Invasion of Infectious Diseases in Finite Homogeneous Populations

We consider the initial invasion of an infectious disease in a finite, homogeneous population. Methodology for evaluating the basic reproduction number, R(0), and the probability mass function of secondary infections is presented. The impact of finite population size, and infectious period distribution (between exponential, two-phase gamma, and constant), is assessed. Implications for infectious disease invasion and estimation of infectious disease model and parameters from data of secondary infections by initially infected individuals in naive, finite, homogeneous populations are reported. As any individual interacts with a finite number of contacts during their infectious period, these results are important to the study of infectious disease dynamics.