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

Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 1 Dimension of parameters and variables used in simulations

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

Here \(x=\frac{X}{N}\), \(y=\frac{Y}{N}\), \(z=\frac{Z}{N}\), \(\beta=\frac{\beta_{0}}{\mu}\), \(\alpha=\frac{\alpha_{0}}{\mu}\), \(\lambda=\frac{\lambda_{0}}{\mu}\), \(\gamma=\frac{\gamma_{0}}{\mu}\).