Learning from simulating with system dynamics in healthcare: evaluating closer care strategies for elderly patients

Figures & data

Table 1. The overall method for the modelling case.

Step	Definition of the step	Description of how the step was conducted in the study
Initial discussions and study buy-in	The first step included discussions to identify potential areas of study and analyse the suitability of different modelling and simulation paradigms.	The healthcare personnel from the modelling team had experience in applying DES to analyse the operations in an ED (see Goienetxea Uriarte et al. (2017)). However, the present study required increasing the problem boundary, not including only the functional perspective in a specific department but also the structural perspective between actors in the HCS. It was important to be able to evaluate policies of moving the offered care to patients from one actor (e.g., ED) to another (e.g., PC) to achieve benefits of scale or quality. The complexity of identifying trade-offs between minimising resources and maximising patient care and quality, and their time-dependent nature considering short-term and long-term consequences in the analysis, were discussed as the qualifiers for choosing SD as the simulation paradigm for this study.
Planning the study	The study was planned following a process for conducting simulation studies based on Banks et al. (2014) and Sterman (2000).	An initial plan was established together with the complete modelling team that was later adjusted during the project. The modelling team met every week.
Problem formulation	An iterative step with the purpose to focus the study, articulating the problem, and selecting its boundaries. The outcome from this step was iteratively improved via the two subsequent steps: setting of objectives and model conceptualisation.	The problem formulation was initially very open: how could closer care be offered for all types of patients in the region? A workshop for exploring this problem was organised by the modelling team together with different stakeholders and subject matter experts from PC, EDs, and other departments of the hospital. This workshop showed a very varied view of what closer care meant for each stakeholder. Therefore, further definition of the problem formulation was carried out in the modelling team in regular meetings over four months, where different statistical patient data were analysed, and multiple focuses were explored to formulate the problem boundary. The purpose of this process was to obtain an understanding of the existing challenges and to identify a relevant modelling scope.
Setting of objectives	The setting of objectives included defining the model purpose to searching for specific solutions within the model, affecting the selection criteria on what to include and what to omit.	The study of different cohort patient data and exploring potential problem formulations led to defining the objectives to guide the model-building process. It was decided that a qualitative and a quantitative model with different focuses were needed. The qualitative model would analyse a larger system perspective and the simulation model would just focus on some specific parts.The qualitative model aimed to study how the elderly care need was generated and how it could be reduced, considering also an increase in quality care for these patients.The quantitative model aimed to evaluate three closer care initiatives for the selected patient groups at the regional level, analysing the possible cost reduction effects and possible improvements in the quality of care. The problem formulation and the defined objectives were agreed upon with the decision-makers. The qualitative model aimed to study how the elderly care need was generated and how it could be reduced, considering also an increase in quality care for these patients. The quantitative model aimed to evaluate three closer care initiatives for the selected patient groups at the regional level, analysing the possible cost reduction effects and possible improvements in the quality of care. The problem formulation and the defined objectives were agreed upon with the decision-makers.
Data collection	This was the step to obtain the needed data and the empirical findings fundamental to building the model, but also to obtain the correct mathematical relations and define structural relations for the studied phenomena.	The data collection step was a vital part of the problem formulation process and provided an understanding of the problem at hand. But it was also important for selecting the focus of the study. Statistical data from the regional HCS was studied in detail and sorted on different diagnoses, age groups, years, etc. The search for a relevant problem and the matching with closer care strategies led to the specific data collection regarding elderly patients with/without multimorbidity and with a FA behaviour. Also, empirical data from three specific closer care initiatives were obtained from successful pilot projects. Qualitative data were obtained from interviews and discussions with the modelling team and subject matter experts mainly from PC and ED.
Model conceptualization/Dynamic hypothesis	This step included the definition of the conceptual model including the main structural elements of the studied problem. Hypotheses of how the problem dynamics are endogenously generated from the feedback structures within the selected boundaries were also formulated (Sterman, 2000).	The analysis of data, workshops, and discussions with the stakeholders and the modelling team provided the required knowledge to define a qualitative conceptual model of elderly patients’ care-seeking behaviour. The modelling with causal loop diagrams (CLD) resulted in a conceptual model extensively reported in Linnéusson and Goienetxea Uriarte (2021). A simplified CLD over the studied dynamics is presented in Section 7.1. The process of CLD model building created a common view of the studied phenomena and the considered dynamic hypotheses within the team.
Model translation	This step resulted in a quantified simulation model to enable testing scenarios. The model translation step therefore included specifications of structure, decision rules, parameter estimations, behavioural relationships, initial conditions and tests for consistency with the aim of the model.	The model translation step was carried out by the modelling team in regular meetings for three months by iterating several times the creation, verification, and validation steps of the SD model.First, the base model was designed and verified towards available data, including how the structures could represent and replicate the facts obtained from the healthcare databases and total cost estimations. When it was validated, the consequences of potential closer care strategies were discussed. It resulted in an SD model to calculate the three scenarios, where statistical data from the region was merged with the empirical data from the pilot cases. See Section 4 for more details in this step. First, the base model was designed and verified towards available data, including how the structures could represent and replicate the facts obtained from the healthcare databases and total cost estimations. When it was validated, the consequences of potential closer care strategies were discussed. It resulted in an SD model to calculate the three scenarios, where statistical data from the region was merged with the empirical data from the pilot cases. See Section 4 for more details in this step.
Verification and validation/Testing	The model was tested to examine its capacity to reproduce the required behaviour. SD models are causal-descriptive as well as “statements as to how real systems actually operate in some aspects” (Barlas, 1996), emphasising the importance of structure validation and examining a model’s capacity to explain how the behaviour arises. The usefulness of a model mainly determines its validation (Sterman, 2000). Hence, if the model can be considered relevant and assist decision-making in the real world, it supports validation (Bertrand & Fransoo, 2002).	The model translation, verification, and validation processes were conducted mainly by the modelling team. Tests for consistency (direct structure tests to confirm structure and parameter settings), were based on historical data and face validation (Sargent, 2011), where each sub-structure and equation formulation were carefully analysed. The choice of how to represent the SD model, with a focus on extrapolating the pilot cases to the regional level and combining them with the regional healthcare data resulted in a more specific perspective than the qualitative conceptual model which had a bigger perspective.As soon as all feedback loops were closed and units checked in the simulation model, the manual parameter testing identified improvements in consistency. Moreover, simulation allowed extreme condition and behaviour sensitivity tests in the Vensim software. As soon as all feedback loops were closed and units checked in the simulation model, the manual parameter testing identified improvements in consistency. Moreover, simulation allowed extreme condition and behaviour sensitivity tests in the Vensim software.
What-if scenarios/Policy formulation and evaluation	To support the policy formulation and evaluation, what-if scenarios were explored.	The what-if scenarios, depicted in Table 2, included three closer care strategies: 1) the introduction of care coordinators in the ED; 2) the use of mobile health clinics; and 3) the introduction of proactive care in PC. These were compared and combined to analyse their impact on reducing the visits to the ED, the number of hospitalisations and days at the hospital, as well as the resulting costs. Furthermore, an additional set of experiments were designed and explored, presented in Table 3. See Sections 4 and 6 for more details on this step.
Decision-making	Presentation of the results to decision-makers (customers of the study).	Once the study was finalised, the results were presented to the regional healthcare board that was in charge of evaluating and implementing the closer care initiatives in the region.

