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Theoretical Health Inequality Model (THIM)



By Ross Richardson (2015)


The Theoretical Health Inequality Model (THIM) was developed by Wolfson et al. (2016) to understand why cities in the US and UK with higher income inequality have lower health-adjusted life expectancy, while Australian, Canada and Swedish cities do not. The model is motivated by the theory that low income households living near high income households tend to benefit from better infrastructure and amenities such as hospitals, which may be denied to them if living in a city partitioned into rich and poor neighbourhoods (the “gates and ghettos” case). The model specifically tries to demonstrate this relationship by varying the  heterogeneity within each neighbourhood and across neighbourhoods.

THIM is a computationally heavy model with lots of interactions, however agents also undergo demographic transitions modelled by stochastic processes represented by regressions, so it is ideal in representing a hybrid AB and MS model. The model recreates stylized individual-level relationships among health status, education, income, mortality rates and neighbourhood mobility. There are multiple levels featured in THIM, from individuals and parent-child dyads, to neighbourhoods and cities. The interactions between the states of individuals and across a hierarchy of aggregation levels are represented in the figure below. These levels allow to capture the roles of parental transmission of socio-economic status and health advantage to children, the impact of average neighbourhood income on school, and overall city-wide patterns of inequality and mortality.

The interaction between states (attributes) of individual agents and across a hierarchy of aggregation levels in the Theoretical Health Inequality Model. For each agent, E is the education level, Y is the income level, H is the health index, D is the mortality probability and L is the geographic location. Source: Wolfson et al. (2016).
Figure: The interaction between states (attributes) of individual agents and across a hierarchy of aggregation levels in the Theoretical Health Inequality Model. For each agent, E is the education level, Y is the income level, H is the health index, D is the mortality probability and L is the geographic location. Source: Wolfson et al. (2016).


THIM features a mix of regular events; each agent updates its status once a year on its birthday, and the system-wide statistics against which an agent measures itself are updated at the start of a new year. There are also irregular events and dynamic scheduling; the time at which each agent gives birth and dies is drawn probabilistically from continuous distributions during the simulation. This means that we cannot know a priori the timing of events at the start of the simulation, and therefore cannot use JAS-mine’s scheduling tools to reduce the number of events that need to be scheduled by scheduling events to apply to the whole population of agents, as we did in the Demo07 demonstration model. In this case, the model’s event schedule scales with the number of agents and not just with the number of processes. Simulating a country on a one-to-one scale would mean potentially having to schedule hundreds of millions of events during run-time.

The priority queue behind JAS-mine’s event schedule keeps the access and insertion of events in the event schedule computationally efficient, with access to the earliest event achieved in constant time, whilst insertion is performed in logarithmic time O(log N) in the worst case. This means that a model simulating the United States on a one-to-one scale containing 300 million agents would only need to check up to around thirty events of the schedule to find the correct place to insert a new event.

Reference:  Wolfson, M., Gribble, S., and Beall, R. (2016). Exploring contingent inequalities - building the theoretical health inequality model. In Grow, A. and van Bavel, J., editors, Agent-Based Modelling in Population Studies: Concepts, Methods and Applications. Springer.


The source code for this model is available below and on GitHub at https://github.com/jasmineRepo/thim.  Executable versions of the demo models including the Theoretical Health Inequality Model can be found at https://sourceforge.net/projects/jas-mine/files/Demo%20Models/.
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THIM.zip
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JAS-mine Simulation,
Oct 20, 2016, 5:03 PM