be able to meet any other agent no matter what $u_i$ it chooses. Mathematically, the chance for agent $i$ and agent $j$ to meet each other depends on the minimum of the activity levels of these two agents, i.e., $\min\{u_i, u_j\}$. In the extreme cases, if agent $i$ decides to meet everyone in the system by choosing $u_i = 1$, then the chance for agent $j$ to meet with agent $i$ is $u_j$. If agent $i$ decides to not meet anyone in the system by choosing $u_i = 0$, then the chance for agent $j$ to meet with agent $i$ is $0$.

Before we derive the system dynamic model, the assumptions are listed below:

1.  In the agent model, we only consider two states: healthy (susceptible) and infected. All healthy agents are susceptible to the disease. There is no recovery and no death for infected agents. There is no incubation period for infected agents, i.e., once infected, the agent can start to infect other healthy agents. To relax this assumption, we may introduce more states for every agent.

2.  The interactions among agents are assumed to be uniform, although it is not true in the real world. In the real 