Locusts are significant agricultural pests. Under favorable environmental conditions flightless juveniles may aggregate into coherent, aligned swarms referred to as hopper bands. These bands are often observed as a propagating wave having a dense front with rapidly decreasing density in the wake. A tantalizing and common observation is that these fronts slow and steepen in the presence of green vegetation. This suggests the collective motion of the band is mediated by resource consumption. Our goal is to model and quantify this effect. We focus on the Australian plague locust, for which excellent field and experimental data is available. Exploiting the alignment of locusts in hopper bands, we concentrate solely on the density variation perpendicular to the front. We develop two models in tandem; an agent-based model that tracks the position of individuals and a partial differential equation model that describes locust density. In both these models, locust are either stationary (and feeding) or moving. Resources decrease with feeding. The rate at which locusts transition between moving and stationary (and vice versa) is enhanced (diminished) by resource abundance. This effect proves essential to the formation, shape, and speed of locust hopper bands in our models. From the biological literature we estimate ranges for the ten input parameters of our models. Sobol sensitivity analysis yields insight into how the band's collective characteristics vary with changes in the input parameters. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations. We thus demonstrate that resource-dependent behavior can explain the density distribution observed in locust hopper bands. This work suggests that feeding behaviors should be an intrinsic part of future modeling efforts.

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Purpose We examine the impacts of dosing strategies of plasmids on bacterial communities in the murine gut by measuring the quantity of plasmids in mouse feces. Methods We fed mice carrier bacteria, E. coli, that contain plasmids with both a reporter gene and an antibiotic resistant gene. We varied the quantity of the plasmid-carrying bacteria and the length of time the mice consumed the bacteria. We also pretreated the gut with broad-spectrum antibiotics and used continuous antibiotic treatment to investigate selection pressure. We collected bacteria from fecal pellets to quantify the number of plasmid-carrying bacteria via plate assay. Results Dosing regimens with plasmid-carrying bacteria resulted in a significantly increased duration of persistence of the plasmid within the gut when supplemented continuously with kanamycin during as well as after completion of bacterial dosing. The carrier bacteria concentration influenced the short-term abundance of carrier bacteria. Conclusion We evaluated the persistence of plasmid-carrying bacteria in the murine gut over time using varying dosage strategies. In future work, we will study how bacterial diversity in the gut impacts the degree of plasmid transfer and the prevalence of plasmid-carrying bacteria over time. Lay Summary Observing how plasmids persist within the gut can help us understand how newly introduced genes, including antibiotic resistance, are transmitted within the gut microbiome. In our experiments, mice were given bacteria containing a genetically engineered plasmid and were examined for the persistence of the plasmid in the gut. We found long-term persistence of the plasmid in the gut when administering antibiotics during and following dosing of the mice with bacteria carrying the plasmid. The use of higher concentrations of carrier bacteria influenced the short-term abundance of the plasmid-carrying bacteria in the gut. Description of Future Works Building on evidence from these initial studies that persistence of plasmids within the gut can be regulated by the dosage strategy, we will explore future studies and models of gene uptake in the context of spatial and taxonomic control and further determine if dosing strategies alter the compositional diversity of the gut microbiome. Graphical abstract

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We consider a system of coupled reaction-diffusion equations that models the interaction between multiple types of chemical species, particularly the interaction between one messenger RNA and different types of non-coding microRNAs in biological cells. We construct various modeling systems with different levels of complexity for the reaction, nonlinear diffusion, and coupled reaction and diffusion of the RNA interactions, respectively, with the most complex one being the full coupled reaction-diffusion equations. The simplest system consists of ordinary differential equations (ODE) modeling the chemical reaction. We present a derivation of this system using the chemical master equation and the mean-field approximation, and prove the existence, uniqueness, and linear stability of equilibrium solution of the ODE system. Next, we consider a single, nonlinear diffusion equation for one species that results from the slow diffusion of the others. Using variational techniques, we prove the existence and uniqueness of solution to a boundary-value problem of this nonlinear diffusion equation. Finally, we consider the full system of reaction-diffusion equations, both steady-state and time-dependent. We use the monotone method to construct iteratively upper and lower solutions and show that their respective limits are solutions to the reaction-diffusion system. For the time-dependent system of reaction-diffusion equations, we obtain the existence and uniqueness of global solutions. We also obtain some asymptotic properties of such solutions.