Analyzing Epidemic Contact Tracing with Queuing Theory

It is crucial to prevent escalation of an exponentially spreading epidemic early on. This can be done cost-effectively with contact tracing, which tries to find the unknown contagious people and make their health status common knowledge with testing. There is uncertainty regarding the epidemic situation and the success of tracing. The epidemic will escalate if contact tracing is staffed without taking the uncertainty into account, increasing costs needed to regain control over the situation. I propose using queuing theory to set the labour resources robustly for contact tracing with a suitable risk buffer. This is done by incorporating the Erlang's C queuing model into a macro-epidemiological framework with cautious heterogenous agents. The results are that following the queuing theory based resource allocation rule keeps the epidemic contained in most cases, reduces the total costs and supports a livelier economy, compared to an alternative rule where the uncertainty is not taken into account. I also answer how to use a given fixed resource efficiently, i.e. which scheduling policy to choose, and what happens when real world constraints prevent following the robust resource allocation rule?