Active Control and Sustained Oscillations in actSIS Epidemic Dynamics

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Abstract

An actively controlled Susceptible-Infected-Susceptible (actSIS) contagion model is presented for studying epidemic dynamics with continuous-time feedback control of infection rates. Our work is inspired by the observation that epidemics can be controlled through decentralized disease-control strategies such as quarantining, sheltering in place, social distancing, etc., where individuals can actively modify their contact rates in response to observations of the infection levels in the population. Accounting for a time lag in observations and categorizing individuals into distinct sub-populations based on their risk profiles, we show that the actSIS model manifests qualitatively different features as compared with the SIS model. In a homogeneous population of risk-averters, the endemic equilibrium is always reduced, although the transient infection level can overshoot or undershoot. In a homogeneous population of risk-tolerating individuals, the system exhibits bistability, which can also lead to reduced infection. For a heterogeneous population comprised of risk-tolerators and risk-averters, we prove conditions on model parameters for the existence of a Hopf bifurcation and sustained oscillations in the infected population.

Original languageEnglish (US)
Pages (from-to)807-812
Number of pages6
JournalIFAC-PapersOnLine
Volume53
Issue number5
DOIs
StatePublished - 2020
Event3rd IFAC Workshop on Cyber-Physical and Human Systems, CPHS 2020 - Beijing, China
Duration: Dec 3 2020Dec 5 2020

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering

Keywords

  • active feedback
  • contagion processes
  • decentralized control
  • epidemic models
  • heterogeneity
  • oscillation

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