A common conversation between an older adult and a nurse about health-related issues includes topics such as troubles with sleep, reasons for walking around nighttime, pain conditions, etc. Such a dialogue can be regarded as a "natural" dialogue emerging from the participating agents' lines of thinking, their roles, needs and motives, while switching between topics as the dialogue unfolds. The purpose of this work is to define a generic model of purposeful human-agent dialogue activity including different types of argumentation dialogues, suitable for health-related topics. This is done based on analyses of scenarios, personas and models of human behavior. The model will be shared between the human and the agent, allowing for adaptation to the human's reasoning, needs and motives.