1: immediate isolation of infected agents.

    The activity levels of infected agents immediately drop to $u^*$, while others remain $u$. The scenario for $u = 1/M$ and $u^* = 0.1/M$ is illustrated in \[fig:open\_loop\]. Immediate isolation significantly slows down the growth of the infections rate. As expected, it has the best performance in terms of flattening the curve, same as the lockdown case. The trajectory also has a $S$ shape.

-   Case 2: delayed isolation of infected agents.

    The activity levels of infected agents drop to $u^*$ after $T$ days, while others remain $u$. In the simulation, $u = 1/M$ and $u^* = 0.1/M$. The scenarios for $T=1$ and $T=2$ are illustrated in \[fig:open\_loop\]. As expected, the longer the delay, the faster the infection rate grows, though the growth of the infection rate is still slower than the “no intervention" case. Moreover, the peak growth rate (when $50\%$ agents are infected) is higher when the delay is longer.

-   Case 3: lockdown.

    The activity levels of all agents drop to $u^*$. The scenario for $u^* = 0.1/M$ is illustrated in \[fig:open\_loop\]. As expected, it has the best performance in terms of flattening the curve, same as the immediate isolation case.

