Non-Markovian models of cell cycle and immune status

We will begin by presenting a fairly general structured model, in which individuals are described by a variable that changes over time according to some process (deterministic or stochastic) until a critical moment occurs (for example: death or reproduction) at time T. T is a random variable whose distribution depends on the initial state of the individual. Once the critical moment has passed, the state of the model modifies according to some law that depends on the state at the critical moment. Such a general model has many applications. We will present a more detailed application to a model of the cell cycle and briefly a certain immunological model. One of the main issues considered will be to show how such a model can be describe by semigroup operators and how to study its asymptotic behaviour.

References

1. K. Pichór, R.R., Cell cycle length and long-time behaviour of an age-size model, Math. Methods Appl. Sci. 2022.

2. K. Pichór, R.R., Asymptotic properties of a general model of immune status, SIAM (in press).