Table 2. Description of the scenarios tested in the model.

Scenario	Description	Model structure implications
Care Coordinators scenario (CC scenario)	The scenario introduces care coordinators at all the EDs in the region to enable more accurate risk assessments for elderly patients with high care needs. In the long run, these patients are continuously followed up and offered care via PC. Based on pilot cases, the results of this approach are an increased quality of care and a reduction of unnecessary hospitalisations. In the long run, this is also reducing the FA behaviour, eliminating unnecessary visits to the ED in the first place.	The CC scenario sub-structure defines the consequences for the different target groups, where the effects are calculated in the BS2 structure. The expected effect is a reduction in the number of hospitalisations and ED visits due to reduced re-hospitalisations.
Mobile health clinics scenario (MHC scenario)	MHC is composed of a nurse and a physician to provide person-centred care to fragile patients in their homes. This initiative deployed on a large scale may reduce unnecessary visits to the ED, as well as in many cases even hospitalisation days.	The MHC scenario sub-structure is incorporated in two of the patient target groups in BS2. The expected effect is a reduction in visits to the ED. However, also an increment in the length of stay for those in need of care.
Proactive Care in PC scenario (PC scenario)	The scenario introduces more resources to conduct preventive and proactive care for elderly patients via PC, including risk and function assessments, drug reviews, etc. This action leads to a reduced number of visits to the ED.	The PC scenario sub-structure defines the added costs from more thorough consultations at PC. The expected effect is a reduction in the number of visits to ED for all patients calculated in BS2.

