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Abstract This study investigates the nutrient-driven adaptability of foraging efforts in producer-grazer dynamics. We develop two stoichiometric producer-grazer models: a base model incorporating a fixed energetic cost of feeding and an adaptive model where feeding costs vary over time in response to environmental conditions. By comparing these models, we examine the effects of adaptive foraging strategies on population dynamics. Our adaptive model suggests a potential mechanism for evolutionary rescue, where the population dynamically adjusts to environmental changes, such as fluctuations in food quality, by modifying its feeding strategies. However, when population densities oscillate in predator-prey limit cycles, fast adaptation can lead to very wide amplitude cycles, where populations are in danger of stochastic extinction. Overall, this increases our understanding of the conditions under which nutrient-driven adaptive foraging strategies can yield benefits to grazers. 

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. 

Increasing temperatures have raised concerns over the potential effect on disease spread. Temperature is a well known factor affecting mosquito population dynamics and the development rate of the malaria parasite within the mosquito, and consequently, malaria transmission. A sinusoidal wave is commonly used to incorporate temperature effects in malaria models, however, we introduce a seasonal malaria framework that links data on temperature-dependent mosquito and parasite demographic traits to average monthly regional temperature data, without forcing a sinusoidal t to the data. We introduce a spline methodology that maps temperature-dependent mosquito traits to time-varying model parameters. The resulting non-autonomous system of differential equations is used to study the impact of seasonality on malaria transmission dynamics and burden in a high and low malaria transmission region in Malawi. We present numerical simulations illustrating how temperature shifts alter the entomological inoculation rate and the number of malaria infections in these regions. 

Death is a common outcome of infection, but most disease models do not track hosts after death. Instead, these hosts disappear into a void. This assumption lacks critical realism, because dead hosts can alter host–pathogen dynamics. Here, we develop a theoretical framework of carbon‐based models combining disease and ecosystem perspectives to investigate the consequences of feedbacks between living and dead hosts on disease dynamics and carbon cycling. Because autotrophs (i.e. plants and phytoplankton) are critical regulators of carbon cycling, we developed general model structures and parameter combinations to broadly reflect disease of autotrophic hosts across ecosystems. Analytical model solutions highlight the importance of disease–ecosystem coupling. For example, decomposition rates of dead hosts mediate pathogen spread, and carbon flux between live and dead biomass pools are sensitive to pathogen effects on host growth and death rates. Variation in dynamics arising from biologically realistic parameter combinations largely fell along a single gradient from slow to fast carbon turnover rates, and models predicted higher disease impacts in fast turnover systems (e.g. lakes and oceans) than slow turnover systems (e.g. boreal forests). Our results demonstrate that a unified framework, including the effects of pathogens on carbon cycling, provides novel hypotheses and insights at the nexus of disease and ecosystem ecology. 

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.