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2 Author's persona copy Journa of Hospita Infection 9 () e8 Avaiabe onine at Journa of Hospita Infection journa homepage: Modeing the transmission dynamics of meticiin-resistant Staphyococcus aureus in Beijing Tongren hospita J. Wang a,y, L. Wang b, P. Maga c,y.wang d, J. Zhuo e,x.lu a, S. Ruan b, * a Cinica Laboratory, Beijing Tongren Hospita, Capita Medica University, Beijing, China b Department of Mathematics, University of Miami, Cora Gabes, FL, USA c Institut de Mathématiques de Bordeaux, UMR CRS and IRIA sud-ouest Anubis, Université de Bordeaux, Bordeaux, France d Emergency Ward, Beijing Tongren Hospita, Capita Medica University, Beijing, China e Respiratory Intensive Care Unit, Beijing Tongren Hospita, Capita Medica University, Beijing, China artice info summary Artice history: Received 8 December Accepted August by J.A. Chid Avaiabe onine October Keywords: Meticiin-resistant Staphyococcus aureus Mathematica modeing Vounteers Transmission dynamics Basic reproduction number Semi-professiona vounteers work in many tertiary care hospitas in China as heathcare assistants. Proper infection contro measures are needed to reduce nosocomia transmission invoving vounteers. A compartmenta mode was constructed to describe the transmission characteristics of meticiin-resistant Staphyococcus aureus (MRSA) in the emergency ward (EW) and respiratory intensive care unit (RICU) for vounteers in Beijing Tongren Hospita, Beijing, China. The mode consists of components describing uncoonized and coonized patients, uncontaminated and contaminated heathcare workers (HCWs), and uncontaminated and contaminated vounteers. The basic reproduction number (R ) was cacuated, and the dependence of R on various mode parameters was anaysed. Moreover, simuations of the mode were performed for comparision with the reported data on the numbers of coonized patients in the EW and RICU from March 9 to 8 February, respectivey. Sensitivity anaysis of R showed that increasing handwashing compiance among HCWs and vounteers woud reduce the risk of transmission dramaticay. As vounteers care for patients on a one-toone basis, this study showed that the number of MRSA-positive patients woud increase if vounteers were repaced by HCWs. Therefore, in addition to improving hand hygiene among HCWs, the empoyment of propery trained vounteers is an attractive aternative to decrease MRSA and other muti-drug resistant bacteria infections in the hospita setting. Ó The Heathcare Infection Society. Pubished by Esevier Ltd. A rights reserved. Introduction Meticiin-resistant Staphyococcus aureus (MRSA) infection is associated with considerabe morbidity and mortaity among inpatients,, and accounts for e8% of tota staphyococca infection in China. Patients coonized with MRSA are more ikey to deveop infection., Behaviours of heathcare workers (HCWs) have been shown to be key determinants in MRSA transmission. e8 Thus, prevention of MRSA acquisition or transmission mediated by HCWs is critica in reducing MRSA infection. * Corresponding author. Address: Department of Mathematics, University of Miami, Cora Gabes, FL -, USA. Te.: þ 8 ; fax: þ E-mai address: ruan@math.miami.edu (S. Ruan). y Present address: Cinica Laboratory, Affiiated Hospita of Inner Mongoia Medica Coege, Hohhot, China. In China, semi-professiona vounteers work in many tertiary care hospitas. These vounteers have ess training than HCWs, care for patients on a one-to-one basis, and are known to be ess compiant with handwashing than HCWs. 9, The daiy work of vounteers incudes taking care of patients daiy ives, heping patients transfer from one unit to another, reporting irreguar resuts to doctors, etc. They do not usuay share work stations with HCWs. It is not cear whether the current infection contro measures are effective to contro MRSA transmission on wards with vounteers. Hence, it is important to assess the roe of vounteers in MRSA transmission in order to identify reasonabe infection contro programmes for the whoe hospita setting. Mathematica modeing has provided a means to study the transmission dynamics of nosocomia pathogens in hospitas, incuding investigations of patient and HCW contact patterns, and HCW- and patient-mediated transmission. e Most studies have 9-/$ e see front matter Ó The Heathcare Infection Society. Pubished by Esevier Ltd. A rights reserved. doi:./j.jhin..8.9