Table 3. Overview of approximate effects from the closer care strategies to key parameters. Updated from Linnéusson and Goienetxea Uriarte (2021).

Closer Care Strategy	Target group	Average number of visits to ED/year	Average number of times the patient is hospitalised/ED visit	Average number of days/hospitalisation	Effect on costs
Base scenario	Gr1	0.24	.492	9.2	Current cost
	Gr2	.909	0.816	16.59
	Gr3	.549	0.597	9.25
CC scenario	11% of (.1* Gr1+Gr2+Gr3)	revisits reduced by ~ 15%	~30% less, of which ~ 83% had zero revisits	No effect	Included in the current cost
MHC scenario	Gr2	0.9→0.8	Reduced from fewer ED visits	~7% increase	Included in the current cost
	Gr3	~40% reduction		No effect
PC scenario	.1* Gr1+Gr2+Gr3	~20% reduction	Reduced from fewer ED visits	No effect	1.5 * PC visits

Figure 1. Simplified CLD over elderly patients’ care-seeking behaviour.

Figure 2. Overview of the parts in the SD model.

Figure 3. Total healthcare costs for the different scenarios.

Figure 4. Total visits at the EDs per year for the different scenarios.

Figure 5. Total hospitalisation costs for the different scenarios.

Figure 6. Hospitalization days for all patient groups for the different scenarios.

Table 4. Description of the DOE for the dynamic scenarios.

Variable and origin equation	SD model changes	Dynamic CC scenario	Dynamic MHC scenario	Dynamic PC scenario
getMM = initConst getMM * (Elderly withoutMM/initPopEwoMM)	Introduce a variable: effQualCareTotPop = totPop/demographyIndex It reduces people getMM by the normalised effect of an increasingly healthier population by: getMM/effQualCareTotPop	The reactive screening by CCs at EDs implies better risk identification and is assumed to make 2% less getMM	No effect, patients must be risk identified to receive this care	The screening at PC implies fewer patients are likely to getMM due to proactive risk identification.Max effect is assumed; a 10% reduction in getMM Max effect is assumed; a 10% reduction in getMM
lifespanElderly and riskMortalityEwoMM	No changes are implemented. And no effects are considered. However, the riskMortalityEwoMM could be considered affected by the dynamic PC scenario, due to the assumed new blend of EwoMM in the stock, using a normalised relation to population growth as for getMM.
Elderly new MM = INTEG (getMM + newElderly MM – getBetter – stayMM – drMM, initPopMM × 0.52)	Better care shifts the balance between the flows draining this stock. It follows the logic pattern where the ratioMortalityMM can shift towards ratioStayMM, but not directly towards ratioGetBetter, instead, the ratioStayMM can shift into ratioGetBetter, but cannot shift into ratioMortalityMM; following the pattern: ratioMortalityMM → ratioStayMM → ratioGetBetter.
ratioMortalityMM = 0.2	Change ratio	Early but reactive risk identification at the ED, therefore no effect	No effect	Proactive risk identification and as an effect ratioMortalityMM change to .1
ratioStayMM = 0.3	Change ratio	Reactive risk identification considers changing a third of the current flow to getBetter (0.3 × 2/3 = a change in ratioStayMM to 0.2	No effect	Proactive risk identification reduce the ratio by half ((current .3) + (added from change above .1))/2 = a change in ratioStayMM to .2
ratioGetBetter = 0.5	Change ratio	Given the changes above, provide a value in ratioGetBetter of 0.6	No effect	Given the changes above, provide a value in ratioGetBetter of .7
avgMortalityMM >1Y = 3 × 52 * 1.1	Affect the average, current value of 3.3 years	Small effect, prolong average with 25%	This cohort is the target group for MHC, prolonging the average by 50% by avoiding hospital	No proactive effect is considered for those who remain MM and thus no changes in the average value

Figure 7. Hospitalization days for the respective patient groups for the CC scenarios.

