All living things are made up of cells. In the human body, there are many different types of cell, which come in all sizes and shapes, and their structures are also different based on the role they perform.
This talk has two parts. The first part deals with modelling a nerve cell. A nerve cell, or neuron, is a type of cell in the nervous system which controls all activities of the human body. It receives, processes and transmits information through electrical and chemical signals. In this talk, we study two models for the growth of neural cells, namely a discrete model and a continuous model. In the second part of the talk, we consider the interaction between cells in the immune system. In particular, we model a process known as phagocytosis, for which one cell type fully encloses and consumes unwanted cells, debris or particulate matter. Phagocytosis plays a significant role in the immune system through the destruction of pathogens and the inhibiting of cancerous cells. In this talk, we combine a model of cell-cell adhesion and predator-prey modelling to generate a new model for phagocytosis that is capable of relating the interaction between cells in both space and time. Numerical simulations are presented, demonstrating the behaviours of cells during the process of phagocytosis.