Background Nucleic acid test (NAT) could effectively control the spread of COVID-19 caused by large-scale sports competitions. However, quantitative analysis on the appropriate frequency of NAT is scarce, and the cost-effectiveness and necessity of high-frequency NAT remain to be fully explored and validated. This study aims to optimize the COVID-19 surveillance strategies through cost-effectiveness analysis for the Tokyo 2020 Olympic Games and the upcoming Beijing 2022 Olympic Winter Games. Methods A total of 18 scenarios were designed regarding the NAT frequency, symptom monitoring, and strengthening close-contact control. An agent-based stochastic dynamic model was used to compare the cost-effectiveness of different NAT scenarios and optimize the surveillance strategies. The dynamics of the proposed model included the arrival and departure of agents, transmission of the disease according to Poisson processes, and quarantine of agents based on regular NATs and symptom onset. Accumulative infections, cost, and incremental cost-effectiveness ratio (ICER) were simulated in the frame of the model. ICER was used to compare the cost-effectiveness of different scenarios. Univariate sensitivity analysis was performed to test the robustness of the results. Results In Scenario 16, where the competition-related personnel (CRP) received NAT daily and national sports delegation (NSD) with quarantined infections accepted an additional NAT daily, accumulative infection was 320.90 (90 initial infections), the total cost was (United States Dollar) USD 8 920 000, and the cost of detecting out each infection was USD 27 800. Scenario 16 would reduce the total cost by USD 22 570 000 (avoid 569.61 infections), USD 1 420 000 (avoid 47.2 infections) compared with Scenario 10 (weekly NAT, strengthened close contact control) and Scenario 7 (daily NAT, no strengthened close contact control), respectively. Sensitivity analysis showed that the result was most sensitive to the change in basic reproductive number. Conclusions High-frequency NATs such as bidaily, daily, and twice a day were cost-effective. NAT daily for CRP with strengthening close-contact control could be prioritized in defense against COVID-19 at large-scale sports competitions. This study could assist policymakers by assessing the cost-effectiveness of NAT scenarios and provide the host country with an optimal COVID-19 surveillance strategy. Graphical Abstract

Ever since the pioneering human–environment interaction model of criminal behavior [M. B. Short, M. R. DOrsogna, V. B. Pasour, G. E. Tita, P. J. Brantingham, A. L. Bertozzi and L. B. Chayes, A statistical model of criminal behavior, Math. Models Methods Appl. Sci. 18 (2008) 1249–1267] was published, many mathematical agent-based residential burglary models have been proposed. In order to reach an improved balance among model accuracy, analysis simplicity and real-world data fitting tractability, we introduce in this paper a multi-scale hybrid interacting-particle-system model of criminal behavior in a discrete setting. We assume that agents’ actions are governed by independent Poisson clocks, while the environment variable evolves on a separate finer discrete spatial-temporal scale. Furthermore, as we refine the second scale to its scaling limit, the hybrid system converges to a piecewise deterministic Markov process (PDMP). Through a martingale approach and infinitesimal generator analysis, we provide a formal derivation for the convergence. Computer simulations of coupled hybrid and PDMP systems both exhibit spatio-temporal aggregates of crime and show excellent agreement between the two, which supports our theoretical derivation of the scaling limit. The methodology and results we develop here indicate a way to establish connections for the proposed crime models.