Mathematical modelling and its application to social care

Introduction

The use of mathematical models has gained much prominence through their use in facilitating economic evaluation. However, models have also been used in a number of other decision-making contexts including risk assessment and service planning and capacity modelling.

Objectives

This review aimed to present an overview of mathematical modelling and its current and potential role in informing decisions surrounding the management and delivery of social care. The
purposes of the review were to:

1. briefly describe the model development process and the most common methodological forms of mathematical models used to inform health care policy decision-making;
2. review the use of mathematical modelling in the evaluation of social care interventions, and;
3. consider developing and applying existing modelling approaches within a social care context.

Findings

This review summarises key mathematical modelling methods, with a focus upon those methods currently applied within healthcare modelling, and suggests previous and potential applications of these methods within the field of social care.

A summary is offered of the model development process, including the use of problem structuring methods, literature reviewing, elicitation and uncertainty analysis. Specific modelling methods such as decision trees, state transition models and discrete event simulation are described, with an outline of their strengths and limitations. Current approaches for quantifying outcomes within health economic evaluation are also briefly discussed.

The review highlights particular issues which may need to be considered when applying these modelling methods to social care.