The issue of trust is a primary concern for individuals in distributed collaborative environments (DCEs), particularly in emergencies such as the COVID-19 pandemic. In these environments, collaboration and access to services are achieved through collaborative activities, so collaborators must have a certain level of trust to participate in and achieve the goals of these activities. Most of the trust models proposed for DCEs do not consider collaboration as a factor influencing trust, so they do not help users determine who to trust, what level of trust to assign, and why trust is important during collaborative activities. In this work, we propose a new trust model for DCEs that considers collaboration as an influencing factor in evaluating users' trust levels according to the goals they want to achieve during a collaborative activity. One of the strengths of our proposed model is that it also assesses the trust of a collaborative teams. Our model relies on three trust components-recommendation, reputation, and collaboration-to assess trust relationships, and we dynamically assign weights to each trust component using the weighted moving average and ordered weighted averaging combination algorithm to increase flexibility. The healthcare case prototype we developed demonstrates that our trust model is an effective approach for reinforcing trustworthiness in DCEs.