This paper discovers an emerging area of application of the advanced Multivalued Logic (MVL), – a collaboration between humans and autonomous machines in the first responder teams (firefighters, search-and-rescue operators, disaster response personnel, and military special operations forces). We developed an approach to formalization of the collaboration protocols (also known as contagion protocols) that model the human-machine teaming in emergency missions. MVL techniques satisfy the requirements of encoding the states of stress and trust, and their propagation between the teammates. Advanced MVL techniques are also useful for other applications, such as modeling the contagion of infection, or the spread of rumors, ideas, panic, and fear.