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Table 2 Summary of studies included at full paper review (SDM) and studies included at full paper review (ABM)

From: Mathematical modelling for health systems research: a systematic review of system dynamics and agent-based models

Paper/Year/Ref

Purpose

Sector of health system modelled

Key results

Software platform

System dynamics models (SDMs)

Al-Khatib (2016) [48]

Assess the impact of key factors on the hospital waste management system and compare the future total waste output between private, charitable and government hospitals.

ā€¢ Model simulates hospital waste management in Nablus, Palestine.

ā€¢ Focus on three different types of hospital (private, charitable and government hospitals).

ā€¢ The amount of waste generated heavily dependent on the number of beds.

ā€¢ Waste treatment was dependent on staff training and the enforcement of legislation.

ā€¢ iThink.

Alonge (2017) [30]

Explore effective implementation structure for improving health system performance through pay-for-performance (P4P) initiative.

ā€¢ The model is a generic representation of the pay for performance initiative in primary health facilities in Afghanistan.

ā€¢ P4P initiative would likely have a beneficial impact on the volume and quality of health services if correctly implemented.

ā€¢ May prove ineffective if the impact of gaming is not mitigated or if the method for distributing financial rewards are inadequate.

ā€¢ MATLAB and Simulink.

Ansah (2014) [49]

Assess the impact of different long-term care (LTC) capacity policies on uptake of acute care, demand for and utilisation of LTC services.

ā€¢ Generic representation of LTC utilisation and resources for care and is not based or set in a particular health facility.

ā€¢ Proactive adjustment of LTC capacity stemmed the number of acute care visits but required a modest increase in staff.

ā€¢ Movement of health staff (through delayed training or from LTC to the acute care sector) will impede the success of this policy.

ā€¢ Does not state.

Brailsford (2004) [50]

To determine how emergency and on demand care is currently configured and what policies could alleviate pressure on the health system.

ā€¢ Entire healthcare system that provides emergency centres etc) in Nottingham, England.

ā€¢ Significant impact on elective hospital admissions as emergency cases are currently prioritised.

ā€¢ Redirecting certain elderly patients to appropriate services relieved pressure on emergency services.

ā€¢ STELLA.

Brailsford (2010)a [43]

Investigate how local authorities such as Hampshire County Council (HCC) can improve access to services and support for older people, in particular assess the long-term impact of a new contact centre for patients.

ā€¢ HCC system for long-term care, including a call centre that older patients can access to receive advice or be directed to appropriate care.

ā€¢ The number of patients who contact the call centre on a second occasion (having failed to make contact the first time) where the health status of the patient has now deteriorated, fell drastically after the introduction of two additional call handlers.

ā€¢ SDM is Vensim, DES model is Simul8.

Cepoiu-Martin (2018) [51]

To examine patient transition from home to supportive living (SL) or long term care (LTC) in persons with dementia and discern policy impact on the deficit of nurses and health care assistants.

ā€¢ The Alberta Continuing Care System comprising of home living, SL or LTC services.

ā€¢ Introducing benchmarks for hiring nurses and health care assistants in SL and LTC facilities will result initially in a greater deficit of staff but will stabilise the ratio of health professionals to patients in the long term.

ā€¢ Does not state.

Chaerul (2008) [37]

To determine key factors that impact the management of hospital waste and predict future waste output.

ā€¢ The model describes hospital waste management in the City of Jakarta, Indonesia.

ā€¢ Hospital waste disposal is impacted by the reluctance of a densely populated cityto allow further waste to be dumped in landfill sites.

ā€¢ The simulation indicated that existing and new landfill sites will be at full capacity by 2011 and 2020, respectively.

ā€¢ STELLA.

Ciplak (2012) [52]

To predict future healthcare waste production and optimise the management of healthcare waste.

ā€¢ Healthcare waste generation from healthcare facilities, the single healthcare waste treatment facility and alternative waste treatment facilities in Istanbul, Turkey.

ā€¢ Employing stringent waste separation strategies would relieve the pressure on already at capacity waste treatment facility in Istanbul.

