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We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (Willing or Unwilling/Unable), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies the existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles. 

With evidence mounting on the benefits of equity-minded and active mathematics instruction, increasing numbers of mathematics faculty members are seeking to transform their instruction. Yet, many lack the skills and/or confidence to make the transition. To support faculty in meaningful instructional improvement, the authors of this paper facilitate frequent and innovative professional development (PD) guided by a community of practice framework. PD is intentionally designed to be incremental and supportive. Using one-on-one interview data from ten faculty participants who participated in PD on equity-minded and active mathematics instruction, we report on three crucial characteristics of a community of practice: the domain, the community, and the practice. Findings have implications for mathematics departments that aspire to support instructors to transform their teaching. Incremental PD guided by a community of practice framework could support faculty through the challenges of instructional transformation.