Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 1 / 6A / a / Solution

The $\beta YN$ interaction converts supporters into opponents. The $\alpha YN$ interaction converts opponents into undecided people, while $\zeta U$ converts undecided people into opponents. Summing the three equations gives $(Y+N+U{)}^{\prime }=0$, as required for a fixed population.