3 Author's persona copy J. Wang et a. / Journa of Hospita Infection 9 () e8 used deterministic differentia equation modes which aggregate patient and HCW popuations into compartments such as coonized or uncoonized patients, and contaminated or uncontaminated HCWs, and empoy the RosseMacdonad mode structure for vector-borne diseases., A stochastic version of such modes has aso been proposed to study the transmission of MRSA in an intensive care unit. Foowing a simiar modeing structure, the authors constructed a compartmenta mode to describe the transmission characteristics of MRSA in the emergency ward (EW) and respiratory intensive care unit (RICU) for vounteers in Beijing Tongren Hospita, Beijing, China. The aim of this study was to anayse the transmission dynamics of MRSA in wards with both professiona HCWs and vounteers, and to assess various infection prevention programmes to improve the contro of MRSA and other muti-drug-resistant bacteria infections in simiar hospitas. Methods Patients and procedures This study was conducted in Beijing Tongren Hospita, a -bed university-affiiated teaching hospita. Seventy vounteers worked at the hospita, distributed over various wards, and a were managed by the Hospita Administration Centre of ursing Workers. Twentythree vounteers worked on the EW and two worked on the RICU. As the majority of patients admitted to the EW are criticay i and are usuay transferred to other units, the prevention of MRSA transmission is particuary important. There are beds in the EW and seven beds in the RICU. The EW is further divided into two areas; a seven-bed intensive care unit (ICU) and a -bed genera open-bay ward. Patients on the EW are usuay moved frequenty between the two areas, depending on the severity and progression of their iness. Coection of data on MRSA For the EW, MRSA screening was performed seectivey for patients at admission if any of the foowing criteria were met: transferred from other wards within the hospita, transferred from another hospita, received home heath care, used antibiotics within the previous year, or had a history of an antibiotic-resistant organism. e Thereafter, patients in the genera open-bay wards had nasa swabs every three days when MRSA carriers were on the ward, and every seven days when no MRSA carriers were on the ward. For a patients in the ICU, screening was performed at admission and every two days thereafter. For the RICU, a patients were screened for MRSA carriage at admission and were samped every two days thereafter unti discharge. Before samping started, a consent form was obtained for each patient and the study was approved by the hospita ethics committee. Cinica cutures were obtained as indicated at the discretion of the attending physician. Specimens were obtained from the nares, axia, groin, any wound or esion, and surgica incision (where appropriate). Specimens for detection of MRSA were performed using standard aboratory methods. Automated repetitive-sequence-based poymerase chain reaction (Diversiab System, biomérieux, Marcy Etoie, France) was used for moecuar typing to confirm the strain a //9 //9 //9 //9 //9 /8/9 /9/9 //9 //9 //9 // // b..... //9 //9 //9 //9 //9 /8/9 /9/9 //9 //9 //9 // // Figure. umbers of meticiin-resistant Staphyococcus aureus positive patients from (a) the emergency ward ( beds) and (b) the respiratory intensive care unit (seven beds) in Beijing Tongren Hospita from March 9 to 8 February.

4 Author's persona copy J. Wang et a. / Journa of Hospita Infection 9 () e8 reatedness between cases. The numbers of MSRA-positive patients in the EW and RICU from March 9 to 8 February are shown in Figure, which demonstrates that MRSA is endemic on these two wards. a schematic iustration of the mathematica compartments. Baseine parameters were obtained from the iterature,,, and estimated through computerized records from Beijing Tongren Hospita from March 9 to February (see Tabe I). Basic mode To describe the transmission dynamics of MRSA in patients, HCWs and vounteers in the EW and RICU in Beijing Tongren Hospita, the patients were divided into two groups: uncoonized [P U ] and coonized [P C ]. o distinction was made between coonized and infected patients. The HCWs and vounteers were aso grouped into two subpopuations: uncontaminated HCWs [H U ] and contaminated HCWs [H C ], and uncontaminated vounteers [V U ] and contaminated vounteers [V C ], respectivey. It was assumed that patients are admitted to the hospita at a rate, and a portion are coonized with MRSA. d U and d C represent the discharge rates for uncoonized and coonized patients, respectivey. Patients can become coonized through contact with contaminated HCWs and vounteers, respectivey, according to mass-action aw: ð hþb PH P U ðtþh C ðtþ and ð xþb PV P U ðtþv C ðtþ, whereh describes the hand hygiene of HCWs, and x describes the hand hygiene of vounteers. It was assumed that the transmission rate for vounteers (b PV ) was ower than the transmission rate for HCWs (b PH )asvounteersonycareforonepatientatatime.hcwscanbecomecontaminated through contact with coonized patients, b PH P C ðtþh U ðtþ,ascan vounteers, b PV P C ðtþv U ðtþ. /g H and /g V represent the durations of contamination of HCWs and vounteers, respectivey. Figure shows Parameter estimate An investigator observed the daiy care activities of HCWs and vounteers over three -h periods (9:e: am, :e: pm, :e: pm), repeated on three different days, incuding compiance with handwashing and other infection contro measures, and patient care activities. Contact pate samping was empoyed to detect MRSA coonies on the hands of HCWs/vounteers before and after medica care of MRSA-positive patients. HCWs/vounteers were asked to wash their hands thoroughy before contact with patients. MRSA was transferred to the hands of HCWs/vounteers in 9 out of observed contacts with patients or their oca environment (9/, 9.