We model insect colony propagation or survival from nature using differential equations. We ask you to analyze and report on what is going on and develop an optimal strategy for success of a natural phenomena.
Your responses are to contain traditional elements of good reporting, complete statement of the problem - copied from the problem or reformulated in your own words, your analysis and results, and discussion of issues relevant to the analyses and results.
In considering the life cycle of colonies of insects it is believed that the colony appears to maximize the number of reproducer insects at the end of its season. This enables the colony to spread its genes and thus propagate its own kind in an optimal fashion. But how does the colony do this? One could consider different models for hibernating (e.g., wasp) and non-hibernating (e.g., honey bees) insects. The non-hibernating case is more complex due to the need to build up substantial resources and hives to survive the winter.
We consider an energy model for the colony in which we discuss two kinds of insects in the colony, workers and reproducers (or queens).