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The division of labor (DOL) and task allocation among groups of ants living in a colony is thought to be highly efficient, and key to the robust survival of a colony. A great deal of experimental and theoretical work has been done toward gaining a clear understanding of the evolution of, and underlying mechanisms of these phenomena. Much of this research has utilized mathematical modeling. Here we continue this tradition by developing a mathematical model for a particular aspect of task allocation, known as age-related repertoire expansion, that has been observed in the minor workers of the ant species emph{Pheidole dentata}. In fact, we present a relatively broad mathematical modeling framework based on the dynamics of the frequency with which members of specific age groups carry out distinct tasks. We apply our modeling approach to a specific task allocation scenario, and compare our theoretical results with experimental data. It is observed that the model predicts perceived behavior, and provides a possible explanation for the aforementioned experimental results.
Some bacteria and archaea possess an immune system, based on the CRISPR-Cas mechanism, that confers adaptive immunity against phage. In such species, individual bacteria maintain a cassette of viral DNA elements called spacers as a memory of past inf
This paper describes a mathematical model for the spread of a virus through an isolated population of a given size. The model uses three, color-coded components, called molecules (red for infected and still contagious; green for infected, but no long
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Disease transmission is studied through disciplines like epidemiology, applied mathematics, and statistics. Mathematical simulation models for transmission have implications in solving public and personal health challenges. The SIR model uses a compa
Probabilistic modeling is fundamental to the statistical analysis of complex data. In addition to forming a coherent description of the data-generating process, probabilistic models enable parameter inference about given data sets. This procedure is