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BMC Health Serv Res. 2019 Nov 19;19(1):845. doi: 10.1186/s12913-019-4627-7.

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

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Department of Global Health and Development, London School of Hygiene and Tropical Medicine, 15-17 Tavistock Place, London, WC1H 9SH, UK.
Department of Global Health and Development, London School of Hygiene and Tropical Medicine, 15-17 Tavistock Place, London, WC1H 9SH, UK.
Department of Mathematics, University College London, London, UK.
Sia Partners UK, London, UK.
Information Systems Department, College of Computing and Information Sciences, Makerere University, P.O. Box 7062, Kampala, Uganda.
Ifakara Health Institute, PO Box 78373, Dar es Salaam, Tanzania.
Department of Gender Studies, School of Humanities and Social Sciences, University of Zambia, 10101, Lusaka, Zambia.
Economic and Business Research Programme, University of Zambia, Institute of Economic and Social Research, P O Box 30900, 10101, Lusaka, Zambia.
Department of Public Health, Environments and Society, London School of Hygiene and Tropical, London, UK.



Mathematical modelling has been a vital research tool for exploring complex systems, most recently to aid understanding of health system functioning and optimisation. System dynamics models (SDM) and agent-based models (ABM) are two popular complementary methods, used to simulate macro- and micro-level health system behaviour. This systematic review aims to collate, compare and summarise the application of both methods in this field and to identify common healthcare settings and problems that have been modelled using SDM and ABM.


We searched MEDLINE, EMBASE, Cochrane Library, MathSciNet, ACM Digital Library, HMIC, Econlit and Global Health databases to identify literature for this review. We described papers meeting the inclusion criteria using descriptive statistics and narrative synthesis, and made comparisons between the identified SDM and ABM literature.


We identified 28 papers using SDM methods and 11 papers using ABM methods, one of which used hybrid SDM-ABM to simulate health system behaviour. The majority of SDM, ABM and hybrid modelling papers simulated health systems based in high income countries. Emergency and acute care, and elderly care and long-term care services were the most frequently simulated health system settings, modelling the impact of health policies and interventions such as those targeting stretched and under resourced healthcare services, patient length of stay in healthcare facilities and undesirable patient outcomes.


Future work should now turn to modelling health systems in low- and middle-income countries to aid our understanding of health system functioning in these settings and allow stakeholders and researchers to assess the impact of policies or interventions before implementation. Hybrid modelling of health systems is still relatively novel but with increasing software developments and a growing demand to account for both complex system feedback and heterogeneous behaviour exhibited by those who access or deliver healthcare, we expect a boost in their use to model health systems.


Agent-based; Health systems; Hybrid; Modelling; System dynamics; Systematic review

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