious (red) individuals in the healthcare facility network. Initial fraction of the colonized individuals is 0.1% uniformly distributed in the whole population. Sets of parameters being perturbations of the SIS reference values reported in Table 1 (set type: MRSA) as indicated in legends.
Fig 11.
Dependence of MRSA network-wide prevalence in healthcare facilities and corresponding community-nodes (reported for the last day) on different values of γc parameter in the community-nodes.
Parameter γh = 1/365 is kept constant for all the hospitals. Initial fraction of the infectious individuals is 0.1% uniformly distributed in the whole population. (a) Data presented on log-log scale. (b) Data presented on semilog(x) scale.
Fig 12.
Final MRSA prevalence in the individual healthcare facilities and community-nodes.
Final prevalence in the individual healthcare facilities and community-nodes depending on the value of γc parameter (vertical axis) for: (a) all considered hospitals, (b) corresponding community nodes. Initial condition for all simulations is the same: 0.1% uniformly-distributed colonized patients. Facilities are sorted by increasing average size.
Fig 13.
System-wide phase ends in healthcare facilities and correlation coefficients.
(a) System-wide phase ends in healthcare facilities for different γc. (b) Dependence of the correlation coefficients on γc value (semi-log scale), corrA is the correlation coefficient between final hospital prevalences and corresponding communities prevalences; corrB—correlation coefficient between final hospital prevalences and average length of stay in hospitals; corrC—correlation coefficient between final community prevalences and average length of stay in corresponding hospitals; corrD—final prevalence in hospitals and hospital in-degrees; corrE—final prevalence in hospitals and hospital out-degrees; corrF—final prevalence in community nodes and community out-degrees. Initial condition for all simulations is the same 0.1% uniformly-distributed colonized patients.
Fig 14.
Distribution of length of stay and the dependence between the average length of stay and average prevalence.
(a) Distribution of length of stay (in days) for all the considered hospitals (164 units). (b) Average length of stay vs. average prevalence calculated for each hospital.