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We apply a non-autonomous model with time-dependent mosquito birth, death and biting rates to integrate the impact of the periodicity of weather on the spread of Zika. We define the basic reproduction number<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathscr {R}}_{0}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:msub><mml:mi>R<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><\/mml:math><\/jats:alternatives><\/jats:inline-formula>as the spectral radius of a linear integral operator and show that the global dynamics is determined by this threshold parameter: If<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathscr {R}}_0 &lt; 1,$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mi>R<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><mml:mo>&lt;<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>then the disease-free periodic solution is globally asymptotically stable, while if<jats:inline-formula><jats:alternatives><jats:tex-math>$${\\mathscr {R}}_0 &gt; 1,$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:msub><mml:mi>R<\/mml:mi><mml:mn>0<\/mml:mn><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn>1<\/mml:mn><mml:mo>,<\/mml:mo><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>then the disease persists. We show numerical examples to study what kind of parameter changes might lead to a periodic recurrence of Zika.<\/jats:p>","DOI":"10.1007\/s11538-020-00844-6","type":"journal-article","created":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T07:08:45Z","timestamp":1613718525000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Threshold Dynamics in a Model for Zika Virus Disease with Seasonality"],"prefix":"10.1007","volume":"83","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0258-2019","authenticated-orcid":false,"given":"Mahmoud A.","family":"Ibrahim","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Attila","family":"D\u00e9nes","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,2,17]]},"reference":[{"issue":"11","key":"844_CR1","doi-asserted-by":"publisher","first-page":"e49085","DOI":"10.1371\/journal.pone.0049085","volume":"7","author":"M Andraud","year":"2012","unstructured":"Andraud M, Hens N, Marais C, Beutels P (2012) Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches. 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