%). Therefore, d was estimated to be.9. Handwashing compiance rates of vounteers were.% (/) on the EW and.% (/) on the RICU. Corresponding figures for HCWs were.% (/) and.% (/). ote that b PH ¼ u q PH (contact rate, patientsehcws), where q PH ¼ number of patients (tota number of contacts between HCWs and patients per day)/(tota number of patients tota number of HCWs in the ward). b PV ¼uq PVH (contact rate, patientsevounteers), where q PH ¼ number of patients(tota number of contacts between vounteers and patients per day)/(tota number of patients tota number of vounteers in the ward). Ony effective contacts between patients Admission Admission Uncoonized Patients P U Coonization Coonized Patients P C Discharge Discharge Uncontaminated HCWs H U Contamination Decontamination Contaminated HCWs H C Uncontaminated Vounteers V U Contamination Decontamination Contaminated Vounteers V C Figure. A compartmenta mode of transmission dynamics of meticiin-resistant Staphyococcus aureus among patients, heathcare workers (HCWs) and vounteers in Beijing Tongren Hospita.

5 Author's persona copy J. Wang et a. / Journa of Hospita Infection 9 () e8 Tabe I Baseine parameters and estimates for the transmission of meticiin-resistant Staphyococcus aureus for vounteers in the emergency ward (EW) and respiratory intensive care unit (RICU) at Beijing Tongren Hospita Parameter Symbo Baseine vaue Source EW RICU Tota number of beds Tongren Tota number of HCWs H Tongren Tota admissions per day.9. Tongren Fraction of admissions per day Coonized patients f.. Tongren Length of stay Uncoonized patients / d U Tongren Coonized patients /d C Tongren Hand hygiene compiance HCWs h.. Observed Vounteers x.. Observed Transmission probabiity d.9 Observed per contact Transmission rate Coonized patients to HCWs b PH. Estimated Coonized patients to vounteers b PV. Estimated Duration of contamination HCWs /g H / / Austin et a. Vounteers /g V / / Tongren HCW, heathcare worker. and vounteers were cacuated, which were composed of two parts: contacts that occurred when a vounteer had contacts with other patients in the ward, and effective contacts between a vounteer and his/her dedicated patient. Baseine parameters and their estimates are isted in Tabe I. Resuts Mode simuations Mode simuations using the parameter vaues given in Tabe I were performed for comparision with the reported data on the numbers of coonized patients in the EW and RICU in Beijing Tongren Hospita from March 9 to 8 February. The resuts are compared in Figure. Since the popuations in the EW and RICU were sma, the numerica simuations were performed according to the stochastic mode, and compared with the simuations using the deterministic mode for both the EW and RICU (Figure ). Simuations using the stochastic mode appeared to provide a better expanation of the transmission dynamics for sma popuations. However, when using the deterministic mode, the basic reproduction number (R ) can be expressed in terms of mode parameters, and various contro and prevention measures can be proposed and evauated by sensitivity anaysis of R. Since b PV represents the transmission rate between patients and vounteers, it is possibe to anayse the effect of using vounteers on MRSA transmission. The transmission rate is the proportion of contacts between coonized and uncoonized individuas that resut in infection. Thus, in numerica terms, it is transmission probabiity per contact x contact rate. As vounteers interact with patients on a one-to-one basis, the transmission rate from vounteers to patients a a Coonized patients b Coonized patients o. of patients b o. of patients 8 Figure. Mode simuations using baseine parameters from Tabe I for the numbers of patients coonized with meticiin-resistant Staphyococcus aureus (soid ine) compared with the actua data (dotted ine)for (a) the emergency ward and (b) the respiratory intensive care unit at Beijing Tongren Hospita. Fifteen-day averages were used to pot the data. Figure. umerica simuations for both the deterministic and stochastic modes over one year corresponding to (a) the emergency ward and (b) the respiratory intensive care unit, using the parameters in Tabe I. Soid ines correspond to the deterministic mode and dotted ines correspond to the stochastic mode.

