{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,15]],"date-time":"2026-10-15T06:08:53Z","timestamp":1792044533320,"version":"4.4.0"},"reference-count":27,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T00:00:00Z","timestamp":1770249600000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Education, Youth and Sports of the Czech Republic","award":["through the e-INFRA CZ (ID: 90254 to A.R.)"],"award-info":[{"award-number":["through the e-INFRA CZ (ID: 90254 to A.R.)"]}]},{"name":"European Union under the REFRESH","award":["CZ.10.03.01\/00\/22_003\/0000048"],"award-info":[{"award-number":["CZ.10.03.01\/00\/22_003\/0000048"]}]},{"name":"European Union under the REFRESH","award":["CZ.10.03.01\/00\/22_003\/0000048"],"award-info":[{"award-number":["CZ.10.03.01\/00\/22_003\/0000048"]}]},{"DOI":"10.13039\/501100004242","name":"Princess Nourah Bint Abdulrahman University","doi-asserted-by":"publisher","award":["PNURSP2025R895"],"award-info":[{"award-number":["PNURSP2025R895"]}],"id":[{"id":"10.13039\/501100004242","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"\n Rift Valley Fever (RVF) is a vector-borne, transmissible zoonotic disease in animals and humans caused by RVF virus and transmitted primarily by mosquitoes and biting flies. According to the World Health Organization (WHO), RVF outbreaks have great public health and economic impact, with up to 90% mortality in lambs and approximately 10% in adult sheep. Besides small ruminants, RVF affects cattle, camels, and goats and induces abortion storms and neonatal mortality at high rates, whereas humans develop severe febrile illness, hemorrhagic fever, or encephalitis in extreme cases. In this study, a deterministic epidemic model is developed and studied to investigate the RVF transmission dynamics under inclusion of delay differential equations and an entropy-based global stability approach to capture the time-dependent effect of disease progression. The model separates the ruminant population into susceptible, vaccinated, infected, and recovered, and the mosquito population into susceptible and infected. Positivity, and boundedness are demonstrated as basic dynamical properties. Two equilibria are found and compared: Rift Valley Fever\u2013Free Equilibrium (RVFFE) and Rift Valley Fever Endemic Equilibrium (RVFEE). The basic reproduction number (\n \n \n \n \n \n \n \n R<\/mml:mi>\n <\/mml:mrow>\n \n 0<\/mml:mn>\n <\/mml:mrow>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>\n ) is derived and local and entropy-based global stability are examined by the Routh\u2013Hurwitz criteria and LaSalle\u2019s invariance principle. Sensitivity analysis reveals the contribution of critical parameters on disease transmission and persistence. Numerical simulations performed using MATLAB\u2019s built-in DDE23 solver assist in revealing the effect of delay on infection dynamics and susceptibility with time. The implications provide tremendous insight into the role of temporal considerations and parameter uncertainty in the transmission dynamics of RVF and enable better understanding as well as potential control strategies for this emerging zoonotic disease.\n <\/jats:p>","DOI":"10.1371\/journal.pone.0341046","type":"journal-article","created":{"date-parts":[[2026,2,5]],"date-time":"2026-02-05T18:51:14Z","timestamp":1770317474000},"page":"e0341046","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":2,"title":["Entropy-based analysis of Rift Valley fever transmission dynamics using delay differential equations"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6443-9966","authenticated-orcid":true,"given":"Ali","family":"Raza","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mansoor","family":"Alsulami","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6349-8553","authenticated-orcid":true,"given":"Marek","family":"Lampart","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Umar","family":"Shafique","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eman Ghareeb","family":"Rezk","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2026,2,5]]},"reference":[{"issue":"1","key":"pone.0341046.ref001","doi-asserted-by":"crossref","first-page":"457","DOI":"10.1007\/s40808-022-01508-1","article-title":"Optimal control assessment of Rift Valley fever model with vaccination and environmental sanitation in the presence of treatment delay","volume":"9","author":"OD Falowo","year":"2022","journal-title":"Model Earth Syst Environ"},{"key":"pone.0341046.ref002","doi-asserted-by":"crossref","first-page":"1206089","DOI":"10.3389\/fcimb.2023.1206089","article-title":"Quantifying Rift Valley fever virus transmission efficiency in a lamb-mosquito-lamb model","volume":"13","author":"GM Bron","year":"2023","journal-title":"Front Cell Infect Microbiol"},{"issue":"1","key":"pone.0341046.ref003","doi-asserted-by":"crossref","first-page":"3904","DOI":"10.1038\/s41598-024-53774-x","article-title":"Ability of a dynamical climate sensitive disease model to reproduce historical Rift Valley Fever outbreaks over Africa","volume":"14","author":"A Chemison","year":"2024","journal-title":"Sci Rep"},{"key":"pone.0341046.ref004","doi-asserted-by":"crossref","first-page":"1049633","DOI":"10.3389\/fvets.2023.1049633","article-title":"Modeling the effectiveness of targeting Rift Valley fever virus vaccination using imperfect network information","volume":"10","author":"TA Sulaimon","year":"2023","journal-title":"Front Vet Sci"},{"issue":"1","key":"pone.0341046.ref005","doi-asserted-by":"crossref","first-page":"15342","DOI":"10.1038\/s41598-023-42596-y","article-title":"Ecological and subject-level drivers of interepidemic Rift Valley fever virus exposure in humans and livestock in Northern Kenya","volume":"13","author":"M Muturi","year":"2023","journal-title":"Sci Rep"},{"key":"pone.0341046.ref006","article-title":"Localized Rift Valley Fever Virus Persistence Depends on a High Transovarial Transmission Fraction","author":"MK Rostal","year":"2023","journal-title":"bioRxiv"},{"issue":"12","key":"pone.0341046.ref007","doi-asserted-by":"crossref","DOI":"10.1371\/journal.pone.0337556","article-title":"Computational analysis of stochastic delay dynamics in maize streak virus","volume":"20","author":"S Iqbal","year":"2025","journal-title":"PLoS One"},{"key":"pone.0341046.ref008","doi-asserted-by":"crossref","first-page":"100583","DOI":"10.1016\/j.onehlt.2023.100583","article-title":"Rift Valley fever in West Africa: A zoonotic disease with multiple socio-economic consequences","volume":"17","author":"B Tinto","year":"2023","journal-title":"One Health"},{"key":"pone.0341046.ref009","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.2217\/fvl-2023-0119","article-title":"Rosmarinic Acid Inhibits Rift Valley Fever Virus: In Vitro, Computational and Analytical Studies","volume":"18","author":"F Farouk","year":"2023","journal-title":"Future Virology"},{"issue":"6","key":"pone.0341046.ref010","doi-asserted-by":"crossref","first-page":"75","DOI":"10.33003\/fjs-2023-0706-2174","article-title":"Mathematical modeling of the spread of vector borne diseases with influence of vertical transmission and preventive strategies","volume":"7","author":"W Atokolo","year":"2024","journal-title":"FJS"},{"key":"pone.0341046.ref011","doi-asserted-by":"crossref","unstructured":"Chemison A, Defrance D, Ramstein G, Caminade C. Impact of global warming and Greenland ice sheet melting on malaria and Rift Valley fever. In: EGU General Assembly Conference Abstracts, 2023. 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Coupling an agent-based model with a mathematical model of Rift Valley fever for studying the impact of animal migrations on the Rift Valley fever transmission. 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