Population dynamics modelling of child protection populations in Australia

Growing service demand is a perennial challenge for child protection systems in Australia, with the number of children involved in child protection (CP) investigations and admitted to out-of-home care (OOHC) increasing across Australian states and territories in the last decades. Since OOHC is costly and its effects on outcomes for children and youth are ambiguous, such a demand growth has attracted much scrutiny. While factors influencing involvement in CP and placement in OOHC have been studied extensively, a review of existing research literature shows that no study has applied mathematical formulations of population dynamics to model CP population structures and trends. This study intends to fill the gap by asking the research question, "How can we use population dynamics modelling to study the macro-dynamical structures of CP populations across Australian states and territories?" Two population dynamics models of a generic child protection system were constructed, one with four sub-populations and the other with three sub-populations. The models describe how the sub-populations evolve with time, simulate their interactions, and elucidate effects such as "churn" – repeated involvement with CP, both in terms of CP investigations and OOHC admissions. Analytical solutions of the system differential equations were obtained. Applying the model solutions together with annual aggregate new and repeat client data from 2015-16 to 2017-18 to all Australian states and territories, this study obtained estimations of the investigation rates and OOHC admission rates for the sub-populations, trends of the sub-populations, as well as cross-sectional prevalence and lifetime prevalence of involvement in CP. The results show that both the investigation rates and OOHC admission rates for repeat clients were much higher than those for new clients across the states and territories. It was estimated that if the current rate scenarios persist, OOHC populations across the states and territories will approach asymptotic values significantly higher than the current values. How CP sub-populations response to changes in the CP process rates have also been investigated using hypothetical scenarios. This study contributes to CP population research in three dimensions. Theoretically and methodologically, this is the first application of population dynamics models to study the macro structure and trends of CP populations. Empirically, the models allow us to estimate CP prevalence and rates. Practically, the models allow us to estimate future trends of CP populations and to study how CP populations react to rate scenario changes which in turn, may result from practice or policy changes. As in all modelling efforts, there are limitations and caveats. These include making the assumption that there is no system capacity limit in OOHC, thus making the models linear; not considering age structure; not considering socio-economic conditions and ethnic differences; and last but not least, having very limited data which are essential to such kind of modelling efforts. While future works have already been planned to address some of these limitations, any further progress will depend on the availability of high frequency data, from which conditions related to model limitations can be better understood and models can be better constrained.