Periodic solution of the DS-I-A epidemic model with stochastic perturbations | Zendy

Songnan Liu | Zendy; Xiaojie Xu | Zendy

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Periodic solution of the DS-I-A epidemic model with stochastic perturbations

Author(s) -

Songnan Liu,

Xiaojie Xu

Publication year - 2019

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1908219l

Subject(s) - mathematics , epidemic model , lyapunov function , stochastic modelling , statistical physics , mathematical economics , statistics , demography , nonlinear system , population , physics , quantum mechanics , sociology

The paper introduces DS-I-A model with periodical coefficients. First of all, we show that there is a unique positive solution of the stochastic model. Furthermore we deduce the conditions under which the disease will end and continue. At last, we draw a conclusion that there exists nontrivial positive periodic solution for the stochastic system by stochastic Lyapunov functions. Simulations are also carried out to confirm our analytical results.

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