$$ \begin{aligned} I' &= -bkIS \\ S' &= bkIS - akS(S+R) \\ R' &= akS(S+R) \end{aligned} $$
where $I'=S'=R'=0$. The inspection of equation system indicates that equilibrium stated are only possible if $S=0$?
2026-03-28 03:32:53.1774668773
Equilibrium point rumor propagation model
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Assuming that $S$ and $R$ are nonnegative, yes. You get $R'=0$ only if $S=0$ or $S+R=0$. If you allow $S$ or $R$ to be negative, then there are also equilibria with $I=0, S=-R$.