Dynamics of Zika Virus Epidemic in Random Environment

  • Yusuke Asai
  • Xiaoying HanEmail author
  • Peter E. Kloeden
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 200)


A mathematical model for Zika virus dynamics under randomly varying environmental conditions is developed, in which the birth and loss rates for mosquitoes, and environmental influence are modeled as random processes. The resulting system of random ordinary differential equations are studied by the theory of random dynamical systems and dynamical analysis. First the existence, uniqueness, positiveness and boundedness of solutions are discussed. Then the long term dynamics in terms of existence and geometric structures of random attractors and forward omega limit sets are investigated. Moreover, sufficient conditions under which the prevalence of Zika virus among human beings decreases monotonically to zero, as well as conditions under which an epidemic occurs are established.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Hygiene, Graduate School of MedicineHokkaido UniversitySapporoJapan
  2. 2.Department of Mathematics and Statistics221 Parker Hall Auburn UniversityAuburnUSA

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