考虑输入和接种的时滞新型冠状病毒传播模型的最优控制策略

Optimal Control Strategy of Delayed COVID-19 Propagation Model Considering Input and Inoculation

为了研究外部输入、疫苗接种和自我防护对新型冠状病毒传播的影响,建立了一个五维时滞新型冠状病毒传播模型,并考虑其最优控制问题。首先理论分析了最优控制的存在性,其次使用极值原理得到了最优控制的表达式,最后通过数值模拟发现:外部输入大大增加了疾病的传播风险;相比疫苗接种,自我防护受控制成本影响较小;控制力度越大,感染者数量越少,且最优控制效果最佳;自我防护控制效果优于疫苗接种控制效果。结果表明:外部输入对疾病的传播产生着重要影响;对于单一控制,自我防护相比疫苗接种更应被推广;对于综合控制,最优控制效果最好。该研究结果可为相关部门开展疫情常态化防控提供一定的理论参考。

In order to study the influence of external input,vaccination and self-protection on the transmission of COVID-19,a five dimensional delayed COVID-19 propagation model was established,and its optimal control problem was considered.Firstly,the existence of optimal control was theoretically analyzed.Secondly,the expression of optimal control was obtained using the extreme value principle.Finally,through numerical simulation,the following were found:External inputs greatly increase the risk of disease transmission;compared with vaccination,self-protection is less affected by the cost of control;the greater the control efforts,the fewer the number of infected individuals;the optimal control effect is the best,and the self-protection control effect is better than the vaccination control effect.The results indicate that external inputs have a significant impact on the spread of diseases;For single control,self-protection should be promoted more than vaccination;For comprehensive control,the optimal control effect is the best.The results of this study can provide a certain theoretical reference for relevant departments to carry out normalized epidemic prevention and control.