are $M$ agents in the environment. Initially, $m_0$ agents are infected. Agents are indexed from $1$ to $M$. Every agent has its own state and control input. The model is in discrete time. The time interval is set to be one day. The evolution of the infection rate for consecutive days depends on agents’ actions. The questions of interest are: How many agents will eventually be infected? How fast they will be infected? How can we slow down the growth of the infection rate?

Agent Model
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We consider two state values for an agent, e.g., for agent $i$, $x_i = 0$ means healthy (susceptible), $x_i = 1$ means infected. Everyday, every agent $i$ decides its level of activities $u_i\in[0,1]$. The level of activities for agent $i$ can be understood as the expected percentage of other agents in the system that agent $i$ wants to meet. For example, $u_i = 1/M$ means agent $i$ expects to meet one other agent. The actual number of agents that agent $i$ meets depends not only on agent $i$’s activity level, but also on other agents’ activity level. For example, if all other agents choose an activity level $0$, then agent $i$ will not 