This thesis is devoted to the mathematical modeling of infectious diseases and public health giving particular attention to the study of the infection by the human papillomavirus (HPV). We propose several mathematical models to understand and explain health behavior and to guide the identification, development, and implementation of disease prevention programs. The majority of the mathematical models constructed in this work are based on ordinary differential equations describing the average dynamics underlying the infectious disease under study. The mathematical tools that we have used to analyze such models include global stability analysis of equilibria via Lyapunov’s direct method, numerical bifurcation analysis, global sensitivity analysis using the method of Sobol, and optimal control theory. The mathematical models proposed here cover two of the dominant sub-disciplinary fields that address the study of infectious diseases: (i) modeling of between-host dynamics of infectious disease transmission and (ii) modeling within-host dynamics of infectious diseases, that is, modeling pathogen-immune interactions. Between-host models have been widely used to aid public health officers to make optimal decisions about disease control. Within-host models commonly study the interactions of the pathogen and the host defense mechanisms throughout an infection. The main goal of this work is to use mathematical modeling to better understand the causes of a disease, the complexity in the disease transmission mechanism and to evaluate and optimatize various detection, prevention, and vaccination programs aiming to control the spread of the infection