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Table 1 Dimension of parameters and variables used in simulations

From: Optimal control of a rumor propagation model with latent period in emergency event

Variable or parameter Dimension Implication
x, w, y, z Dimensionless Proportional population
X, W, Y, Z Hundred thousand Day−1 Population
Λ Hundred thousand Day−1 The number of immigration population
\(\beta_{0}\) Unity. Day−1 Rumor propagation coefficient
\(\lambda_{0}\) Unity. Day−1 Rumor stifler coefficient
\(\alpha_{0}\) Dimensionless Change rate for exposed
\(\gamma_{0}\) Dimensionless Change rate for spreaders
θ Dimensionless Believe and spread rate
μ Dimensionless The emigration rate
N Hundred thousand Total population
  1. Here \(x=\frac{X}{N}\), \(y=\frac{Y}{N}\), \(z=\frac{Z}{N}\), \(\beta=\frac{\beta_{0}}{\mu}\), \(\alpha=\frac{\alpha_{0}}{\mu}\), \(\lambda=\frac{\lambda_{0}}{\mu}\), \(\gamma=\frac{\gamma_{0}}{\mu}\).