6 Author's persona copy is ess than that from HCWs to patients. If there were no vounteers, an approximatey equa number of HCWs woud have to repace these vounteers. Equa transmission rates were used for both HCWs and vounteers to describe the situation if there were no vounteers. Figure shows that if vounteers were repaced by HCWs (i.e. b PV ¼b PH ), the number of coonized patients woud increase; this was confirmed by anaysis of R. Basic reproduction number R is a very usefu and important concept in modeing and studying the transmission dynamics of infectious diseases,, that represents the number of patients who are coonized with MRSA by an index case patient at the beginning of the epidemic. From the point of view of infection contro, the infection and spread of MRSA can be controed in a hospita if R <, whereas if R >, MRSA has become endemic in the hospita. This study aimed to determine factors that affect the spread and contro of MRSA in the hospita by anaysing the dependence of R on various mode parameters (i.e. sensitivity anaysis). The expicit expression of R is derived in the Appendix in the case where f ¼ (i.e. when no coonized patients are admitted to hospita). Sensitivity anayses of R were undertaken in terms of the mode parameters, such as the transmission rate between patients and vounteers, hand hygiene constants of HCWs and vounteers, ength of hospita stay for uncoonized and coonized patients, and duration of contamination of HCWs and vounteers (see Figure ). Using parameter vaues for the EW, Figure a shows that R wi increase when the transmission rate between patients and vounteers (b PV ) increases. Figure b shows that increasing the hand hygiene constant of HCWs or vounteers wi reduce the risk of transmission; however, the effect of hand hygiene among vounteers is more dramatic. According to the mode, if the ength of hospita stay of patients (both uncoonized and coonized) is shortened or the duration of cross-transmission (for both HCWs and vounteers) is reduced, R wi aso decrease (figures not shown). The simuations in R based on parameter vaues for the RICU show simiar resuts and are not given here. This study had imitations. In the process of cacuating R,itwas assumed that f ¼. Therefore, the possibiity of other vaues of f was excuded, eading to imprecision of R. Coonized patients.. Figure. umbers of meticiin-resistant Staphyococcus aureus positive patients on the emergency ward with vounteers and heathcare workers (HCWs) (b PV ¼., soid ine) and HCWs aone (b PH ¼., dotted ine). This indicates that the number of coonized patients woud increase if the vounteers were repaced by HCWs. J. Wang et a. / Journa of Hospita Infection 9 () e8 a R b R Discussion β....8 ξ (...) and η ( ) Figure. Simuations of the basic reproduction number (R ) in terms of the mode parameters, using parameter vaues for the emergency ward. (a) Contact rate between patients and vounteers. (b) Hand hygiene compiance of heathcare workers (soid ine) and vounteers (dotted ine). The contro of antibiotic-resistant bacteria infections in China is very difficut due to the huge popuation size, the arge number of patients in hospitas, and the high transmission rate between HCWs and patients,. Mathematica modeing can improve understanding of the current situation, and hep in the deveopment of effective strategies to reduce prevaence rates. Traditiona strategies incude reducing transmission rates between patient and nurses. In this study, the introduction of vounteers provides more options in designing contro intervention strategies. Meanwhie, decreasing the transmission rates between patients and HCWs and between patients and vounteers, whie increasing hand hygiene compiance of HCWs and vounteers, are a important in controing infection based on the sensitivity anaysis of R for these parameters. However, among these parameters, an increase in handwashing compiance for HCWs and vounteers woud decrease R most dramaticay, as the dependence is amost inear. If vounteers were repaced by HCWs and handwashing compiance was not %, MRSA transmission woud increase as HCWs care for more than one patient. The simuation resuts can be expained by previous studies, which showed that increasing the workoad of HCWs was cosey associated with higher nosocomia infection rates. Empoyment of vounteers woud decrease the workoad of HCWs dramaticay. Cohort nursing is known to be one of the most effective ways to prevent cross-transmission.,8 The vounteer system in the study hospita is simiar to cohort nursing, and vounteers can conduct many PV

