Table 5.

Investigations based on epidemic models.

Sources	Contents
SIR model: $\frac{\mathit{dS}}{\mathit{dt}}=-\mathit{\beta SI}$,$\frac{\mathit{dI}}{\mathit{dt}}=\mathit{\beta SI}-\mathit{\gamma I}$,$\frac{\mathit{dR}}{\mathit{dt}}=\mathit{\gamma I}$
Stone et al. (2007))	Analyzed the nonlinear dynamics of recurrent diseases by referring the SIR model.
Zaman et al. (2008)	Presented a helpful model for controlling the infections based on the SIR model.
Kar and Batabyal (2011)	Studied a vaccination case by using nonlinear mathematical method of the epidemic model.
SIRS model: $\frac{\mathit{dS}}{\mathit{dt}}=-\mathit{\beta SI}+\mathit{\alpha R}$,$\frac{\mathit{dI}}{\mathit{dt}}=\mathit{\beta SI}-\mathit{\gamma I}$,$\frac{\mathit{dR}}{\mathit{dt}}=\mathit{\gamma I}-\mathit{\alpha R}$
Xu et al. (2010)	Investigated saturation incidence and temporary immunity by using a delayed SIRS model.
Xia et al., 2009)	Analyzed how nonuniform transmission affects the critical threshold of SIRS model on scale free networks.
Agiza et al. (2003)	Studied phase transitions in some epidemic models like SIRS which is defined on small-world networks.
SEIR model: $\frac{\mathit{dS}}{\mathit{dt}}=-\mathit{\beta SI}$, $\frac{\mathit{dI}}{\mathit{dt}}=\mathit{\alpha E}-{\gamma }_{2}I$, $\frac{\mathit{dE}}{\mathit{dt}}=\mathit{\beta SI}-\left(\alpha +{\gamma }_1\right)E$, $\frac{\mathit{dR}}{\mathit{dt}}={\gamma }_{1}E+{\gamma }_{2}I$
Li et al. (1999)	Investigated transmission of infection in people who directly contacted the host
Dukic et al. (2012)	Tracked the evolution of the infectious disease over time based on an epidemic model.
Lekone and Finkenstädt (n.d.)	Investigated the daily incidence and mortality time of Ebola virus based on SEIR model