## 3 Results
As can be seen from Figure 3, the number of recovered cases would increase with the increase in medical resources and the number of deaths would decrease gradually. When the medical resources value is \(M\geq 6\times 10^{5}\), the number of recovered cases would reach its maximum and stabilize whereas the number of deaths would reach its minimum and stabilize. Further increases in medical resources would have no effect on the number of recovered cases or the number of deaths. This indicates that when medical resources are greater than \(6\times 10^{5}\), they would be sufficient for the treatment of patients. The numbers of recovered cases and deaths would be determined by the characteristics of each specific infectious disease. When the medical resources are less than \(6\times 10^{5}\), the reduction in medical resources would result in fewer recovered cases and more deaths. Due to overburdened medical resources, patients would not receive timely treatment. In this paper, the minimum amount of medical resources at which medical resources would not be overwhelmed is called \"safe medical resources\", which is denoted as \(M_{0}\). For self-limiting infectious diseases, the sum of the numbers of recovered cases and deaths is constant; so, the influence of the parameters \(k,v_{1},v_{2}\) and \(M\) on the number of deaths is considered below. First of all, we considered the case in which the isolation rates of hospitalized mildly and severely infected individuals were the same, i.e., \(v_{1}=v_{2}=v\). We let \(k=5\) and Figure 4 shows the evolution results of the number of deaths according to medical resources at the different isolation rates of hospitalized individuals and the evolution results of safe medical resources according to those isolation rates. Figure 4: With the fixed parameter \(k=5\): (**a**) evolution results of the number of deaths according to medical resources at the different isolation rates of hospitalized individuals; (**b**) evolution results of safe medical resources according to those isolation rates. Figure 3: (**a**) Evolution results of the recovered cases when the medical resources is \(M\in[10^{4},9.5\times 10^{5}]\). (**b**) Evolution results of the deaths when the medical resources is \(M\in[10^{4},9.5\times 10^{5}]\). In Figure 4a, the greater the isolation rates of hospitalized mildly and severely infected individuals, the fewer the deaths. When the isolation rate is fixed, the number of deaths would decrease gradually with the increase in medical resources and when the medical resources increase to a certain value, the number of deaths would remain unchanged. This is because when the medical resources are few, they would be overwhelmed and when the medical resources reach the safe value, the timely treatment of hospitalized and isolated individuals would be guaranteed, which would result in the number of deaths remaining unchanged. Interestingly, safe medical resources are non-monotonic in relation to the isolation rates of hospitalized individuals, as shown in Figure 4b. When the isolation rate of hospitalized individuals is less than 0.12, the safe medical resources would increase with the increase in isolation rate. However, when the isolation rate of hospitalized individuals is greater than 0.12, the safe medical resources would begin to decrease gradually. In other words, the fewer medical resources there are, the more necessary it would be to increase the isolation rate of hospitalized individuals so that medical resources would not be overwhelmed. Secondly, we considered the situation in which the isolation rate of hospitalized mildly infected individuals was not as same as the isolation rate of hospitalized severely infected individuals.