Adaptive Susceptibility and Heterogeneity in Contagion Models on Networks

Renato Pagliara, Naomi Ehrich Leonard

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Contagious processes, such as spread of infectious diseases, social behaviors, or computer viruses, affect biological, social, and technological systems. Epidemic models for large populations and finite populations on networks have been used to understand and control both transient and steady-state behaviors. Typically it is assumed that after recovery from an infection, every agent will either return to its original susceptible state or acquire full immunity to reinfection. We study the network SIRI (Susceptible-Infected-Recovered-Infected) model, an epidemic model for the spread of contagious processes on a network of heterogeneous agents that can adapt their susceptibility to reinfection. The model generalizes existing models to accommodate realistic conditions in which agents acquire partial or compromised immunity after first exposure to an infection. We prove necessary and sufficient conditions on model parameters and network structure that distinguish four dynamic regimes: infection-free, epidemic, endemic, and bistable. For the bistable regime, which is not accounted for in traditional models, we show how there can be a rapid resurgent epidemic after what looks like convergence to an infection-free population. We use the model and its predictive capability to show how control strategies can be designed to mitigate problematic contagious behaviors.

Original languageEnglish (US)
Article number9057446
Pages (from-to)581-594
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2021

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


  • Adaptive systems, complex networks
  • multiagent systems
  • propagation of infection
  • spreading dynamics


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