A diffusion model for mosquito control trials with spillover

A diffusion model for mosquito control trials with spillover | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article A diffusion model for mosquito control trials with spillover Thomas Smith, Luzia N Felber, Neal A Alexander, Pélagie E.B. Aboa, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5423058/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Mar, 2026 Read the published version in Trials → Version 1 posted 5 You are reading this latest preprint version Abstract Background Mosquito movement is ubiquitous and complicates the design of cluster randomized trials (CRTs) of vector control interventions because it can cause spillover between trial arms. There has been no analytical approach to quantify the impact of this spillover on trial power, and a precautionary principle is generally used in trial design, leading to CRTs with very large clusters and extensive buffer zones between arms. Methods The diffusion equation was solved to give a mathematical model for mosquito displacement in a cluster randomized trial. This provides an explicit function for calculating the bias in efficacy estimates due to mosquito movement. Substituting this into a conventional formula for the power gives adjusted power estimates and indicates how the exclusion of data from buffer zones affects bias and power. The method is illustrated with the baseline data from an intervention trial against Aedes aegypti in Côte d’Ivoire. Results Despite the small size of the Côte d’Ivoire trial, it has adequate power to detect true intervention efficacy of ≥0.4, even in the presence of considerable spillover. If the spillover extends over a wide distance, the power will be considerably increased by using buffer zones. Conclusions The analytical approach can be incorporated into power calculations for CRTs with geographical spillover, whenever the diffusion model is considered an acceptable approximation. The example suggests that the key to obtaining adequate power in the presence of spillover is the inclusion of a sufficiently large number of clusters, even if only a small amount of data can be obtained from each cluster. The method can be implemented in a publicly available R package. Full Text Cite Share Download PDF Status: Published Journal Publication published 19 Mar, 2026 Read the published version in Trials → Version 1 posted Editorial decision: Minor revision 19 Dec, 2025 Reviewers agreed at journal 30 May, 2025 Reviewers invited by journal 05 Mar, 2025 Editor assigned by journal 18 Feb, 2025 First submitted to journal 09 Nov, 2024 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5423058","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":424603849,"identity":"c0f1af99-2f62-4f43-bcbf-0918307219fd","order_by":0,"name":"Thomas Smith","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+klEQVRIiWNgGAWjYBAC+xsQmoeB/wDDAcYGGwYGZh6wSAIuLWwSEFqOQSKB4cDBhjTitRgzgBgHGw6DbcSvRbr56IYffxgSGyS4Ew9/3HE+cTs778GPPxjs8nBqkTmWdrO3DaiF/+yGAwfP3E7c2cyXLM3DkFyM22E5Zjd4G/4nNjDkArW03U7ccJjHQJqB4QBQBLeWm3/+MNRDtZwDaTH++YOAlts8bAwwWw6AtJhJ8ODVkpZ2WxbolzYJoJazbcnGGw7zpVnzGCTj0ZJ87OYbYIj185/d/KGyzU52w/mzh2/+qLDDqQWhF5VrQEj9KBgFo2AUjAJ8AAA5WmHc0mkkKQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-3650-9381","institution":"Swiss Tropical \u0026 Public Health Institute \u0026 University of Basel","correspondingAuthor":true,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Smith","suffix":""},{"id":424603850,"identity":"9d90ea72-b56a-4532-b512-a9d40480baae","order_by":1,"name":"Luzia N Felber","email":"","orcid":"","institution":"Swiss Tropical and Public Health Institute: Schweizerisches Tropen- und Public Health-Institut","correspondingAuthor":false,"prefix":"","firstName":"Luzia","middleName":"N","lastName":"Felber","suffix":""},{"id":424603851,"identity":"f8f53525-e596-435d-8a0b-bfff1d4c6853","order_by":2,"name":"Neal A Alexander","email":"","orcid":"","institution":"London School of Hygiene \u0026 Tropical Medicine","correspondingAuthor":false,"prefix":"","firstName":"Neal","middleName":"A","lastName":"Alexander","suffix":""},{"id":424603852,"identity":"b700be8c-2715-4d95-9eed-0c047606e912","order_by":3,"name":"Pélagie E.B. 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