The aim of this course is to present some examples of stochastic models suitable for population dynamics.
The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems that can be modelled by PDMPs, explain how they can be simulated.
The second part will focus on random models for cell division when the whole branching population is taken into account. I'll present two data sets from biological experiments trying to determine whether cell division is symmetric or not. I'll explain how statistic tools can help answer this question.[-]

The aim of this course is to present some examples of stochastic models suitable for population dynamics.
The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems that can be modelled by PDMPs, explain how they can be simulated.
The second part will focus on random models for cell division when the whole branching population is taken into account. I'll present two data sets from biological experiments trying to determine whether cell division is symmetric or not. I'll explain how statistic tools can help answer this question.[-]

We are interested in monitoring patients in remission from cancer. Our aim is to detect their relapses as soon as possible, as well as detect the type of relapse, to decide on the appropriate treatment to be given. Available data are some marker level of the rate of cancerous cells in the blood which evolves continuously but is measured at discrete (large) intervals and through noise. The patient's state of health is modeled by a piecewise deterministic Markov process (PDMP). Several decisions must be taken from these incomplete observations: what treatment to give, and when to schedule the next medical visit. After presenting a suitable class of controlled PDMPs to model this situation, I will describe the corresponding stochastic control problem and will present the resolution strategy that we adopted. The objective is to obtain an approximation of the value function (optimal performance) as well as build an explicit policy applicable in practice and as close to optimality as possible. The results will be illustrated by simulations calibrated on a cohort of a clinical trial on multiple myeloma provided by the Center of Cancer Research in Toulouse.[-]

The aim of this course is to present some examples of stochastic models suitable for population dynamics.
The first part will introduce a class of continuous time models called piecewise deterministic Markov processes (PDMPs). Their trajectories are deterministic with jumps at random times. They are especially suitable to model phenomena with different time scales: a fast time-sacla corresponding to the deterministic behaviour and a slow time-scale corresponding to the jumps. I'll present different biological systems that can be modelled by PDMPs, explain how they can be simulated.
The second part will focus on random models for cell division when the whole branching population is taken into account. I'll present two data sets from biological experiments trying to determine whether cell division is symmetric or not. I'll explain how statistic tools can help answer this question.[-]