Existence of periodic solutions of a periodic SEIRS model with general incidence

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• 作者：Joaquim P. Mateus^a ; ^{jmateus@ipg.pt" class="auth_mail" title="E-mail the corresponding author} ; Cé ; sar M. Silva^b ; ^{csilva@mat.ubi.pt" class="auth_mail" title="E-mail the corresponding author} ;
• 关键词：Epidemic model ; Periodic ; Stability
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：34
• 期：Complete
• 页码：379-402
• 全文大小：891 K

文摘

For a family of periodic SEIRS models with general incidence, we prove the existence of at least one endemic periodic orbit when some condition related to class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630116X&_mathId=si2.gif&_user=111111111&_pii=S146812181630116X&_rdoc=1&_issn=14681218&md5=9365f9f25ed1ec365831ba31296a4f5d" title="Click to view the MathML source">R₀class="mathContainer hidden">class="mathCode"> holds. Additionally, we prove the existence of a unique disease-free periodic orbit, that is globally asymptotically stable when class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S146812181630116X&_mathId=si3.gif&_user=111111111&_pii=S146812181630116X&_rdoc=1&_issn=14681218&md5=528f0e01312611767b516b82acfc72eb" title="Click to view the MathML source">R₀<1class="mathContainer hidden">class="mathCode">. In particular, our main result generalizes the one in Zhang et al. (2012). We also discuss some examples where our results apply and show that, in some particular situations, we have a sharp threshold between existence and non existence of an endemic periodic orbit.