Before revision:   We further show that it is the agents moving once between any two states  following the stochastic strategy  who are less likely to be infected than those not having (or not opting for) such a movement choice, when the risk of getting infected during the travel is not considered  .
After revision:  The objective for an agent is to stay in the lower infected state between their two choices. We further show that it is the agents moving once between any two states following the stochastic strategy who are less likely to be infected than those not having (or not opting for) such a movement choice, when the risk of getting infected during the travel is not considered .