Figure 8. Total healthcare costs for the CC scenarios.

Figure 9. Total healthcare cost per year for the MHC scenarios.

Figure 10. Hospitalization days for FAMM and MM patient groups for the PC scenarios.

Figure A1. System dynamics model over the care needs of elderly patients in the healthcare system.

Table A1. List of Equations ofthe SD modelover the Care Need of Elderly Patients in the Healthcare System.

PARAMETER	EQUATION	UNITS	COMMENT
visitsPCphysicianPerMM=	3.11	visit/(Year*Person)
sumEDandHospitalizationCostsPerYear=	sumCostEDvisitsPerYear+sumCostHospitalizationDaysPerYear	$/Year
CostMHC=	IF THEN ELSE(rampUpTimeMHC >0, ResourcesMHC, 0)	$/Year
visitsPCnurseEwoMM=	(1 + 0.1*tblProPCforEwoMM(implementProPC))*visitsPCnursePerEwoMM*Elderly withoutMM	visit/Year	0.1 share of EwoMM are affected by ProPC
visitsPCnurseMM=	tblProPCforMM(implementProPC)*visitsPCnursePerMM*sumMMpatients	visit/Year
rampUpCC=	IF THEN ELSE(rampUpTimeCC = 0, 0, (RAMP(1/(WeeksPerYear*rampUpTimeCC), 0, WeeksPerYear*rampUpTimeCC)))	Dmnl
rampUpMHC=	IF THEN ELSE(rampUpTimeMHC = 0, 0, (RAMP( 1/(WeeksPerYear*rampUpTimeMHC), 0, WeeksPerYear*rampUpTimeMHC)))	Dmnl
rampUpProCarePC=	IF THEN ELSE(rampUpTimeProCarePC = 0, 0, (RAMP(1/(WeeksPerYear*rampUpTimeProCarePC),0, WeeksPerYear*rampUpTimeProCarePC)))	Dmnl
effMHC1=	1‐0.224	Dmnl	For 22.4% the improvement from MHC1 could be seen
visitsPCphysicianPerEwoMM=	1.85	visit/(Year*Person)
visitsPCphysicianMM=	tblProPCforMM(implementProPC)*visitsPCphysicianPerMM*sumMMpatients	visit/Year
MHC1reduceEDvisitsMM=	enrolledToMHC1*visitsEDperYearMHC1patients*effMHC1	visit/Year
visitsPCphysicianEwoMM=	(1 + 0.1*tblProPCforEwoMM(implementProPC))*visitsPCphysicianPerEwoMM*Eld erly withoutMM	visit/Year	0.1 share of EwoMM are affected by ProPC
visitsPCnursePerMM=	3.51	visit/(Year*Person)
visitsPCnursePerEwoMM=	1.77	visit/(Year*Person)
shareMHC1forMM=	tblMMaffectedByMHC1(rampUpMHC)	Dmnl	implementation gives max reduction of visits to ED
visitsEDperYearAndPersonFAMM=	tblMHC2reduceFAMMvisitsED(rampUpMHC)	visit/(Year*Person)	effect avg visits from MHC
visitsEDperYearAndPersonMM=	tblMHC1effMMvisitsED(rampUpMHC)	visit/(Year*Person)
effMHC2=	0.472	Dmnl	For 52.8% the improvement from MHC could be seen
shareMHC2forFAMM=	tblFAMMaffectedByMHC2(rampUpMHC)	Dmnl	implementation gives max reduction of FAMM visits to ED
MHC2reduceEDvisitsFAMM=	enrolledToMHC2*visitsEDperYearMHC2patients*effMHC2	visit/Year
ratioGetBetter=	0.5	Dmnl/Year
totHealthCareCostPerYear=	costVisitsPC+sumEDandHospitalizationCostsPerYear+CostMHC	$/Year
assessmentsED FAMM=	(MHC2reduceEDvisitsFAMM+visitsEDperYearFAMM*PCreduceEDvisitsFAMM)/W eeksPerYear‐CCeffReHospitsFAMM	visits/Week
controlValueEwoMM=	demographyIndex*controlShareEwoMM	people
controlValueMM=	demographyIndex*controlShareMM	people
sumMMpatients=	outputMM‐enrolledToMHC1‐ enrolledToMHC2+enrolledToMHC1+enrolledToMHC2	people
assessmentsED MM=	(visitsEDperYearMM*PCreduceEDvisitsMM+MHC1reduceEDvisitsMM)/WeeksPer Year‐CCeffReHospitsMM	visits/Week
costIncreaseProPC=	costVisitsPC‐currentCostVisitsPC	$/Year
controlShareMM=	1‐controlShareEwoMM	Dmnl
