口罩配戴與社區規模對 COVID-19 持續流行隨機滅絕機率的影響

Abstract

背景與研究動機: COVID-19全球大流行造成超過7百萬例確診染疫死亡及對社會與經濟造成巨大衝擊。隨著疫情從大流行階段過渡到持續流行狀態，每月確診數及死亡數相較以往下降，但控制疫情難度依然存在。儘管疫苗接種在2021年初在減少感染方面發揮關鍵作用，但隨著Delta及Omicron等具強大免疫逃脫特性變異株出現，造成大量突破性感染，疫苗已不再能夠有效預防病毒傳播，目前僅剩預防重症效果。許多先前防疫措施，例如接觸者追蹤及隔離等現已不再適用，在此背景下，口罩配戴作為一種重要的非藥物防護措施，顯得尤為重要。本研究旨在模擬口罩配戴對COVID-19持續流行時代傳播動態指標―社區傳播閾值（Critical community size）―的影響，以了解口罩配戴在持續流行階段疫情控制中在群體層次的效果。通過這些模擬和分析，本研究希望為公共衛生政策的制定提供科學依據，幫助社區和政府在面對COVID-19及未來可能出現的傳染病時能夠更有效地應對和控制疫情，最終保護公共健康和安全。這項研究的重要性不僅在於應對當前的疫情挑戰，還在於為未來的公共衛生危機提供可行的策略和措施。

方法: 在本研究中，我們採用了多種方法來探討口罩配戴對COVID-19流行動態的影響。基於SEIR模型進行了COVID-19的隨機模擬，並考慮了自然免疫的衰退效應，這使得我們的模型更接近現實情況。為了引入隨機效應，我們使用了Process Noise Approach，這樣可以模擬更多現實中的隨機波動。對於疾病滅絕的定義，我們設定為連續兩周無新病例報告，這是一個標準的公共衛生指標，用於衡量疫情控制的有效性。在模型模擬部分，我們首先以麻疹模擬作為標竿。這一部分利用麻疹SIR隨機模型與觀察性研究對Critical community size計算的結果進行比對，檢測三種噪音項變異數的設置，為後續的COVID-19模擬的噪音項的變異數設置提供了一個基準。COVID-19的模擬包括大流行時代和持續流行時代的流行動態模擬。大流行時代的結果用於驗證模型，檢驗噪音項的變異數設置。在持續流行時代的模擬中，我們考慮了不同的口罩配戴比例以評估其對疫情控制及流行動態的影響，特別是其對病毒傳播速率和疾病滅絕機率的影響。

結果: 麻疹模擬結果得到噪音變項變異數為感染人數兩倍的負二項式分布的設定最符合觀察到的麻疹Critical community size（300,000-500,000人）。關於COVID-19大流行時代前期的模擬，在包含口罩配戴、採檢隔離、接觸追蹤、邊境管控的組合式防疫措施下，COVID-19 的Critical community size計算出來大於23,000,000人，社區中疫情不會爆發，與台灣2020-2021年間在大部分時間成功達到每天零確診的實際情況一致；而當模擬開放邊境使境外移入感染人數暴增60倍時，Critical community size也降到23,000,000人之下，顯示不再能維持零確診，與台灣2022年3月開始開放邊境導致疫情全面大爆發的實際情況一致，模型的模擬很好的對應到台灣在大流行時代的流行動態情況，顯示模型設定與噪音項變異數設置符合外部驗證。在持續流行時代的模擬中，發現口罩配戴確實可以降低感染發生率，無論是在大或小人口規模的社區都是如此，並且隨著口罩配戴比例上升及人口規模下降，開始有疾病滅絕的現象發生。進一步分析發現，無口罩配戴的情況下，病毒傳播速度較快，感染人數持續增加，導致疾病滅絕幾乎不可能發生，Critical community size低於10,000人。然而，隨著口罩配戴比例的增加，Critical community size顯著增大。在75%口罩配戴比例下，病毒傳播得到有效控制，感染人數顯著減少。而在90%口罩配戴比例下，疫情得到更強有力的遏制，Critical community size進一步增大，顯示出高比例口罩配戴在控制疫情中的重要性，依據不同的移入感染數口罩配戴可將Critical community size增大到大致為 35,000 到160,000人。此外，我們還研究了境外移入感染數對Critical community size的影響。結果顯示，高境外移入感染數會顯著增加疫情的傳播風險，使得Critical community size變小。

結論: 在COVID-19持續流行時代，高比例口罩配戴可顯著降低COVID -19感染發生率，增加疫情滅絕機率，並擴大Critical community size，使人口規模在閾值以下的社區能夠達到無疫情狀態。