ā€¢ Up to 77% of healthcare waste could be diverted to alternative treatment technologies that do not require treatment at the incineration facility.

ā€¢ Vensim.

De Andrade (2014) [53]

To examine the reasons for delayed ST-segment elevation myocardial infarction (STEMI) treatment and explore interventions that can speed up wait time in primary care facilities.

ā€¢ A primary care hospital and a Percutaneous Coronary Intervention Centre (PCI) in Brazil.

ā€¢ It was observed that 50% reduction in waiting time for patients is possible under a combination of interventions targeting ECG transmission and PCI centre team feedback time and patient transfer waiting time.

ā€¢ Vensim.

Desai (2008) [54]

To forecast demand for older peopleā€™s services and explore the future impact of challenges that accompany an ageing population.

ā€¢ Adult Services Department of Hampshire County Council including 13 different types of care package that can be offered by the funding and assessment body.

ā€¢ Providing care packages only to critical patients reduced the overall number of patients receiving acute care.

ā€¢ Savings can be made by increasing the number of unqualified care workers which can be fed back into care funding.

ā€¢ STELLA.

Djanatliev (2012)b [47]

Presenting the functionality of the Prospective Health Technology Assessment (ProHTA) tool, which can simulate the impact of optimised technology prospectively before physical development.

ā€¢ Mobile Stroke Unit (MSU) case study was simulated for Berlin, includes a generic hospital with emergency services where patients are taken by the MSU.

ā€¢ In the simulation implementing MSU, 18.2% of patients received thrombolysis treatment compared with 10.6% in the simulation without MSU.

ā€¢ Fewer patients were also found to have developed severe disability in the simulation with MSU as a consequence of faster implemented treatment, reducing the long term costs for rehabilitation and care.

ā€¢ AnyLogic.

Eleyan (2013) [55]

To predict general and medical waste generation for a complex hospital waste management system.

ā€¢ Model simulates hospital waste management in three hospitals based in Jenin, Palestine.

ā€¢ Increases in the amount of hospital waste are consistent with bed occupancy. Over the next 20ā€‰years, the total amount of waste generated will rise as will the total cost of treating hazardous waste.

ā€¢ iThink.

Esensoy (2018) [28]

Transformation of stroke care to implement best practice.

ā€¢ The model describes six sectors of Ontario health care system and the patient flow between them.

ā€¢ When stroke best practice policy has been implemented (compared to the base case scenario), there is a reduction in length of stay across all sectors.

ā€¢ A reduction in bed utilisation was also observed with a 10 and 11.1% reduction in acute care and rehab sectors, respectively.

ā€¢ Vensim.

Ghaffarzad. (2013) [32]

To explore physician decision making behind scheduled caesarean delivery (CD), unplanned CD and vaginal delivery (VD) and examine factors that influence procedure variation.

ā€¢ The model does not reflect a particular hospital but is parameterised using patient information from hospital discharge databases in Florida.

ā€¢ The biggest impact on physician delivery decision is from the delayed effect of colleague past experience.

ā€¢ Turning off all learning experiences reduces physician delivery variation for scheduled CD delivery from 6.5 to 4.7%.

ā€¢ Vensim.

Lane (1998) [56]

Explore the factors that lead to delays in Accident and Emergency Departments (A&E) and to elective admissions.

ā€¢ A&E department at major inner-London teaching hospital coded in the study as ā€˜St Daneā€™sā€™.

ā€¢ Reduction in bed numbers increases emergency admission waiting times and delays and cancellations to elective surgery admissions.

ā€¢ Increases in demand push the system to breaking point, with patients waiting hours to be admitted and health workers at full capacity.

ā€¢ Does not state.

Lane (2000) [57]

The model depicts the performance of Accident and Emergency (A&E) at acute hospitals, investigating the sensitivity of waiting times to hospital bed numbers.

ā€¢ A&E department at Inner-London teaching hospital coded in the study as ā€˜St Daneā€™sā€™.

ā€¢ Reducing bed capacity increased the % of elective cancellations, negating the impact on other performance measures.

