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Article
Global Properties of a Two-Scale Network Stochastic Delayed Human Epidemic Dynamic Model
Nonlinear Analysis: Real World Applications (2012)
  • Divine Wanduku, University of South Florida
  • G. S. Ladde, University of South Florida
Abstract
Complex population structure and the large-scale inter-patch connection human transportation underlie the recent rapid spread of infectious diseases of humans. Furthermore, the fluctuations in the endemicity of the diseases within patch dwelling populations are closely related with the hereditary features of the infectious agent. We present an SIR delayed stochastic dynamic epidemic process in a two-scale dynamic structured population. The disease confers temporary natural or infection-acquired immunity to recovered individuals. The time delay accounts for the time-lag during which naturally immune individuals become susceptible. We investigate the stochastic asymptotic stability of the disease free equilibrium of the scale structured mobile population, under environmental fluctuations and the impact on the emergence, propagation and resurgence of the disease. The presented results are demonstrated by numerical simulation results.
Keywords
  • Disease-free steady state,
  • Stochastic asymptotic stability,
  • Threshold value,
  • Positively invariant set,
  • Lyapunov functional
Disciplines
Publication Date
April, 2012
DOI
10.1016/j.nonrwa.2011.08.017
Citation Information
Divine Wanduku and G. S. Ladde. "Global Properties of a Two-Scale Network Stochastic Delayed Human Epidemic Dynamic Model" Nonlinear Analysis: Real World Applications Vol. 13 Iss. 2 (2012) p. 794 - 816
Available at: http://works.bepress.com/divine-wanduku/3/