TY - JOUR
T1 - Bistability and Resurgent Epidemics in Reinfection Models
AU - Pagliara, Renato
AU - Dey, Biswadip
AU - Leonard, Naomi Ehrich
N1 - Publisher Copyright:
© 2018 IEEE.
Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 2018/4
Y1 - 2018/4
N2 - Spreading processes that propagate through local interactions have been studied in multiple fields (e.g., epidemiology, complex networks, social sciences) using the susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) frameworks. SIR assumes individuals acquire full immunity to the infection after recovery, while SIS assumes individuals acquire no immunity after recovery. However, in many spreading processes individuals may acquire only partial immunity to the infection or may become more susceptible to reinfection after recovery. We study a model for reinfection called Susceptible-Infected-Recovered-Infected (SIRI). The SIRI model generalizes the SIS and SIR models and allows for study of systems in which the susceptibility of agents changes irreversibly after first exposure to the infection. We show that when the rate of reinfection is higher than the rate of primary infection, the SIRI model exhibits bistability with a small difference in the initial fraction of infected individuals determining whether the infection dies out or spreads through the population. We find this critical value and show that when the infection does not die out there is a resurgent epidemic in which the number of infected individuals decays initially and remains at a low level for an arbitrarily long period of time before rapidly increasing toward an endemic equilibrium in which the fraction of infected individuals is non-zero.
AB - Spreading processes that propagate through local interactions have been studied in multiple fields (e.g., epidemiology, complex networks, social sciences) using the susceptible-infected-recovered (SIR) and susceptible-infected-susceptible (SIS) frameworks. SIR assumes individuals acquire full immunity to the infection after recovery, while SIS assumes individuals acquire no immunity after recovery. However, in many spreading processes individuals may acquire only partial immunity to the infection or may become more susceptible to reinfection after recovery. We study a model for reinfection called Susceptible-Infected-Recovered-Infected (SIRI). The SIRI model generalizes the SIS and SIR models and allows for study of systems in which the susceptibility of agents changes irreversibly after first exposure to the infection. We show that when the rate of reinfection is higher than the rate of primary infection, the SIRI model exhibits bistability with a small difference in the initial fraction of infected individuals determining whether the infection dies out or spreads through the population. We find this critical value and show that when the infection does not die out there is a resurgent epidemic in which the number of infected individuals decays initially and remains at a low level for an arbitrarily long period of time before rapidly increasing toward an endemic equilibrium in which the fraction of infected individuals is non-zero.
KW - Nonlinear systems
KW - compartmental systems
KW - contagion dynamics
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U2 - 10.1109/LCSYS.2018.2832063
DO - 10.1109/LCSYS.2018.2832063
M3 - Article
AN - SCOPUS:85057641694
VL - 2
SP - 290
EP - 295
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
SN - 2475-1456
IS - 2
ER -