ā€¢ Deterioration of services is not attributed to lack of bed capacity but insufficient provision of A&E doctors who reach 100% utilisation.

ā€¢ iThink.

Lattimer (2004) [36]

To evaluate ā€˜front doorā€™ services of local emergency and urgent care facilities and test proposals for system change.

ā€¢ Entire healthcare system that provides emergency or on demand care (GP, NHS Direct, Walk in centres etc) in Nottingham.

ā€¢ Reducing emergency admissions from GP by 4% showed successive reduction in occupancy levels in A&E.

ā€¢ Interventions to lower admissions of patients over 60 resulted in a 1% reduction per annum in bed occupancy over 5ā€‰years.

ā€¢ STELLA.

Mahmoudia. (2017) [58]

To explore the intended and unintended consequences of Intensive Care Unit (ICU) resource and bed management policies on patient mortality, emergency departments (ED) and general wards.

ā€¢ Generic model of ICU, ED and general hospital wards.

ā€¢ Whilst general ward admission control is not as effective at reducing ICU and ED occupancy rates, it outperforms other policies with regards to reducing patient mortality, arguably the more important ICU management performance measure.

ā€¢ Does not state.

Meker (2015) [59]

To describe performance-based payment systems (PBPS) in second-step public hospitals and the impact on process measures in hospitals.

ā€¢ Second-step public hospitals in Turkey.

ā€¢ With reduced performance payments, physicians move to the private sector decreasing staff levels, reducing time spent with patients leading to a dramatic decrease of correct diagnosis and treatment.

ā€¢ Does not state.

Mielczarek (2016)a [44]

To estimate the future demand for healthcare from patients with cardiac disease.

ā€¢ Future demand for cardiac disease care in Wroclaw Region, Poland.

ā€¢ Older population (over 60) will generate increasing demands for care, specifically the growth of cardiac patients was observed as more intense in men than women (increases of 34.4 and 30.15% respectively).

ā€¢ Does not state.

Rashwan (2015) [31]

To explore the flow of elderly patients through the Irish healthcare system and anticipate the growing demand for services over the next 5 years.

ā€¢ Generic emergency care facility in Ireland and six possible discharge locations.

ā€¢ Under increasing demand, a combination of all three policies was necessary to significantly reduce elderly frail patientsā€™ length of stay in acute hospitals and reduce delayed discharge numbers.

ā€¢ Does not state.

Semwanga (2016) [60]

To capture the dynamics of the Ugandan health system and evaluate what impact interventions might have on neonatal care.

ā€¢ Does not focus on one type of health facility but incorporates different services and levels of care offered to this group.

ā€¢ Integrating community health education, free delivery kits and motorcycle coupons has the biggest impact on reducing neonatal death.

ā€¢ Interventions targeting socioeconomic status had a greater impact on reducing neonatal mortality than those targeting service delivery.

ā€¢ STELLA.

Taylor (2005) [33]

To examine the impact of shifting cardiac catheterization (CC) services from tertiary to secondary level for low risk investigations and explore how improvements could be made to services.

ā€¢ The CC service pathways at two English district general hospitals, referred to using the pseudonyms ā€˜Veinbridge Hospitalā€™ and ā€˜Ribsley Hospitalā€™.

ā€¢ Significant and stable improvements in service (reducing waiting list time and overall costs of service) were achieved with the implementation of strict referral guidelines for patients.

ā€¢ STELLA.

Walker (2003) [61]

To model patient flow from feeder hospitals to a sub acute extended care hospital to show the impact of local rules used by the medical registrar (medical admitting officer).

ā€¢ A single extended care facility in Victoria (Australia) and patient flow from feeder hospitals.

ā€¢ Using the local rule, the cost of care exceeds the budget by 6%. Without the local rule, costs were 3% under budget. ļ»æ

ā€¢ The unprioritized list maintains waiting lists at a level that effectively short-circuits the feeder hospital second local rule of moving high acuity patients on to the wait list of the sub-acute hospital.

