Bulletin of Mathematical Biology

, Volume 80, Issue 8, pp 2049–2087 | Cite as

Transmission Dynamics of an SIS Model with Age Structure on Heterogeneous Networks

  • Shanshan Chen
  • Michael Small
  • Yizhou Tao
  • Xinchu Fu
Original Article


Infection age is often an important factor in epidemic dynamics. In order to realistically analyze the spreading mechanism and dynamical behavior of epidemic diseases, in this paper, a generalized disease transmission model of SIS type with age-dependent infection and birth and death on a heterogeneous network is discussed. The model allows the infection and recovery rates to vary and depend on the age of infection, the time since an individual becomes infected. We address uniform persistence and find that the model has the sharp threshold property, that is, for the basic reproduction number less than one, the disease-free equilibrium is globally asymptotically stable, while for the basic reproduction number is above one, a Lyapunov functional is used to show that the endemic equilibrium is globally stable. Finally, some numerical simulations are carried out to illustrate and complement the main results. The disease dynamics rely not only on the network structure, but also on an age-dependent factor (for some key functions concerned in the model).


Basic reproduction number Infection age Scale-free network Global stability 



This work was jointly supported by the NSFC Grants 11572181 and 11331009. SC was also supported with funding from ARC Linkage Grant LP130101055. Part of this work was done while SC, YT and XF visited the Center for Mathematical Sciences at Huazhong University of Science and Technology, Wuhan, China.


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanghai UniversityShanghaiChina
  2. 2.School of Mathematics and StatisticsUniversity of Western AustraliaCrawleyAustralia
  3. 3.Mineral ResourcesCSIROKensingtonAustralia

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