Stochastic models of cell population dynamics and tick-borne virus transmission

When modelling cellular population dynamics, many mathematical models consider exponential inter-event times. Despite being the most convenient choice from a mathematical and computational perspective, the exponential distribution overestimates the probability of short division times. In Chapter 3, I consider a multi-stage model of the cell cycle to maintain the advantages of a Markovian model, while improving on exponential times to division. With this structure in place, cell generations are introduced in the model to link theoretical predictions with experimental data. The model with cell generations is parameterised making use of CFSE data and Bayesian methods. Then, in order to study fate correlation of cellular siblings, in Chapter 4, I pro- pose a mathematical model that makes use of the theory of branching processes. Cells are categorised based on their fate, either division or death, which is decided at birth. The applicability of this approach is shown by considering a data set of stimulated B cells produced with time-lapse microscopy. The last chapter of this thesis aims to shed light on the role of co-feeding and co-transmission in the spread of a vector-borne virus. Thus, a population of ticks interacts with a population of hosts (small or large vertebrates). First, I consider a single infection whose dynamics is modelled through both deterministic and stochastic models. The basic reproduction number is computed by means of the next generation matrix approach. When modelling co-infection with two different viruses (or two strains of the same virus), a deterministic model is proposed to study only co-feeding transmission, accounting also for co-transmission of the virus. A series of stochastic descriptors of interest are computed when considering all the routes of transmission.