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In multiple academic disciplines, having a perceived gender of `woman' is associated with a lower than expected rate of citations. In some fields, that disparity is driven primarily by the citations of men and is increasing over time despite increasing diversification of the profession. It is likely that complex social interactions and individual ideologies shape these disparities. Computational models of select factors that reproduce empirical observations can help us understand some of the minimal driving forces behind these complex phenomena and therefore aid in their mitigation. Here, we present a simple agent-based model of citation practices within academia, in which academics generate citations based on three factors: their estimate of the collaborative network of the field, how they sample that estimate, and how open they are to learning about their field from other academics. We show that increasing homophily -- or the tendency of people to interact with others more like themselves -- in these three domains is sufficient to reproduce observed biases in citation practices. We find that homophily in sampling an estimate of the field influences total citation rates, and openness to learning from new and unfamiliar authors influences the change in those citations over time. We next model a real-world intervention -- the citation diversity statement -- which has the potential to influence both of these parameters. We determine a parameterization of our model that matches the citation practices of academics who use the citation diversity statement. This parameterization paired with an openness to learning from many new authors can result in citation practices that are equitable and stable over time. Ultimately, our work underscores the importance of homophily in shaping citation practices and provides evidence that specific actions may mitigate biased citation practices in academia.