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\end{equation}
\end{equation}
We define $\lambda=\beta/\gamma$ as the effective infection rate of this model. From the above equation, we can find that when $\lambda>1$, the steady-state value of I is $i=(\beta-\gamma)/\beta=1-1/\lambda$, an endemic disease state is obtained in this case (indicates that there will be a number of infected individuals in the population at the final state). However, when $\lambda<1$, we have$i\to0(t\to\infty)$, which means that there will be no I state individuals in the population finally and is called a healthy state. Therefore, $\lambda=1$ is a threshold value of the SIS model, which is also known as the basic reproduction number <ref>Heffernan J M, Smith R J, Wahl L M. Perspectives on the basic reproductive ratio[J]. Journal of the Royal Society Interface, 2005, 2(4): 281-293.</ref>
We define $\lambda=\beta/\gamma$ as the effective infection rate of this model. From the above equation, we can find that when $\lambda>1$, the steady-state value of I is $i=(\beta-\gamma)/\beta=1-1/\lambda$, an endemic disease state is obtained in this case (indicates that there will be a number of infected individuals in the population at the final state). However, when $\lambda<1$, we have$i\to0(t\to\infty)$, which means that there will be no I state individuals in the population finally and is called a healthy state. Therefore, $\lambda=1$ is a threshold value of the SIS model, which is also known as the basic reproduction number.<ref>Heffernan J M, Smith R J, Wahl L M. Perspectives on the basic reproductive ratio[J]. Journal of the Royal Society Interface, 2005, 2(4): 281-293.</ref>
在这里，我们将$\lambda=\beta/\gamma$定义为该模型的有效感染率。 从上式可知，当$\lambda>1$时，I的稳态值为$i=(\beta-\gamma)/\beta=1-1/\lambda$，表明终态时人群中存在一定比例的受感染者，也就是说当$\lambda>1$时，整体人群处于地方性疾病状态。 但是，当$\lambda<1$时，我们有$i\to0(t\to\infty)$，这意味着最终人群中将没有I状态个体，整体人群被称为健康状态。 综上，$\lambda=1$是SIS模型的传播阈值，也称为基本再生数。
在这里，我们将$\lambda=\beta/\gamma$定义为该模型的有效感染率。 从上式可知，当$\lambda>1$时，I的稳态值为$i=(\beta-\gamma)/\beta=1-1/\lambda$，表明终态时人群中存在一定比例的受感染者，也就是说当$\lambda>1$时，整体人群处于地方性疾病状态。 但是，当$\lambda<1$时，我们有$i\to0(t\to\infty)$，这意味着最终人群中将没有I状态个体，整体人群被称为健康状态。 综上，$\lambda=1$是SIS模型的传播阈值，也称为基本再生数。