Citation
Cameron Nowzari, Preciado Victor M., George Pappas. "Stability analysis of generalized epidemic models over directed networks". 53rd Conference on Decision and Control, IEEE, 15, December, 2014.

Abstract
In this paper we propose a generalized version of the Susceptible-Exposed-Infected-Vigilant (SEIV) disease spreading model over arbitrary directed graphs. In the standard SEIV model there is only one infectious state. Our model instead allows for the exposed state to also be infectious to healthy individuals. This model captures the fact that infected individuals may act differently when they are aware of their infection. For instance, an individual may be exposed to a disease and infectious, but not aware of the disease. On the other hand, when the individual is aware of the infection, different actions may be taken, such as staying home from work, causing less chance for spreading the infection. This model generalizes the standard SEIV model which is already known to generalize many other infection spreading models available. We use tools from nonlinear stability analysis to suggest a coordinate transformation that allows us to study the stability of the origin of a relevant linear system. We provide a necessary and sufficient condition for when the disease-free equilibrium is globally exponentially stable. We then extend the results to the case where the infection parameters are not homogeneous among the nodes of the network. Simulations illustrate our results.

Electronic downloads

• https://www.src.org/library/publication/p069676/. (Link to paper on SRC website.)
• http://dx.doi.org/10.1109/CDC.2014.7040360
• http://dx.doi.org/10.1109/CDC.2014.7040360

• HTML

  Cameron Nowzari, Preciado Victor M., George Pappas. <a
  href="http://www.terraswarm.org/pubs/288.html"
  >Stability analysis of generalized epidemic models over
  directed networks</a>, 53rd Conference on  Decision
  and Control, IEEE, 15, December, 2014.

• Plain text

  Cameron Nowzari, Preciado Victor M., George Pappas.
  "Stability analysis of generalized epidemic models over
  directed networks". 53rd Conference on  Decision and
  Control, IEEE, 15, December, 2014.

• BibTeX

  @inproceedings{NowzariVictorMPappas14_StabilityAnalysisOfGeneralizedEpidemicModelsOverDirected,
      author = {Cameron Nowzari and Preciado Victor M. and George
                Pappas},
      title = {Stability analysis of generalized epidemic models
                over directed networks},
      booktitle = {53rd Conference on  Decision and Control},
      organization = {IEEE},
      day = {15},
      month = {December},
      year = {2014},
      abstract = {In this paper we propose a generalized version of
                the Susceptible-Exposed-Infected-Vigilant (SEIV)
                disease spreading model over arbitrary directed
                graphs. In the standard SEIV model there is only
                one infectious state. Our model instead allows for
                the exposed state to also be infectious to healthy
                individuals. This model captures the fact that
                infected individuals may act differently when they
                are aware of their infection. For instance, an
                individual may be exposed to a disease and
                infectious, but not aware of the disease. On the
                other hand, when the individual is aware of the
                infection, different actions may be taken, such as
                staying home from work, causing less chance for
                spreading the infection. This model generalizes
                the standard SEIV model which is already known to
                generalize many other infection spreading models
                available. We use tools from nonlinear stability
                analysis to suggest a coordinate transformation
                that allows us to study the stability of the
                origin of a relevant linear system. We provide a
                necessary and sufficient condition for when the
                disease-free equilibrium is globally exponentially
                stable. We then extend the results to the case
                where the infection parameters are not homogeneous
                among the nodes of the network. Simulations
                illustrate our results. },
      URL = {http://terraswarm.org/pubs/288.html}
  }
  

Posted by Barb Hoversten on 21 Mar 2014.