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Correspondingly, various control measures such as non-pharmaceutical interventions (NPIs) would be taken to alleviate the spreading of pathogens. In pandemic modeling, there is a general assumption that the effectiveness of NPIs is a fixed process and could be quantified as a constant value or a probability distribution. Recently, an increasing number of studies have recognized the phenomenon of NPIs\u2019 waning effect called NPI fatigue. However, the quantitative description of NPIs waning process is still lacking. In the paper, we propose a modified SEIR model called SVEIC-NLC to quantify the impact of NPI fatigue on pandemics. SVEIC-NLC borrows inspiration from Newton\u2019s law of cooling (NLC) to characterize the waning process of NPIs in reducing the transmission rates of pandemics. To the best of our knowledge, SVEIC-NLC is the first pandemic compartmental model to incorporate the concept of NPI fatigue explicitly. To validate the design of SVEIC-NLC, we conduct three case studies using COVID-19 in Germany, Greece, and the Philippines. The experimental results illustrate that the introduction of NLC process evidently improves the accuracy of the pandemic compartmental model SVEIC, displaying the validation of SVEIC-NLC. Further, SVEIC-NLC is also compared to six other cutting-edge methods for predicting daily confirmed cases across three US states, demonstrating superior predictive performance over these methods. In conclusion, the waning process of NPIs should be considered when an appropriate NPI measure is carried out. The proposed SVEIC-NLC model provides a novel and practical framework for understanding and managing pandemic dynamics under real-world conditions of NPI adherence fatigue.<\/jats:p>","DOI":"10.1007\/s41060-025-00748-5","type":"journal-article","created":{"date-parts":[[2025,3,30]],"date-time":"2025-03-30T23:37:55Z","timestamp":1743377875000},"page":"4723-4739","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Quantifying the waning effect of non-pharmaceutical interventions with case study in COVID-19"],"prefix":"10.1007","volume":"20","author":[{"given":"Hu","family":"Cao","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Longbing","family":"Cao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Shiqiang","family":"Jin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2025,3,28]]},"reference":[{"issue":"2","key":"748_CR1","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1093\/infdis\/125.2.161","volume":"125","author":"TM Mack","year":"1972","unstructured":"Mack, T.M.: Smallpox in Europe, 1950\u20131971. 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