| Abstract: |
| Using the technique of edge-based compartmental modelling (EBCM) for the spread
of susceptible-infected-recovered (SIR) diseases in networks, in a recent paper (PloS One, 8(2013),
e69162), Miller and Volz established an SIR disease network model with heterogeneous infectiousness
and susceptibility. In this talk, Using the nature of irreducible cooperative system in the theory of monotonic dynamical system, we prove that the dynamics of the model are completely determined by a critical value p0: When p0 > 0, the disease persists in a globally stable outbreak equilibrium; while when p0 < 0, the disease dies out in
the population and the disease free equilibrium is globally stable. |
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