## 3 Results  
The term \"medical resources\" in this paper refers to the number of hospital beds that can be used to treat severely infected individuals per unit time, which is denoted as \(M\). It was assumed that the recovery period of an emerging self-limiting infectious disease is relatively fixed for mildly and severely infected individuals and is not affected by medical resources. So, for the convenience of analysis, we let \(T_{I_{1}}=T_{H_{1}}=T_{1}\) and \(T_{I_{2}}=T_{H_{2}}=T_{2}\). Assuming that the mildly infected and hospitalized mildly infected individuals who were isolated could always be cured, then \(r_{I_{1}}=\frac{1}{T_{I_{1}}}\), \(r_{H_{1}}=\frac{1}{T_{H_{1}}}\) and \(d_{I_{1}}=d_{H_{1}}=0\). It was assumed that severely infected individuals outside of the hospital environment would die if they did not receive prompt treatment, so \(r_{I_{2}}=0\) and \(d_{I_{2}}=\frac{1}{T_{I_{2}}}\). The cure rate and mortality rate of hospitalized severely infected individuals who were  
Figure 1: Compartment model of infectious disease transmission considering the isolation of hospitalized mildly and severely infected individuals. isolated were satisfied by \(r_{H_{2}}=kd_{H_{2}}\), where \(k>0\) denotes the cure characteristics of infectious diseases under the condition of adequate medical resources. Different \(k\) values can be understood as different infectious diseases with the same recovery period. In what follows, we used model (1) to study the impacts of the isolation rates of hospitalized mildly and severely infected individuals on the emerging infectious diseases. Taking the parameters \(N=S_{0}+1,S_{0}=10^{7}\), \(T_{1}=15\), \(T_{2}=30,\beta=0.33,q=0.8,\alpha=0.25\) and \(k=5\), the evolution results of the population are presented in Figure 2a, where \(v_{1}=v_{2}=0.2\) and medical resources are sufficient (\(M=10^{7}\)). The evolution results of isolated mildly and severely infected individuals are shown in Figure 2b, where \(v_{1}=v_{2}=\{0.2,0.4,0.6\}\). It can be seen from Figure 2a that an exposed individual could cause an outbreak of an infectious disease in a short time. Nearly 80% of susceptible individuals would be infected when medical resources are adequate. After the system stabilizes, the ratio of recovered cases to deaths would be about 17:1. In Figure 2b, it can be seen that with the increase in isolation rate, the peak time of isolated mildly and severely individuals would be delayed and the peak would also decrease with the increase in isolation rate. This means that in the event of an emerging infectious disease pandemic, a rapid increase in isolation rates could reduce the number of infected individuals and thus, reduce the number of isolated individuals. When the peak time of isolated individuals is delayed, more time could be devoted to the replenishment of quarantined resources and medical resources. This also indicates that when developing prevention and control strategies for emerging infectious diseases, the isolation rate should be raised to a higher level; then, the total required quarantined and medical resources would be significantly reduced. When the number of hospitalized and isolated severely infected individuals is less than \(M\), the cure rate \(r_{H_{2}}\) would be determined by the recovery period of the self-limiting infectious disease. When the number of hospitalized and isolated severely infected individuals is greater than \(M\), the cure rate would decrease to \(r^{\prime}_{H_{2}}=r_{H_{2}}min\{1,\frac{M}{H_{2}(t)}\}\) and the mortality rate would be \(d^{\prime}_{H_{2}}=\frac{1}{T_{2}}-r^{\prime}_{H_{2}}\). The evolution results of the number of recovered cases and deaths when \(M\in\{10^{4},9.5\times 10^{5}\}\), under the above parameters, are shown in Figure 3.  
Figure 2: (**a**) Evolution results of the population when \(v_{1}=v_{2}=0.2\) and \(M=10^{7}\); (**b**) evolution results of isolated mildly and severely infected individuals when \(v_{1}=v_{2}=(0.2,0.4,0.6)\).