Analysis of fractional order model on the employees’ negative attitudes towards their workplace

Figures & data

Table 1. Explanations of parameters stated in the model

Symbol	Explanation
µ	Human natural mortality rate
Δ	Employees recruitment rate
δ	Progression rate
γ	Improvement(rehabilitation) rate of negative attitude
ρ	Protection lose rate
β	Negative attitude dissemination rate
ϵ	protection coverage
ω	Rehabilitation lose rate
σ	Rehabilitation probability of exposed
ψ	Rate of employees out from exposed group
ϕ	Modification parameter
κ	protection boosting rate

Table 2. Definitions of state variables

Variable	Definition
S	Employees who are at risk for negative attitude
P	Employees who are protected against negative attitudes
E	Employees who are exposed to negative atittude
A	Employees who have ordinary negative attitude
Q	Employees who have permanent negative attitude
R	Employees rehabilitated from negative attitude

Figure 1. Flow chart of negative attitude employees.

Figure 2. β vs R_eff.

Figure 3. Ε vs R_eff.

Figure 4. γ vs R_eff.

Figure 5. κ vs R_eff.

Figure 6. The time series evaluation of system(8) by varying the initial condition and ${\mathcal{R}}_{\mathit{eff}}<1$.

Figure 7. The time series evaluation of system 8(8) $\begin{array}{ll}{\displaystyle \frac{\mathit{dS}}{\mathit{dt}}}=& (1-\mathit{ϵ})\mathrm{\Delta }+\mathit{\omega R}+(1-\mathit{\kappa })\mathit{\rho P}-({\mathit{\lambda }}_n+\mathit{\mu })\mathit{S},\\ {\displaystyle \frac{\mathit{dP}}{\mathit{dt}}}=& \mathit{ϵ}\mathrm{\Delta }-((1-\mathit{\kappa })\mathit{\rho }+\mathit{\mu })\mathit{P},\\ {\displaystyle \frac{\mathit{dE}}{\mathit{dt}}}=& ={\mathit{\lambda }}_n\mathit{S}-(\mathit{\psi }+\mathit{\mu })\mathit{E},\\ {\displaystyle \frac{\mathit{dA}}{\mathit{dt}}}=& (1-\mathit{\sigma })\mathit{\psi E}-(\mathit{\delta }+\mathit{\gamma }+\mathit{\mu })\mathit{A},\\ {\displaystyle \frac{\mathit{dQ}}{\mathit{dt}}}=& \mathit{\delta A}-\mathit{\mu Q},\\ {\displaystyle \frac{\mathit{dR}}{\mathit{dt}}}=& \mathit{\gamma A}+\mathit{\sigma \psi E}-(\mathit{\omega }+\mathit{\mu })\mathit{R},\end{array}$(8) by varying the initial condition and ${\mathcal{R}}_{\mathit{eff}}>1$.

Figure 8. The impact of β on the $\mathit{S}(\mathit{t})+\mathit{P}(\mathit{t})$.

Figure 9. The impact of β on the $\mathit{A}(\mathit{t})+\mathit{Q}(\mathit{t})$.

Figure 10. The impact of ϵ on the P(t).

Figure 11. The impact of ϵ on the $\mathit{A}(\mathit{t})+\mathit{Q}(\mathit{t})$.

Figure 12. The impact of κ on the P(t).

Figure 13. The impact of κ on the $\mathit{A}(\mathit{t})+\mathit{Q}(\mathit{t})$.

Figure 14. The impact of γ on $\mathit{A}(\mathit{t})+\mathit{Q}(\mathit{t})$.

Data availability statement

All data generated or analyzed in the process of this study are incorporated in this published paper.