We consider a compartmental model adapted to the case of COVID-19 that takes into account the detection of ill individuals and the cost of medical treatment and investigate the effect of a budget constraint. Our analysis shows how the collapse of the budget can drastically change the outcome of an epidemics. We see how with a good testing policy the epidemic might be controllable. By introducing a lockdown period, we show that the final number of deaths can be reduced substantially and observe that a budget collapse introduces rather extreme effects. We find that there exists a well-defined optimal starting point for a lockdown. We also looked at the consequences of a loss of immunity and found that then a budget collapse can occur for smaller costs of medical treatment.

中文翻译：

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模拟类似 COVID-19 的流行病与经济之间的耦合

我们考虑了一种适用于 COVID-19 病例的分区模型，该模型考虑了对患病个体的检测和医疗费用，并研究了预算约束的影响。我们的分析显示了预算的崩溃如何极大地改变流行病的结果。我们看到，如果有良好的检测政策，疫情可能是可控的。通过引入锁定期，我们表明最终死亡人数可以大幅减少，并观察到预算崩溃会带来相当极端的影响。我们发现存在一个明确定义的最佳锁定起点。我们还研究了丧失免疫力的后果，发现如果医疗费用较低，可能会出现预算崩溃。