controlShareEwoMM=	0.861258	Dmnl
deltaCostMHCperPerson=	CostMHC/totPop	$/(Year*Person)
currentCostVisitsPC=	3.4122e + 08	$/Year
ResourcesMHC=	1.25e + 08	$/Year	125 Million SEK per year has been dedicated to MHC
enrolledToMHC2=	shareMHC2forFAMM*EDvisitorsFAMM	people
rampUpTimeMHC=	0	Years
costIncreasePCperPerson=	costIncreaseProPC/totPop	$/(Year*Person)
enrolledToMHC1=	shareMHC1forMM*EDvisitorsMM	people
sumHealthcareCostsPerPerson=	totHealthCareCostPerYear/totPop	$/(Person*Year)
sumCostEDvisitsPerYear=	sumAssessmentsEDperYear*costPerEDvisit	$/Year
sumCostHospitalizationDaysPerYear=	totHospitDaysPerYear*costPerHospitDay	$/Year
costPerHospitDay=	8900	$/Day
visitsEDperYearEwoMM=	Elderly withoutMM*visitsEDperYearAndPersonEwoMM	visit/Year
factorReVisitsEDforEwoMM=	0.15	Dmnl	calibrated factor
tblMHC1effMMvisitsED	([(0,0)‐(1,1)],(0,0.909),(1,0.8))	visit/(Year*Person)	average values based on calculated input data
tblProPCforMM	([(0,0)‐(1,2)],(0,1),(1,1.5))	Dmnl	max 50% increased time at PC
tblProPCeffectEDvisitsMM	([(0,0)‐(1,1)],(0,1),(1,0.8))	Dmnl	max 20% reduction
tblProPCeffectEDvisitsFAMM	([(0,0)‐(1,1)],(0,1),(1,0.8))	Dmnl	max 20% reduction
sumAssessmentsEDperYear=	sumAssessmentsED*WeeksPerYear	visit/Year
FAEDMM >1Y=	Elderly MM >1 Year*ratioFA MMatED	people
factorCCreduceEDvisitsEwoMM=	sumEDvisitsEwoMM/(sumEDvisitsEwoMM+visitsEDperYearMM+sumEDvisitsFAM MperYear)	Dmnl
factorCCreduceEDvisitsMM=	visitsEDperYearMM/(sumEDvisitsEwoMM+visitsEDperYearMM+sumEDvisitsFAM MperYear)	Dmnl
factorCCreduceEDvisitsFAMM=	sumEDvisitsFAMMperYear/(sumEDvisitsEwoMM+visitsEDperYearMM+sumEDvisi tsFAMMperYear)	Dmnl
totCostVisitsPCnurse=	costPerVisitPCnurse*totVisitsPCnurse	$/Year
careCoordinatorEfforts=	ratioCCinterventions*(visitsEDperYearEwoMM+visitsEDperYearMM+sumEDvisits FAMMperYear)	visit/Year
totReducedHospitsFromCC=	effHospitalizationDueToCC*careCoordinatorEfforts/WeeksPerYear	visits/Week
ratioCCinterventions=	0.111*rampUpCC	Dmnl	average ratio of patients who had CC interventions
totHospitDaysPerYear=	hospitDaysPerYearEwoMM+hospitDaysPerYearMM+hospitDaysPerYearFAMM	Days/Year
visitsEDperYearMHC1patients=	1.136	visit/(Person*Year)	visits/year in pilot cases for enrolled in MHC1
PCreduceEDvisitsMM=	tblProPCeffectEDvisitsMM(implementProPC)	Dmnl
visitsEDperYearMM=	(1‐shareMHC1forMM)*EDvisitorsMM*visitsEDperYearAndPersonMM	visit/Year
rampUpTimeCC=	0	Years
rampUpTimeProCarePC=	0	Years
hospitDaysPerVisitMMwithMHC1=	10.69	Days/visit	calculated new average when MHC1 is implemented
hospitDaysPerVisitMM=	16.59	Days/visit	from data
avgHospitDaysPerVisitMM=	shareMHC1forMM*hospitDaysPerVisitMMwithMHC1+(1‐ shareMHC1forMM)*hospitDaysPerVisitMM	Days/visit
sumEDvisitsEwoMM=	factorReVisitsEDforEwoMM*visitsEDperYearEwoMM	visit/Year
FAEDnewMM=	Elderly new MM*ratioFA MMatED	people
costVisitsPC=	totCostVisitsPCphysician+totCostVisitsPCnurse	$/Year
PCreduceEDvisitsFAMM=	tblProPCeffectEDvisitsFAMM(implementProPC)	Dmnl
costPerEDvisit=	3584	$/visit
tblMMaffectedByMHC1(	[(0,0)‐(1,1)],(0,0),(1,0.323))	Dmnl	Regards max 32.3% of the MM group
costPerVisitPCphysician=	355	$/visit
costPerVisitPCnurse=	154	$/visit
