How optimal allocation of limited testing capacity changes epidemic dynamics

Abstract

Insufficient testing capacity has been a critical bottleneck in the worldwide fight against COVID-19. Optimizing the deployment of limited testing resources has therefore emerged as a keystone problem in pandemic response planning. Here, we use a modified SEIR model to optimize testing strategies under a constraint of limited testing capacity. We define pre-symptomatic, asymptomatic, and symptomatic infected classes, and assume that positively tested individuals are immediately moved into quarantine. We further define two types of testing. Clinical testing focuses only on the symptomatic class. Non-clinical testing detects pre- and asymptomatic individuals from the general population, and a concentration parameter governs the degree to which such testing can be focused on high infection risk individuals. We then solve for the optimal mix of clinical and non-clinical testing as a function of both testing capacity and the concentration parameter. We find that purely clinical testing is optimal at very low testing capacities, supporting early guidance to ration tests for the sickest patients. Additionally, we find that a mix of clinical and non-clinical testing becomes optimal as testing capacity increases. At high but empirically observed testing capacities, a mix of clinical testing and non-clinical testing, even if extremely unfocused, becomes optimal. We further highlight the advantages of early implementation of testing programs, and of combining optimized testing with contact reduction interventions such as lockdowns, social distancing, and masking.

The relationship between controllability, optimal testing resource allocation, and incubation-latent period mismatch as revealed by COVID-19

“…Diseases with longer or shorter latent periods, stronger or weaker transmissibility, presymptomatic transmission or preinfectiousness symptom onset or correlated symptom-infectiousness onset, and exponential or gamma period distributions all call for qualitatively similar polices as a function of testing capacity; optimal protocols call for clinical-only testing at testing capacities below a threshold C th , and call for mixed clinical and non-clinical strategies at greater testing capacities. Interestingly, in a previous work (18) where we analyzed optimally reducing the epidemic peak height (rather than total infection size) using the ODE of our model here, we observed the same threshold behavior separating testing capacity regions between optimal clinical-only and mixed strategies. Thus, the threshold behavior appears to be a general feature of optimal allocation strategies under limited testing resources.…”

“…Here, there is no possibility of pre-symptomatic transmission or pre-infectious symptom onset, and the symptomatic population is the entire eventually symptomatic infectious class. This assumption is equivalent to the symptom assumptions of our previous ODE testing and quarantine COVID-19 model in (18). The incubation symptoms assumptions defines P e (x) and P y (x) to be the cumulative distribution function of an incubation period distribution f I (x).…”

“…We adapt the resource allocation testing and quarantine control framework from the ODE model of (18) for and actively seeking testing. Here, we provide the functional forms of test administration and processing rates for clinical and non-clinical testing and sketch the reasoning behind their formulation.…”

“…2.1.2 reduce the IPDE testing and quarantine model in Eq. ( 7) to the ODE testing and quarantine model in (18).…”

Modeling COVID-19 optimal testing strategies in long-term care facilities: An optimization-based approach

“…Of particular interest is the work of [46], where the authors developed an optimization-based compartmental model for planning, testing, and control. Similarly, [47] employed an SEIR model to study the optimal balance between spreading suppression and outbreak detection testing strategies under limited testing capacities. However, the solution framework of these studies is focused on country-wise strategies and not on particular organizations.…”