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Navigating a career as a mathematician in academia, industry, or a national lab was challenging for many families with children before the COVID-19 pandemic. Then, the pandemic hit and the situation was exacerbated. Parents and parents-to-be were tested and challenged in ways unanticipated, with time for parental duties clashing with time for research, teaching, and service, leaving those wishing to be parents contemplating the feasibility of this balancing act of parenthood and work-life in a COVID-19 era and beyond. Many members in our mathematics community experienced these challenges first hand and persevered. Lessons were learned and different methodologies employed as many reimagined what work-life and home-life balance looked like. These lessons and methodologies can be useful in our future endeavors as parent-educators and researchers, and if shared can benefit others who are in parenthood or on the path to parenthood, as they seek to create a better harmony between work and home life. Thus, this article explores and showcases some of the discussions that ensued during a 2022 Joint Mathematics Meeting (JMM) Professional Development Workshop Mathematicians Navigating Parenthood organized by the authors. The article collects key discussion points and lessons learned, putting together useful solutions and resources, as well as unresolved questions. We report on strategies to help parents and parents-to-be succeed as well as present proposals on what departments could implement based on their individual policies to provide a welcoming environment to colleagues with, or expecting, children. 

In this paper, we compare the performance between systems of ordinary and (Caputo) fractional differential equations depicting the susceptible-exposed-infectious-recovered (SEIR) models of diseases. In order to understand the origins of both approaches as mean-field approximations of integer and fractional stochastic processes, we introduce the fractional differential equations (FDEs) as approximations of some type of fractional nonlinear birth and death processes. Then, we examine validity of the two approaches against empirical courses of epidemics; we fit both of them to case counts of three measles epidemics that occurred during the pre-vaccination era in three different locations. While ordinary differential equations (ODEs) are commonly used to model epidemics, FDEs are more flexible in fitting empirical data and theoretically offer improved model predictions. The question arises whether, in practice, the benefits of using FDEs over ODEs outweigh the added computational complexities. While important differences in transient dynamics were observed, the FDE only outperformed the ODE in one of out three data sets. In general, FDE modeling approaches may be worth it in situations with large refined data sets and good numerical algorithms.