We study the spread of an SIRS-type epidemics with vaccination on network. Starting from an exact Markov description of the model  we investigate the mean epidemic lifetime by providing a sufficient condition for the fast extinction , depending on the topology of the network. Then, we pass to consider a first-order mean-field approximation of the exact model . At this point, we dwell on the stability propertiesof the system by relying on the graph-theoretical notion of equitable partition. In the case of graphs possessing this kind of partition, we find a positively invariant set which contain the endemic equilibrium , that can be computed by using a lower-dimensional dynamical system. Finally, in the special case of regular graphs, we show that when the recovery rate is higher than the vaccination rate, the aforementioned invariant set is contained in the domain of attraction of the endemic equilibrium.
We study the spread of an SIRS-type epidemic with vaccination on network. Starting from an exact Markov description of the model , we investigate the mean epidemic lifetime by providing a sufficient condition for fast extinction that depends on the model parameters and the topology of the network. Then, we pass to consider a firstorder mean-field approximation of the exact model and its stability properties, by relying on the graph-theoretical notion of equitable partition. In the case of graphs possessing this kind of partition, we prove that the endemic equilibrium can be computed by using a lower-dimensional dynamical system. Finally, in the special case of regular graphs, we investigate the domain of attraction of the endemic equilibrium.
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epidemics
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the fast extinction , depending on the
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first-order
firstorder
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. At this point, we dwell on the stability propertiesof the system
and its stability properties,
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find a positively invariant set which contain
prove that
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show that when the recovery rate is higher than the vaccination rate, the aforementioned invariant set is contained in
investigate