This dissertation explores a range of topics related to veterinary medicine, food safety, and infectious disease dynamics. This includes assessing veterinarians' perceptions of antibiotic prescription and usage in dairy farming, revealing concerns about the misuse of antibiotics by both veterinarians and farmers. It suggests the need for improved education and communication regarding proper antibiotic use, especially in the treatment of common ailments such as mastitis and calf diarrhea. The study highlights the ethical dilemmas veterinarians face when dealing with client expectations. Additionally, the dissertation examines COVID-19 mitigation strategies in the US food industry, identifying challenges in labor force management, training, and the implementation of safety measures. The research highlights the importance of clear and adaptable guidelines for disease prevention, as well as the potential for mechanization to sustain production during pandemics. Furthermore, it included the assessment of the dynamics of Highly Pathogenic Avian Influenza (HPAI) transmission between waterfowl and backyard poultry via mathematical modeling. The study emphasizes the role of migratory stopover durations in predicting HPAI outbreaks and provides insights for improving future efforts to predict its introduction to backyard poultry farms. Finally, the dissertation included the mathematical modeling of the transmission dynamics of Salmonella Dublin in heifer raising operations (HROs). Findings indicate the efficacy of vaccination and improved cleaning in reducing both epidemiological and economic impacts of the pathogen. This dissertation explores key challenges at the intersection of animal and public health, focusing on infectious disease transmission, antibiotic usage practices, resistance development, and approaches to disease prediction and control. By combining epidemiological, statistical, and modeling techniques, the research highlights determinants shaping antibiotic prescription practices among dairy veterinarians and farmers, provides insights into controlling disease introduction and spread, and evaluates the effectiveness of interventions for managing infections.