The following work is a study on population dynamics and investigates the interplay between individuals heterogeneity and randomicity in natural systems. This thesis consists of two parts: the implementation of a theoretical framework to model the stochastic evolution of structured populations and, in the second part, a set of applications to real natural scenarios.

The initial chapter, Chapter 1, provides a historical introduction to population modelling, justifies the theoretical nature of this work and alleviates the theoretical burden of Chapter 2. In Chapter 2, a framework to quantify the stochastic evolution of age-structured populations is presented, and, at its core, it is founded on a functional Chapman-Kolmogorov Equation. The reader will also be provided (in Chapter 3) with the main Monte Carlo methods to simulate age-structured dynamics. In the first application, an age-structured division-death process is studied, Chapter 4. Such an application aims to quantify the fractional killing of cancer cells despite drug treatment. In periodic drug environments, we discover peaks, named ”survival resonance”, in the survival probabilities of cells for specific configurations, unseen in unstructured populations.

An additional approach on age-structured division-death models is taken in chapter 5 to investigate survival strategies exploited by bacterial or cancer cell to evade drug treatment. Modelling periodic treatments, we recovered the survival resonance and displayed additional extinction peaks. As a last application, a compartmental epidemic model is considered. The interplay between stochastic dynamics and age heterogeneity and its consequences on the dynamics are evident in this study, where a few methods are also presented to describe such scenarios. This chapter showcases the flexibility of the theoretical framework for a model not belonging to the class of branching processes.