7 Author's persona copy J. Wang et a. / Journa of Hospita Infection 9 () e8 nursing tasks, thus reducing muti-patient contact by HCWs. Cohort nursing by fuy trained HCWs woud be even more effective. This study aso investigated the behaviours of vounteers during the study period. Compared with HCWs, more frequent contacts were observed between vounteers and environmenta surfaces, and this may increase the probabiity of transmission of MRSA from the surrounding environment of MRSA patients to other environmenta surfaces and vice versa. Vounteers behaviours may be party infuenced by their ong-term assignment to a ward. However, a recent study reveaed that proper education for vounteers in infection contro can decrease the nosocomia infection rate, 9 which suggests that empoyment of vounteers undergoing nursing training is an aternative approach to nursing care. In concusion, improving the handwashing compiance of vounteers, who cohort nurse patients, wi decrease MRSA transmission dramaticay. Acknowedgements The authors are gratefu to the reviewer for his/her carefu reading, hepfu comments and suggestions which heped to improve the presentation of the paper significanty. Confict of interest statement one decared. Funding sources This work was partiay supported by ationa atura Science Foundation of China Grant 9, ationa Institutes of Heath Grant RGM8, and ationa Science Foundation Grant DMS-8. Appendix The deterministic mode is a system of six ordinary differentia equations: dp U ð hþ dt ¼ð fþ ð hþ dp C dt ¼fþ b PHH C ðtþþ ð xþ b PHH C ðtþþ ð xþ dh U dt ¼ ð hþ b PHP C ðtþh U ðtþþg H H C ðtþ dh C dt ¼ð hþ b PHP C ðtþh U ðtþ g H H C ðtþ dv U dt ¼ ð xþ b PVP C ðtþv U ðtþþg V V C ðtþ dv C dt ¼ð xþ b PV P C ðtþv U ðtþ g V V C ðtþ b PVV C ðtþ P U ðtþ d U P U ðtþ b PVV C ðtþ P U ðtþ d C P C ðtþ When f¼ (i.e. no coonized patients admitted to hospita), the disease-free steady state is obtained: E ¼ðP U ; P C ; H U ; H C ; V U ; V C Þ¼ ; ; ; ; ; d U Then:, sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð hþ b PH R ¼ d U d C g H þ ð xþ b PV d U d C g V The foowing materia shows how R was derived, and determines the stabiity of disease-free equiibrium when f ¼. Theorem If PU ; P C, the soutions are non-negative and remain bounded in the positive cone of R.IfR <, the disease-free steady state E is ocay asymptoticay stabe. If R >, E is unstabe. Proof: Let TðtÞ ¼P U ðtþþp C ðtþþh U ðtþþh C ðtþþv U ðtþþv C ðtþ. Then: dtðtþ dt ¼ d U P U ðtþ d C P C ðtþ minfd U ; d C gtðtþ Thus, the soutions remain bounded in the positive cone of R where the system induces a goba semi-fow. The procedure introduced by van den Driessche and Watmough or Diekmann et a. can be used to evauate R, and determine the stabiity of the disease-free equiibrium. After re-ordering, the disease-free steady state can be written as: E ¼ðP U ; H U ; V U ; P C ; H C ; V C Þ¼ ; ; ; ; ; d U Then: ð xþ b PV V c ðtþ ð hþ b PHH c ðtþþ ð hþ b PHP C ðtþh U ðtþ F ¼ ð xþ b PVP C ðtþv U ðtþ P U ðtþ and: d C P C ðtþ g H H C ðtþ g V V C ðtþ ð hþ V ¼ b ð xþ PHH c ðtþþ b PV V c ðtþ P U ðtþþd U P U ðtþ ð hþ b PHP C ðtþh U ðtþ g H H C ðtþ ð xþ b PVP C ðtþv U ðtþ g V V C ðtþ Since: vf vf vf vp C vh C vv C vf F ¼ vf vf vp C vh C vv C vf vf vf vp C vh C vv C ¼ ð hþ b PHP U ðtþ ð xþ ð hþ b PHH U ðtþ ð xþ b PVV U ðtþ it foows that: Fj E ¼ Simiary: ð hþ b PH d U ð xþ ð hþ b PH ð xþ b PV b PV d U b PV P U ðtþ

8 Author's persona copy 8 d C V ¼ g H g V and: d C V ¼ g H g V So: FV ¼ ð hþb PH d C ð xþb PV d C ð hþb PH d U g H Thus, the Jacobian matrix is: x XI FV ¼ ð hþb PH d C ð xþb PV d C ð xþb PV d U g V ð hþb PH d U g H ð xþb PV d U g V x x " Since x ð hþ b PH d U d C g H þ ð xþ b PV # d U d C g V x ¼, we obtain that: R ¼ r sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FV ð hþ b PH ¼ d U d C g H þ ð xþ b PV d U d C g V By the resuts in van den Driessche and Watmough, the stabiity of the disease-free equiibrium is obtained. References. Cosgrove SE, Sakouas G, Perencevich E, Schwaber MJ, Karchmer AW, Carmei Y. Comparison of mortaity associated with methiciin-resistant and methiciin-susceptibe Staphyococcus aureus bacteremia: a meta-anaysis. Cin Infect Dis ;:e9.. Cosgrove SE, Qi Y, Kaye KS, et a. 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