Dynamics of an SIS network model with a periodic infection rate

Lei Zhang, Maoxing Liu, Qiang Hou, Asma Azizi, Yun Kang

    Research output: Contribution to journalArticlepeer-review

    2 Scopus citations


    Seasonal forcing and contact patterns are two key features of many disease dynamics that generate periodic patterns. Both features have not been ascertained deeply in the previous works. In this work, we develop and analyze a non-autonomous degree-based mean field network model within a Susceptible-Infected-Susceptible (SIS) framework. We assume that the disease transmission rate being periodic to study synergistic impacts of the periodic transmission and the heterogeneity of the contact network on the infection threshold and dynamics for seasonal diseases. We demonstrate both analytically and numerically that (1) the disease free equilibrium point is globally asymptotically stable if the basic reproduction number is less than one; and (2) there exists a unique global periodic solution that both susceptible and infected individuals coexist if the basic reproduction number is larger than one. We apply our framework to Scale-free contact networks for the simulation. Our results show that heterogeneity in the contact networks plays an important role in accelerating disease spreading and increasing the amplitude of the periodic steady state solution. These results confirm the need to address factors that create periodic patterns and contact patterns in seasonal disease when making policies to control an outbreak.

    Original languageEnglish (US)
    Pages (from-to)907-918
    Number of pages12
    JournalApplied Mathematical Modelling
    StatePublished - Jan 2021


    • Amplitude of the infected population
    • Basic reproduction number
    • Degree-based mean field network model
    • Periodicity
    • Scale-free network
    • Seasonal forcing

    ASJC Scopus subject areas

    • Modeling and Simulation
    • Applied Mathematics


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