ā€¢ iThink.

Wong (2010) [62]

To evaluate if smoothing the number of discharges over the week relieves the pressure on emergency departments (ED).

ā€¢ Model describes a general internal medicine (GIM) program at a single tertiary care teaching hospital in Toronto, Canada.

ā€¢ Both scenarios for ā€˜smoothed average caseā€™ were similar, resulting in reduction of GIM in ED by 27% and GIM in ED length of stay by 31%.

ā€¢ For ā€˜every day is a week day caseā€™, larger reductions observed.

ā€¢ Vensim.

Worni (2012) [63]

To estimate what impact a policy to deny reimbursement of total knee arthroplasty (TKA) patient fees will have on venous thromboembolism (VTE) rates and any unintentional consequences.

ā€¢ The model simulates all patients (9.7 million) in the US who have symptomatic osteoarthritis, over 65 and have Medicare insurance.

ā€¢ Model output indicates new policy will result in 3-fold decrease in VTE rates. Fraction of those (in simulation with new policy) with bleeding complications is 6-fold higher and 6-fold more patients ineligible for TKA per year.

ā€¢ Vensim.

Yu (2015) [64]

To explore the driving factors for a high proportion of patients in China not seeking medical care (also known as potential medical demand) and examine possible interventions.

ā€¢ Three main sub-systems; medical demand of patients, outpatients in hospitals and outpatients in community health systems (CHS). It does not describe a specific hospital or CHS.

ā€¢ An increase in the number of CHS and decrease in the number of hospitals was found to induce the biggest decrease in the number of patients not seeking care.

ā€¢ Varying the price of outpatient care in hospitals and CHS had minimal impact on increasing the number of patients who seek care.

ā€¢ Vensim.

Zulkepli (2012)a [45]

Present a case study using hybrid modelling (SDM-DES), explore patient flow in an integrated care system (IC) and the impact of patient admission on health professional stress level.

ā€¢ Three main sub-systems; patient flow through critical care facility, patient flow through intermediate care assessment and motivation and stress levels of health professionals.

ā€¢ Due to high demand of intermediate care services but limited spaces bed blocking may occur, with an increase in patient admissions leading to an increase to health professional stress level.

ā€¢ SDM is Vensim, DES model is Simul8.

Agent-based models (ABMs)

Alibrahim (2018) [23]

To explore the effect of patient choice on the healthcare market, specifically providers that form accountable care organisations (ACO).

ā€¢ A generalised simulation of patient (Medicare beneficiary, over 65ā€‰years old who has or can develop congestive heart failure) choice of medical provider (hospital or primary care physician facility) in the United States.

ā€¢ Where providers were allowed to opt out of ACO network, they were able to optimise their own profits by not implementing a disease management programme - this led to a reduction in the overall quality of care, driving patients to attend alterative care facilities reducing the utilisation of that facility.

ā€¢ AnyLogic.

Djanatliev (2012)b [47]

Presenting the functionality of the Prospective Health Technology Assessment (ProHTA) tool, which can simulate the impact of optimised technology prospectively before physical development.

ā€¢ Mobile Stroke Unit (MSU) case study was simulated for Berlin, includes a generic hospital with emergency services where patients are taken by the MSU.

ā€¢ In the simulation implementing MSU, 18.2% of patients received thrombolysis treatment compared with 10.6% in the simulation without MSU.

ā€¢ Fewer patients were also found to have developed severe disability in the simulation with MSU as a consequence of faster implemented treatment, reducing the long term costs for rehabilitation and care.

ā€¢ AnyLogic.

Einzinger (2013) [65]

To create a tool capable of comparing reimbursement schemes in outpatient care.

ā€¢ Compared different reimbursement schemes for Austrian outpatient health sector simulating the vast majority of health insured persons in Austria.

ā€¢ Creation of a tool that can be used to compare health care reimbursement schemes in Austria.

ā€¢ AnyLogic.

Hutzsch. (2008) [66]

To determine which mix of patients should be admitted to specialised hospitals to optimise resource utility and to consider the impact of unplanned patient arrivals on this process.

