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Bacterial diseases have historically accounted for a high burden of morbidity and mortality worldwide. While antibiotic therapy and immunisations have significantly improved clinical outcomes in the last couple of centuries, the rate at which new treatments and vaccines are being developed has slowed down. One way to accelerate innovation in the field is by understanding the host-bacteria interactions that take place in vivo and affect the clinical outcome of the disease, the response to treatment and the immunological response following vaccination. Mechanistic mathematical models are being increasingly used to advance our understanding about unobservable, host-pathogen interactions in vivo. These models allow us to develop hypotheses about the underlying biological mechanisms responsible for an observable and measurable outcome (e.g. the number of bacteria in a tissue of interest) and use them to try to match what has been experimentally or clinically observed. In this thesis, I have developed mechanistic models and used them in conjunction with experimental data on systemic murine Salmonella Typhimurium infections to: 1. characterise the effects of different vaccine preparations on the immune system of the host and its response to a secondary bacterial challenge, 2. compare the effects of different antibiotic classes on bacterial populations residing in different organs, and predict whether the residual bacteria following antibiotic treatment differ in their proliferative capacity, 3. develop a new, flexible methodological tool for a priori experimental design in studies of bacterial dynamics at the level of the population within the host.