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In this paper, we propose a new epidemic model to investigate the effect of EV71 vaccination on the spread of HFMD with multiple pathogenic viruses in mainland China. In addition, suitable periodic transmission functions are designed, with a two-year period and taking into consideration the effects of opening and closing of schools. After defining the basic reproduction number <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><\/mml:mrow><\/mml:math>, we prove that the disease-free equilibrium is globally asymptotically stable if <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&lt;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:math>, and there exists at least one positive periodic solution and the disease is uniformly persistent if <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msub><mml:mrow><mml:mi>R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>0<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>&gt;<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:mrow><\/mml:math>. We use the model to simulate the HFMD reported data in mainland China from January 2008 to June 2019. The numerical experiments show that increasing the vaccinated rate can effectively control the spread of HFMD in mainland China, yet the disease does not become extinct. Moreover, if we can control the baseline contact rate of infectious individuals and the recovery rate of symptomatic infectious individuals under certain conditions, which can be achieved by improving protective measures and medical conditions, then the disease will be eliminated.<\/jats:p>","DOI":"10.1155\/2020\/8763126","type":"journal-article","created":{"date-parts":[[2020,1,9]],"date-time":"2020-01-09T18:31:54Z","timestamp":1578594714000},"page":"1-18","source":"Crossref","is-referenced-by-count":6,"title":["Modeling Periodic HFMD with the Effect of Vaccination in Mainland China"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8324-1333","authenticated-orcid":true,"given":"Lei","family":"Shi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"},{"name":"Department of Mathematics, Honghe University, Mengzi 661199, 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