To study such a complex system, we propose the Micro-Agent model of individuals and the Stochastic Micro-Agent population model. They are defined in the Hybrid Systems framework. These models are general enough to describe biological, as well as, robotic agents. Using them, we develop a theory, which is based on the probability density function of the Micro-Agent state. This function connects the state of each Micro-Agent to the state of population within a probabilistic framework.

This work is motivated by the modeling of T-cell receptors down-regulation dynamics of the T-cell population mixed with antigen presenting cells. The work includes the numerical examples related to both this application and to the optimal control of a large-size robotic population.

There is evidence that prions form polymers or aggregates, most likely with additional stability. Some or all of these polymers attach to the similar naturally produced protein and convert it to the infectious variety. Polymers also split. Altogether, both the overall quantity of infectious proteins, and the number of polymer strands, increase. To model these phenomena, we represent prion polymer length as a continuous structure variable. We obtain a system of two partial differential equations modeling interaction of the infectious and non-infectious conformations of prion protein within an infected individual. We use this system to create numerical simulations of disease progress within such an individual. Under some circumstances, we can simplify to a system of three ordinary differential equations. In the ODE case, we discuss steady states, their stability, and relative parameter changes that affect their viability.