Forecasting the trend of COVID-19 under Imperfect Vaccination using the Homotopy Perturbation Method

Forecasting the trend of COVID-19 under Imperfect Vaccination using the Homotopy Perturbation Method | 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 Article Forecasting the trend of COVID-19 under Imperfect Vaccination using the Homotopy Perturbation Method Tawakalt Abosede Ayoola, Adedapo Ismaila Alaje, Hikmat Muhammad, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6564252/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Since its onset in late 2019, the COVID-19 pandemic, which was brought on by the new SARS-CoV-2 virus, has seriously upended economies, societies, and healthcare systems throughout the world. In order to control and comprehend the virus's quick spread, A new mathematical model is created, analysed and used to forecast the time growth of COVID-19 under the consequence of imperfect vaccination. The qualitative analysis involves establishing the model's positive invariant region and its solution. The model was confirmed to be linearly stable at the steady states of disease-free and endemic. Analysis of sensitivity, based on basic reproduction number, revealed that transmission, vaccination, and recruitment rates are key factors in COVID-19 spread, with vaccination reducing transmission by 74% and the transmission rate lowering it by 95%. Using the homotopy perturbation method, the model was semi-analytically solved, and results simulated with Maple software indicated a high probability of reducing the susceptible population to zero within a year of widespread vaccine coverage. However, waning immunity due to imperfect vaccination could reverse this trend within a year and a half, increasing susceptibility and decreasing recovery rates. Therefore, booster vaccines are crucial for sustaining immunity, controlling exposure, and managing long-term disease transmission. Health sciences/Diseases Physical sciences/Mathematics and computing COVID-19 transmission imperfect vaccination homotopy perturbation method sensitivity analysis SARS-CoV-2 Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted 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. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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-6564252","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":454583748,"identity":"84f1ce9c-2e46-4eb7-9cd3-69bd0f6427d7","order_by":0,"name":"Tawakalt Abosede 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In order to control and comprehend the virus's quick spread, A new mathematical model is created, analysed and used to forecast the time growth of COVID-19 under the consequence of imperfect vaccination. The qualitative analysis involves establishing the model's positive invariant region and its solution. The model was confirmed to be linearly stable at the steady states of disease-free and endemic. Analysis of sensitivity, based on basic reproduction number, revealed that transmission, vaccination, and recruitment rates are key factors in COVID-19 spread, with vaccination reducing transmission by 74% and the transmission rate lowering it by 95%. Using the homotopy perturbation method, the model was semi-analytically solved, and results simulated with Maple software indicated a high probability of reducing the susceptible population to zero within a year of widespread vaccine coverage. 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