| Abstract: |
| In this study, we construct a time-delayed multi-group SIR epidemic model to consider the effect of behavior change. We derive the basic reproduction number ${\cal R}_0$ and show that the disease-free equilibrium is globally asymptotically stable if ${\cal R}_0 < 1$, whereas an endemic equilibrium exists if ${\cal R}_0 > 1$. For a special two-group case with urban and non-urban areas, we obtain sufficient conditions for a Hopf bifurcation which destabilizes the endemic equilibrium and causes a stable limit cycle. By performing the sensitivity analysis, we obtain biological insights that the size of ${\cal R}_0$ and the gap of populations, contact rates and sensitivity of behavior change between urban and non-urban areas can play important roles in the occurrence of the Hopf bifurcation. |
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