Background

The global COVID-19 pandemic has resulted in over 7 million confirmed deaths and has caused immense social and economic disruption. As the pandemic transitions from an acute phase to a sustained endemic state, the monthly number of confirmed cases and deaths has decreased compared to previous periods, yet the challenge of controlling the epidemic remains. Although vaccination played a critical role in reducing infections in early 2021, the emergence of variants such as Delta and Omicron, which have strong immune escape characteristics, has led to numerous breakthrough infections. Vaccines are no longer effective in preventing virus transmission and now primarily help in preventing severe illness. Many previous preventive measures, such as contact tracing and quarantine, are no longer applicable. In this context, mask-wearing has become an especially important non-pharmaceutical protective measure. This study aims to simulate the impact of mask-wearing on the transmission dynamics of COVID-19 during the endemic phase, focusing on the Critical Community Size (CCS) as an indicator. By understanding the specific role and effectiveness of mask-wearing in controlling the epidemic during the endemic phase, this research seeks to provide a scientific basis for public health policy formulation. It aims to help communities and governments respond to and control COVID-19 and future infectious diseases more effectively, ultimately protecting public health and safety. The importance of this study lies not only in addressing current pandemic challenges but also in providing feasible strategies and measures for future public health crises.

Method

In this study, we employed various methods to explore the impact of mask-wearing on the dynamics of COVID-19 transmission. We conducted stochastic simulations of COVID-19 based on the SEIR model and considered the effect of natural immunity waning, making our model more realistic. To introduce stochastic effects, we used the Process Noise Approach, which allows for the simulation of more real-world random fluctuations. We defined the ‘extinction’ of the disease as having no new cases reported for two consecutive weeks, a standard public health indicator for measuring the effectiveness of epidemic control. In the model simulation section, we first used measles simulations as a benchmark. This part utilized the measles SIR stochastic model to compare the results of CCS calculations with observational studies, testing three noise variance settings to provide a benchmark for the subsequent noise variance settings in the COVID-19 simulations. The COVID-19 simulations included the epidemic dynamics during the pandemic and endemic phases. The results from the pandemic phase were used to validate the model and test the noise variance settings. In the endemic phase simulations, we considered different mask-wearing ratios to evaluate their impact on epidemic control and dynamics, particularly their effect on virus transmission rates and the probability of disease extinction.

Result

The results of the measles simulation found that setting the noise variance to twice the number of infections, following a negative binomial distribution, best matched the observed Critical Community Size (CCS) for measles (300,000-500,000 people). Regarding the early phase of the COVID-19 pandemic simulation, under the combined preventive measures of mask-wearing, testing and isolation, contact tracing, and border control, the calculated CCS for COVID-19 was greater than 23,000,000 people. This indicates that the epidemic would not outbreak in the community, consistent with Taiwan's success in achieving zero daily cases for most of 2020-2021. However, when the simulation modeled an open border scenario leading to a 60-fold increase in imported infections, the CCS dropped below 23,000,000 people, indicating that zero cases could no longer be maintained. This aligns with Taiwan's actual situation in March 2022, when opening the borders led to a widespread outbreak. The simulation model accurately corresponded to Taiwan's epidemic dynamics during the pandemic era, showing that the model settings and noise variance configuration were externally validated. In the simulations of the endemic phase, it was found that mask-wearing significantly reduced infection rates, regardless of the community size. As mask-wearing ratios increased and population sizes decreased, instances of disease extinction began to occur. Further analysis revealed that without mask-wearing, the virus spread rapidly, the number of infections continued to rise, and disease extinction was nearly impossible, with the CCS falling below 10,000 people. However, as the mask-wearing ratio increased, the CCS significantly enlarged. With a 75% mask-wearing ratio, virus transmission was effectively controlled, and the number of infections markedly decreased. At a 90% mask-wearing ratio, the epidemic was more robustly contained, and the CCS further increased, demonstrating the importance of high mask-wearing ratios in controlling the epidemic. Depending on the number of imported infections, mask-wearing could increase the CCS to approximately between 35,000 and 160,000 people. Additionally, we analyzed the impact of the number of imported infections on the CCS. The results showed that a high number of imported infections significantly increased the risk of epidemic spread, thereby reducing the CCS.

Conclusion

High surgical mask-wearing rate significantly reduced the incidence rate of COVID-19 during the endemic stage, increased the likelihood of disease extinction, and expanded the CCS, allowing more communities to achieve a state of disease extinction.