hospitDaysPerVisitFAMMwithMHC2=	5.98	Days/visit	calculated new average when MHC2 is implemented
implementProPC=	rampUpProCarePC	Dmnl
hospitDaysPerVisitFAMM=	9.25	Days/visit	from data 190,517
avgHospitDaysPerVisitFAMM=	shareMHC2forFAMM*hospitDaysPerVisitFAMMwithMHC2+(1‐ shareMHC2forFAMM)*hospitDaysPerVisitFAMM	Days/visit
totCostVisitsPCphysician=	costPerVisitPCphysician*totVisitsPCphysician	$/Year
hospitalizationsMM=	ratioHospitsMM*assessmentsED MM‐CCeffHospitsMM	visits/Week
hospitalizationsFAMM=	ratioHospitsFAMM*assessmentsED FAMM‐CCeffHospitsFAMM	visits/Week
hospitalizationsEwoMM=	ratioHospitsEwoMM*assessmentsED EwoMM‐CCeffHospitsEwoMM	visits/Week
assessmentsED EwoMM=	PCreduceEDvisitsEwoMM*visitsEDperYearEwoMM/WeeksPerYear‐ CCeffReHospitsEwoMM	visits/Week
visitsEDperYearMHC2patients=	5.95	visit/(Person*Year)	average for the enrolled to MHC patients
tblProPCforEwoMM	([(0,0)‐(1,2)],(0,0),(1,0.5))	Dmnl	for 10% of the elderly, ProPC increases PC visits 50%
sumEDvisitsFAMMperYear=	visitsEDperYearFAMM+MHC2reduceEDvisitsFAMM	visit/Year
tblFAMMaffectedByMHC2	([(0,0)‐(1,1)],(0,0),(1,0.683))	Dmnl	share of FAMM affected by MHC
tblMHC2reduceFAMMvisitsED	([(0,0)‐(1,6)],(0,5.49),(1,4.495))	visit/(Year*Person)	FA getting care via MHC reduce visits from (5.49) to (4.495)
tblProPCeffectEDvisitsEwoMM	([(0,0)‐(1,1)],(0,1),(1,0.98))	Dmnl	0.98 = 20% reduction for 10% of EwoMM
visitsEDperYearFAMM=	(1‐shareMHC2forFAMM)*EDvisitorsFAMM*visitsEDperYearAndPersonFAMM	visit/Year
pressureED=	assessmentsED EwoMM+assessmentsED MM+assessmentsED FAMM	visit/Week
PCreduceEDvisitsEwoMM=	tblProPCeffectEDvisitsEwoMM(implementProPC)	Dmnl
totReducedReHospitsFromCC=	effReHospitalizationDueToCC*totReducedHospitsFromCC	visits/Week
effReHospitalizationDueToCC=	0.829	Dmnl	82.9% who have met a CC do not re‐hospitalize
CCeffReHospitsMM=	factorCCreduceEDvisitsMM*totReducedReHospitsFromCC	visit/Week
CCeffReHospitsFAMM=	factorCCreduceEDvisitsFAMM*totReducedReHospitsFromCC	visit/Week
CCeffReHospitsEwoMM=	factorCCreduceEDvisitsEwoMM*totReducedReHospitsFromCC	visit/Week
effHospitalizationDueToCC=	0.1613	Dmnl	improved discharge planning avoids hospitalisation
CCeffHospitsEwoMM=	factorCCreduceEDvisitsEwoMM*totReducedHospitsFromCC	visit/Week
CCeffHospitsMM=	factorCCreduceEDvisitsMM*totReducedHospitsFromCC	visit/Week
CCeffHospitsFAMM=	factorCCreduceEDvisitsFAMM*totReducedHospitsFromCC	visit/Week
outputHospitPerYearMM=	hospitalizationsMM*WeeksPerYear	visit/Year
getBetter=	ratioGetBetter*Elderly new MM/WeeksPerYear	people/Week
switchNeutralGrowt=	0	Dmnl
sumAssessmentsED=	(assessmentsED EwoMM+assessmentsED MM+assessmentsED FAMM)	visits/Week
outputHospitPerYearEwoMM=	hospitalizationsEwoMM*WeeksPerYear	visit/Year
outputHospitPerYearFAMM=	hospitalizationsFAMM*WeeksPerYear	visit/Year
hospitDaysPerYearFAMM=	outputHospitPerYearFAMM*avgHospitDaysPerVisitFAMM	Days/Year
newElderlyPerWeekSCB=	IF THEN ELSE(switchNeutralGrowt = 1, (14336/52), (18876 + STEP(1209, 260))/52)	people/Week	Calculated from data
avgHospitDaysPerVisitEwoMM=	9.2	Days/visit	according to data
drMM=	ratioMortalityMM*Elderly new MM/WeeksPerYear	people/Week
