Winning the war against invasive species requires early detection of invasions. Compared to terrestrial invaders, aquatic species often thrive undetected under water and do not garner notice until too late for early action. However, fortunately for managers, apple snails (Family Ampullariidae, Genus Pomacea) provide their own conspicuous sign of invasion in the form of vibrantly colored egg clutches. Managers can potentially use egg clutches laid in the riparian zone as a means of early detection and species identification. To facilitate such efforts, we quantified differences in characteristics (length, width, depth, mass, egg number) of field-laid clutches for the two most common invasive species of apple snail, P. canaliculata and P. maculata, in native and non-native populations. Pomacea canaliculata native and non-native populations differed noticeably only in width. Native P. maculata clutches possessed significantly greater width, mass and eggs numbers compared with native P. canaliculata. Non-native P. maculata clutches significantly exceeded all other populations in all measured characteristics. Consequently, these traits may successfully distinguish between species. Fecundity data also allowed us to develop models that accurately estimated the number of eggs per clutch for each species based on clutch dimensions. We tested one, two and three dimensional models of clutches, including rendering a clutch as either a complete ellipsoid or an ellipsoid intersected by a cylinder to represent the oviposition site. Model comparisons found the product of length and depth, with a different function for each population, best predicted egg number for both species. Comparisons of egg number to clutch volume and mass implied non-native P. canaliculata may be food limited, while non-native P. maculata appeared to produce such enormous clutches by having access to greater nutrients than the native population. With these new tools, researchers and managers can quickly identify, quantify and begin eradication of new non-native apple snail populations.
Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), "cholera is a disease of inequityan ancient illness that today sickens and kills only the poorest and most vulnerable people.. . The map of cholera is essentially the same as a map of poverty." [27] We implement a published model [9] of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water, λ, or the "force of infection," is modeled by the Monod Equation in microbiology. We investigate the sensitivity of the models to some parameters. We use parameter values for cholera in Haiti that are consistent with the ranges in meta-analysis [9] and other sources. We show the results of our numerical approximation of solutions. Our goal is to use this system of nonlinear ordinary differential equations to raise awareness among the mathematics community of the dynamics of cholera. We discuss the enhancement of undergraduate experiences by motivating learning with a real-world context in social justice implications of global health. 1 Overview Cholera is a well-established waterborne disease that spreads through populations of people who are already overly burdened. Controlling cholera will require investment of monetary and human resources, issues beyond the scope of this paper. Here, we seek to understand and illustrate more about the disease through a mathematical model. We begin with an overview of the disease and of the outbreak in Haiti. We review the basic
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