Elements of computer modelling: 12 studies for beginners. Study 3: Rumour propagation model

Abstract

This paper continues our foundational series on computer modelling [1, 2] and introduces the first complete modelling exercise: a rumour propagation model through a community. Beginning with a deliberately oversimplified version that produces unlimited geometric growth, we progressively refine the model across four versions: incorporating varying communication levels among population members (ordinary speakers, talkative individuals, and silent members), accounting for repeat knowers who have already heard the rumour, and finally developing an analogous epidemic model using differential equations. Each version follows the complete modelling cycle established in the preceding studies: problem formulation, simplifying assumptions, mathematical model construction, spreadsheet algorithm development, computational experiment, and critical analysis of results. The progressive refinement demonstrates how identifying a model's weaknesses - particularly overly simplistic assumptions - drives the creation of more realistic versions. Key concepts introduced include model stability, the distinction between artificial and natural growth limitations, and the importance of model testing. The epidemic model in the final section provides an independent exercise that reinforces all acquired skills whilst introducing continuous-time modelling with finite differences.