hospitDaysPerYearEwoMM=	outputHospitPerYearEwoMM*avgHospitDaysPerVisitEwoMM	Days/Year
ratioHospitsEwoMM=	0.492	Dmnl	unplanned hospitalisations from EwoMM ED visits
ratioHospitsMM=	0.816	Dmnl	unplanned hospitalisations from MM ED visits
ratioHospitsFAMM=	0.597	Dmnl	unplanned hospitalisations from FAMM ED visits
changePressureED=	pressureED/startingPressureED	Dmnl
startingPressureED=	2562	visit/Week	calibrated init value “pressureED”
hospitDaysPerYearMM=	outputHospitPerYearMM*avgHospitDaysPerVisitMM	Days/Year
totVisitsPCphysician=	visitsPCphysicianEwoMM+visitsPCphysicianMM	visit/Year
getMM=	initConst getMM*(Elderly withoutMM/initPopEwoMM)	people/Week
totVisitsPCnurse=	visitsPCnurseEwoMM+visitsPCnurseMM	visit/Year
initConst getMM=	0.9 × 0.95*(23934‐868)/52	people/Week	calculated init values
ratioStayMM=	0.3	Dmnl/Year	Calibrated to fit data and keep balance between stocks
ratioMortalityMM=	0.2	Dmnl/Year	Calibrated to fit data and keep balance between stocks
drEwoMM=	riskMortalityEwoMM*Elderly withoutMM/lifespanElderly	people/Week
avgMortalityMM >1Y=	3 × 52 * 1.1	Weeks	Calibrated to fit data and keep balance between stocks
drMM >1Y=	Elderly MM >1 Year/“avgMortalityMM >1Y”	people/Week
ratioMM >1YoverPopMM=	Elderly MM >1 Year/popMM	Dmnl
Elderly MM >1 Year=	INTEG (stayMM‐“drMM >1Y”, initPopMM × 0.48)	people
shareEwoMMoutput=	Elderly withoutMM/totPop	Dmnl
Elderly new MM=	INTEG (getMM+newElderly MM‐getBetter‐stayMM‐drMM, initPopMM × 0.52)	people
newElderly=	newElderlyPerWeekSCB*(1‐ratioNewEwMM)	people/Week
newElderly MM=	newElderlyPerWeekSCB*ratioNewEwMM	people/Week
EDvisitorsFAMM=	FAEDnewMM+“FAEDMM >1Y”	people
popMM=	Elderly new MM+“Elderly MM >1 Year”	people
initPopEwoMM=	initPopulation*(1‐initShareMM)	people	(153801 + 125726)
sumNewElderly=	INTEG (newElderlyPerWeekSCB, 0)	people
sumDeaths=	INTEG (drEwoMM+drMM+“drMM >1Y”, 0)	people
Elderly withoutMM=	INTEG (getBetter+newElderly‐getMM‐drEwoMM, initPopEwoMM)	people
initShareMM=	0.13874	Dmnl
totPop=	Elderly withoutMM+“Elderly MM >1 Year”+Elderly new MM	people
stayMM=	ratioStayMM*Elderly new MM/WeeksPerYear	people/Week
shareMMoutput=	(Elderly new MM+“Elderly MM >1 Year”)/totPop	Dmnl
initPopMM=	initShareMM*initPopulation	people
EDvisitorsMM=	outputMM‐EDvisitorsFAMM	people	non‐FA MM‐patients
ratioFA MMatED=	0.1081	Dmnl	FA of the MMgroup at the ED
personPerVisit=	1	Person/visit
riskMortalityEwoMM=	0.16	Dmnl	Calibrated to fit data and keep balance between stocks
outputMM=	totPop*shareMMoutput	people
ratioNewEwMM=	0.046	Dmnl	ratio elderly turning 65 Yrs already had multimorbidity
visitsEDperYearAndPersonEwoMM=	0.24	visit/(Year*Person)
demographyIndex=	tblDemography(Time)	people
lifespanElderly=	20.2 × 52	Weeks	average additional lifespan after becoming 65
initPopulation=	331745	people
tblDemography	([(0,200000)‐(520,400000)],(0,331670),(520,377000))	people	332000 persons 65+
WeeksPerYear=	52	Weeks/Year
FINAL TIME =	520	Week	The final time for the simulation.
INITIAL TIME =	0	Week	The initial time for the simulation.
SAVEPER =	TIME STEP	Week [0,?]	The frequency with which output is stored.
TIME STEP =	0.25	Week [0,?]	The time step for the simulation.