ā€¢ Cardiothoracic surgery (CTS) and intensive care unit (ICU) at Catharina Hospital Eindhoven (CHE) in the Netherlands. CTS and ICU are broken down into their respective units such as the high care unit of CTS etc.

ā€¢ An additional ward bed on the CTS ward decreased the frequency of sending pre- and post- operative admissions to other wards by a factor of 3 with minimal cost.

ā€¢ The brute force optimiser indicated that the number of IC high care beds should be increased and number of IC beds decreased to gain optimum throughput of patients in simulation.

ā€¢ Java.

Huynh (2012) [20]

To assess the impact of redesigning medication administration process (MAP) workflow for registered nurses to improve medication administration safety.

ā€¢ A local (anonymous) medical centre where nurses are administering medication to patients.

ā€¢ Implementing a protocol for the order of MAP tasks to be performed improved the amount of time spent performing tasks.

ā€¢ When registered nurses performed tasks in the most frequently observed order (in the pilot study) this improved MAP task times.

ā€¢ Netlogo.

Kittipitta. (2016)c [24]

To examine patient flow in an outpatient clinic of an orthopedic department and explore interventions that can improve clinical services to reduce patient waiting times.

ā€¢ Orthopedic department at unidentified community hospital.

ā€¢ Average waiting time for outpatient appointments fell by 32.03% under the new management policy.

ā€¢ AnyLogic.

Liu (2014) [21]

To develop a tool that can be used as a decision support system for managers of emergency departments (ED) to assess risk, allocation of resources and identify weakness in emergency care service.

ā€¢ ED at Hospital of Sabadell (University tertiary level hospital in Barcelona, Spain). The Department is split into sections A (critical patients) and B (least critical patients).

ā€¢ A tool that can be used simulate the behaviour of agents in ED.

ā€¢ Netlogo.

Liu (2016) [25]

To explore how accountable care organisations (ACO) can impact payers, healthcare providers and patients under a shared savings payment model for congestive heart failure (CHF) and achieve optimal outcomes.

ā€¢ A generalised simulation of patients (Medicare beneficiary, over 65ā€‰years old who has or can develop congestive heart failure) seeking care (hospital or primary care physician facility) in Unites States.

ā€¢ Quality orientated providers yielded higher financial returns to the payer agent (which were then shared between providers) than those that were profit-orientated.

ā€¢ AnyLogic.

Viana (2018)c [46]

To examine and improve patient flow through a pregnancy outpatient clinic in light of the uncertainty in demand for services from overdue patients.

ā€¢ Overdue pregnancy outpatient clinic, pregnancy clinic and postnatal clinic at Akershus University Hospital, Norway.

ā€¢ As expected increasing the number of midwives in the clinic reduces resource utilisation but combined with an increase in demand led to an increase in doctor utilisation.

ā€¢ Midwives act as a buffer (or bottleneck) to patients seeing doctors.

ā€¢ AnyLogic.

Yousefi (2017) [67]

To apply group decision-making techniques for emergency department (ED) resource allocation and determine whether this approach improves performance indicators.

ā€¢ A generic ED informed from the literature.

ā€¢ Group-decision making between agents in the ED resulted in on average a 12.7% decrease in total waiting time and 14.4% decrease in the number of patients who left without being seen.

ā€¢ Netlogo.

Yousefi (2018) [22]

To examine the behaviour of patients who leave public hospital emergency departments (ED) without being seen and the impact of preventative policies.

ā€¢ ED at Hospital Risoleta Tolentino Neves, a tertiary hospital in Minas Gerais, Brazil.

ā€¢ After applying preventative policies, average 42.14% reduction in the number of patients leaving without being seen in the ED and average 6.05% reduction in patient length of stay in ED was observed, with most effective policy to fast-track less critical patients after triage.

ā€¢ NetLogo .

  1. Note: aArticles implemented SDM-DES hybrid modelling
  2. bArticles implemented SDM-ABM hybrid modelling
  3. cArticles implemented ABM-DES hybrid modelling