This is the baseline, unspecialized case of the belief-contagion family: a plain Susceptible–Believer–Skeptic (S/I/R) epidemic model running on a generic Erdős–Rényi random graph — every pair of the population's 70 nodes is linked with the same fixed probability, giving no special topology (no classroom clustering, no scale-free academic hierarchy — just uniform random contacts). It is the reference case every demographic variant of this simulator specializes.
The population-level dynamics follow the classic continuous SIR differential equations:
dS/dt = -βSI
dI/dt = βSI - γI
dR/dt = γI
R0 = β/γ
Discretely, on the network, each step of length dt every Believer (I) attempts to convert each Susceptible (S) neighbor independently with per-edge probability 1-e^(-β·dt), and independently loses conviction to Skeptic (R, immune) with probability 1-e^(-γ·dt):
P(S→I via one I-neighbor) = 1 − e^(−β·dt)
P(I→R per step) = 1 − e^(−γ·dt)
- Transmission rate β — how convincing one believer's retelling is per unit time; higher β steepens the initial rise of the I curve.
- Recovery rate γ — how quickly a believer loses conviction and becomes an immune skeptic; higher γ shortens and flattens the I peak.
- Network density — the graph's average degree ⟨k⟩ (expected links per node), set by the Erdős–Rényi edge probability p = ⟨k⟩/(N-1). A believer can only expose its actual graph neighbors, so a sparse network (low ⟨k⟩) throttles spread well below the fully-mixed R0 even at the same β and γ; a dense, near-complete network lets contacts approximate the well-mixed assumption behind the mean-field equations above.
- R₀ = β/γ — the mean-field basic reproduction number: how many new believers one believer generates in a fully-susceptible, fully-mixed population. R0 > 1 means the belief can take off; R0 < 1 means it dies out on its own.