Goienetxea Uriarte, A., Ruiz Zúñiga, E., Urenda Moris, M., & Ng, A. H. C. (2017). How can decision makers be supported in the improvement of an emergency department? A simulation, optimization and data mining approach. Operations Research for Health Care, 15, 102–122. https://doi.org/10.1016/j.orhc.2017.10.003

 Google Scholar

Banks, J., Carson, J. S., II, Nelson, B. L., & Nicol, D. M. (2014). Discrete-event system simulation (Fifth ed.). Pearson Education Ltd.

 Google Scholar

Sterman, J. (2000). Business dynamics: Systems thinking and modeling for a complex world. Irwin McGraw-Hill.

 Google Scholar

Linnéusson, G., & Goienetxea Uriarte, A. (2021). Analyzing closer care strategies for elderly patients: Experience and reflections from modeling with system dynamics. In D. R. M. Fakhimi & T. Boness (Eds.), Proceedings of the Operations Research Society Simulation Workshop 2021 (SW21), Loughborough University (pp. 117–126). Operational Research Society.

 Google Scholar

Barlas, Y. (1996). Formal aspects of model validity and validation in system dynamics. System Dynamics Review: The Journal of the System Dynamics Society, 12(3), 183–210. https://doi.org/10.1002/(SICI)1099-1727(199623)12:3<183:AID-SDR103>3.0.CO;2-4

 Web of Science ®Google Scholar

Bertrand, J. W. M., & Fransoo, J. C. (2002). Operations management research methodologies using quantitative modeling. International Journal of Operations & Production Management, 22(2), 241–264. https://doi.org/10.1108/01443570210414338

 Web of Science ®Google Scholar

Sargent, R. G. (2011). Verification and validation of simulation models Proceedings of the 2011 Winter Simulation Conference (WSC), Phoenix Arizona (pp. 183–198).

 Google Scholar