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

BACKGROUND: 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. METHODS: 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. RESULTS: 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. CONCLUSIONS: 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.

Incentives to change: effects of performance-based financing on health workers in Zambia.

BACKGROUND: Performance-based financing (PBF) has been implemented in a number of countries with the aim of transforming health systems and improving maternal and child health. This paper examines the effect of PBF on health workers' job satisfaction, motivation, and attrition in Zambia. It uses a randomized intervention/control design to evaluate before-after changes for three groups: intervention (PBF) group, control 1 (C1; enhanced financing) group, and control 2 (C2; pure control) group. METHODS: Mixed methods are employed. The quantitative portion comprises of a baseline and an endline survey. The survey and sampling scheme were designed to allow for a rigorous impact evaluation of PBF or C1 on several key performance indicators. The qualitative portion seeks to explain the pathways underlying the observed differences through interviews conducted at the beginning and at the three-year mark of the PBF program. RESULTS: Econometric analysis shows that PBF led to increased job satisfaction and decreased attrition on a subset of measures, with little effect on motivation. The C1 group also experienced some positive effects on job satisfaction. The null results of the quantitative assessment of motivation cohere with those of the qualitative assessment, which revealed that workers remain motivated by their dedication to the profession and to provide health care to the community rather than by financial incentives. The qualitative evidence also provides two explanations for higher overall job satisfaction in the C1 than in the PBF group: better working conditions and more effective supervision from the District Medical Office. The PBF group had higher satisfaction with compensation than both control groups because they have higher compensation and financial autonomy, which was intended to be part of the PBF intervention. While PBF could not address all the reasons for attrition, it did lower turnover because those health centers were staffed with qualified personnel and the personnel had role clarity. CONCLUSIONS: In Zambia, the implementation of PBF schemes brought about a significant increase in job satisfaction and a decrease in attrition, but had no significant effect on motivation. Enhanced health financing also increased stated job satisfaction.