To isolate or not to isolate: the impact of changing behavior on COVID-19 transmission

Abstract

Background: The COVID-19 pandemic has caused more than 25 million cases and 800 thousand deaths worldwide to date. In early days of the pandemic, neither vaccines nor therapeutic drugs were available for this novel coronavirus. All measures to prevent the spread of COVID-19 are thus based on reducing contact between infected and susceptible individuals. Most of these measures such as quarantine and self-isolation require voluntary compliance by the population. However, humans may act in their (perceived) self-interest only.

Methods: We construct a mathematical model of COVID-19 transmission with quarantine and hospitalization coupled with a dynamic game model of adaptive human behavior. Susceptible and infected individuals adopt various behavioral strategies based on perceived prevalence and burden of the disease and sensitivity to isolation measures, and they evolve their strategies using a social learning algorithm (imitation dynamics).

Results: This results in complex interplay between the epidemiological model, which affects success of different strategies, and the game-theoretic behavioral model, which in turn affects the spread of the disease. We found that the second wave of the pandemic, which has been observed in the US, can be attributed to rational behavior of susceptible individuals, and that multiple waves of the pandemic are possible if the rate of social learning of infected individuals is sufficiently high.

Conclusions: To reduce the burden of the disease on the society, it is necessary to incentivize such altruistic behavior by infected individuals as voluntary self-isolation.

Keywords: COVID-19; Game theory; Human behavior; Imitation dynamics; Isolation and quarantine; Perception of risk.

Fig. 1

Flow diagram of the COVID-19 model (6)

Fig. 2

Fitting the baseline COVID-19 model parameters (6) to Arizona data of reported cumulative new cases. The COVID-19 outbreaks data are obtained from Johns Hopkins website [1]

Fig. 3

Contour plot of the COVID-19 reproduction number ${\mathcal{R}}_0$ given in Eq. 2. a Varying quarantine rate ω_Q and hospitalization rate ω_H. b Varying quarantine rate ω_Q and infection rate β

Fig. 4

Contour plot of the COVID-19 reproduction number ${\mathcal{R}}_0$ given in Eq. (2). a Varying quarantine violation rate ν_Q and hospital discharge rate ν_H. b Varying infection rate β and quarantine violation rate ν_Q

Fig. 5

Simulation of the baseline COVID-19 model (6) for the proportions of symptomatically infected (I), quarantined (Q), and hospitalized (H) individuals. Solid lines correspond to base values of the model parameters from Table 2. a Dashed lines correspond to double quarantine (ω_Q=2×0.5326) and hospitalization (ω_H=2×0.7495) rates b Dashed lines correspond to double quarantine violation (ν_Q=2×0.4586) and hospital discharge (ν_H=2×0.0126) rates

Fig. 6

Simulations of the COVID-19 model with dynamic human behavior (16) with various initial proportions x_S(0) of the susceptibles in support of lock-down. The social learning rate of susceptible individuals is κ_S=1. a The progression of the proportion of symptomatically infected individuals I(t). b The progression of the proportion of the susceptible population in support of the closure or lock-down measures. The measures are enacted as long as t≥t_close and x_S(t)≥0.5

Fig. 7

Simulations of the COVID-19 model with dynamic human behavior (16) with various initial proportions x_I(0) of symptomatically infected individuals willing to self-isolate. The social learning rate of infected individuals is κ_I=100, and the sensitivity to self-isolation is ε_I=0.00008. a The progression of the proportion of symptomatically infected individuals I(t). b The progression of the proportion of symptomatically infected population willing to self-isolate

Fig. 8

Simulations of the COVID-19 model with dynamic human behavior (16) for the proportions of all symptomatic infections and behavioral response with low sensitivity to self-isolation ε_I=0.00001. The social learning rates are κ_S=1 and κ_I=100, and x_S(0)=x_I(0)=0.15. Solid lines correspond to the values of the baseline model parameters given in Table 2. a–b Dashed lines correspond to double quarantine (ω_Q) and hospitalization (ω_H) rates c–d Dashed lines correspond to double quarantine violation (ν_Q) and hospital discharge (ν_H) rates

Fig. 9

Simulations of the COVID-19 model with dynamic human behavior (16) showing multiple waves of epidemic while varying susceptible (κ_S) and symptomatic (κ_I) individual social learning rates with low sensitivity to self-isolation ε_I=0.00001. Solid lines correspond to κ_I=20, dashed lines correspond to κ_I=650. a Proportion of symptomatic infections I(t) with one big and two smaller waves (solid lines), κ_S=10. b Proportion of susceptible (x_S) and symptomatic (x_I) individuals adopting positive behavior, κ_S=10. c Proportion of symptomatic infections I(t) with two big and one small wave (solid lines), κ_S=30. d Proportion of susceptible (x_S) and symptomatic (x_I) individuals adopting positive behavior, κ_S=30

Fig. 10

Simulations of the COVID-19 model with dynamic human behavior (16) showing epidemic oscillations with high self-isolation social learning rate. Solid lines correspond to κ_I=650, dashed lines correspond to κ_I=1350; fixed values κ_S=5 and ε_I=0.00001. a Oscillating proportion of symptomatic infections I(t). b Proportion of susceptible (x_S) and symptomatic (x_I) individuals adopting positive behavior

Fig. 11

Simulations of the COVID-19 model with dynamic human behavior (16) showing the damping effect of increased quarantine (ω_Q) and hospitalization (ω_H) rates. Solid lines correspond to base values of ω_Q and ω_H, dashed lines correspond to a 5-fold increase in these values; fixed values κ_S=5, κ_I=1350, and ε_I=0.00001. a Proportion of symptomatic infections I(t). b Proportion of susceptible (x_S) and symptomatic (x_I) individuals adopting positive behavior

Fig. 12

Simulations of the COVID-19 model with dynamic human behavior (16) showing the devastating effect of increased quarantine violation (ν_Q) and hospital discharge (ν_H) rates. Solid lines correspond to base values of ν_Q and ν_H, dashed lines correspond to an 8-fold increase in these values; fixed values κ_S=5, κ_I=650, and ε_I=0.00001. a Proportion of symptomatic infections I(t). b Proportion of susceptible (x_S) and symptomatic (x_I) individuals adopting positive behavior

Fig. 13

Contour plot of the COVID-19 reproduction number ${\mathcal{R}}_0$ given in Eq. (2). a Varying hospitalization rate ω_H and infection rate β. b Varying quarantine rate ω_Q and hospitalization rate ω_H using infection rate β=0.22

Fig. 14

Contour plot of the COVID-19 reproduction number ${\mathcal{R}}_0$ given in Eq. (2). a Varying quarantine violation rate ν_Q and infection rate β. b Varying quarantine violation rate ν_Q and hospital discharge rate ν_H using infection rate β=0.22

Fig. 15

Simulations of the COVID-19 model with dynamic human behavior (16) for the proportions of all symptomatic infections and behavioral response with high sensitivity to self-isolation ε_I=0.00008. The social learning rates are κ_S=1 and κ_I=100, and x_S(0)=x_I(0)=0.15. Solid lines correspond to the values of the baseline model parameters given in Table 2. a–b Dashed lines correspond to double quarantine (ω_Q) and hospitalization (ω_H) rates c–d Dashed lines correspond to double quarantine violation (ν_Q) and hospital discharge (ν_H) rates

Fig. 16

Simulations of the COVID-19 model with dynamic human behavior (16) for the proportions of all symptomatic infections and behavioral response with high sensitivity to self-isolation ε_I=0.00008. Solid lines correspond to κ_I=20, dashed lines correspond to κ_I=650. a–b κ_S=10; c–d κ_S=30