Journal of Biological Dynamics (Jan 2018)

An SIR pairwise epidemic model with infection age and demography

  • Wenjun Jing,
  • Zhen Jin,
  • Juping Zhang

DOI
https://doi.org/10.1080/17513758.2018.1475018
Journal volume & issue
Vol. 12, no. 1
pp. 486 – 508

Abstract

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The demography and infection age play an important role in the spread of slowly progressive diseases. To investigate their effects on the disease spreading, we propose a pairwise epidemic model with infection age and demography on dynamic networks. The basic reproduction number of this model is derived. It is proved that there is a disease-free equilibrium which is globally asymptotically stable if the basic reproduction number is less that unity. Besides, sensitivity analysis is performed and shows that increasing the variance in recovery time and decreasing the variance in infection time can effectively control the diseases. The complex interaction between the death rate and equilibrium prevalence suggests that it is imperative to correctly estimate the parameters of demography in order to assess the disease transmission dynamics accurately. Moreover, numerical simulations show that the endemic equilibrium is globally asymptotically stable.

Keywords