Infectious disease risk depends on both individual risk factors as well as the infectious state of the population, including current cases and immunity to disease from past exposure. For zoonotic diseases, this risk also includes the infectious state of the animal hosts. This is further complicated in diseases where there is an environmental disease reservoir, since external risk factors, such as extreme climatic events (e.g., flooding), can influence transmission risk and the timing and intensity of outbreaks. Furthermore, risk is influenced by behaviour of individuals and public health control measures. Infectious disease models can be used to simplify complex disease systems and help improve our understanding of transmission dynamics and population risk, as well as explore drivers of transmission.An example of a complex disease system is leptospirosis, a neglected zoonotic disease. It is found in all regions of the world, but globally disease burden is highest in the Pacific region. The transmission of leptospirosis is complex, with human infection occurring either as a result of direct contact with infected animals (e.g., rodents and domestic animals), or indirectly via water or soil contaminated with urine of infected animals. As such, many different risk factors can shape the transmission dynamics. Leptospirosis is endemic in many Pacific island countries.For example, Fiji has regular outbreaks, and the frequency and intensity of outbreaks has been increasing in recent years. In this thesis, to explore the transmission of leptospirosis in Fiji, I used two different datasets: surveillance data from 2006-2017, and data from a large cross-sectional seroprevalence survey conducted in 2013.Outbreaks of leptospirosis are often associated with heavy rainfall and flooding events. The climate in Fiji is also highly affected by El Niño-Southern Oscillation, which is a global climate phenomenon arising from changes in sea surface temperatures in the central and eastern tropical Pacific Ocean. However, the exact role of climate in driving outbreaks of leptospirosis has not been well quantified, particularly in the South Pacific. Therefore, using a Bayesian hierarchical mixed effects statistical modelling framework, I quantified the effects of different hydrometeorological indicators on leptospirosis incidence in Fiji, exploring these over both spatial and temporal scales. I found that total rainfall over six weeks, periods of negative sea surface temperature (i.e. La Niña events) and minimum temperature were all positively associated with leptospirosis cases. These results are an essential first step towards the development of a climate-based early warning system. In addition, I used the cross-sectional seroprevalence study to estimate the duration of anti-body persistence to leptospirosis. This has important epidemiological and clinical implications since it can provide insights into the frequency of reinfections and the level of under-reporting, as well as allow for improved interpretation of serosurveys for leptospirosis. Using a reverse catalytic model, I estimated the duration of antibody persistence to be around 7-8 years. Furthermore, using additional data on antibody kinetics, I estimated the most likely timing of infection. I found that most individuals who were seropositive in the 2013 serosurvey were likely to have been infected within the previous two years, which is consistent with surveillance data.This approach allows for richer, longitudinal information to be inferred from cross-sectional studies.Given the disruption to the project from COVID-19 in 2020-21, and the accompanying importance of understanding coronavirus dynamics in 2020-21, I applied similar serocatalytic modelling methods to look at seasonal coronaviruses (CoV); my second disease case study. Seasonal human coronaviruses (HCoVs) have very different transmission patterns from leptospires, with human-human transmission being the primary transmission route. Using seroprevalence data from six studies covering four different circulating season HCoVs, I extended the reverse catalytic model to allow for a different force of infection (the rate at which susceptible individuals acquire infection and seroconvert) by age. The duration of antibody persistence was estimated to last around 1-4 years. This finding has clinical and epidemiological significance but was largely unknown for SARS-CoV-2 at the beginning of the pandemic. Since seasonal HCoVs have been circulating for longer than SARS-CoV-2, they may offer insights into the reinfection patterns of this group of viruses.Finally, I explored how compartmental mechanistic models could be used to bring together climatic drivers and immunity dynamics within one disease framework, providing a more holistic understanding of transmission dynamics. I was particularly interested in diseases such as leptospirosis, which are zoonotic but also have an environmentally-persistent pathogen. Therefore, I systematically reviewed studies detailing models for a suite of environmentally persistent zoonotic diseases (20 diseases in total) and I identified model structures and methodologies that had previously been used. My review highlighted the need for more data-driven modelling of these diseases and for more models to include a holistic One Health approach which considers the human-animal-environment interface of transmission to inform disease prevention and control strategies.Collectively, in this thesis, I show how a range of different data and methods can be used to enhance our understanding of infectious disease dynamics using mathematical and statistical modelling. I used a variety of methods specifically adapted to the setting and disease in question to provide insights into drivers and dynamics of transmission.