Mechanistic mathematical models are often employed to understand the dynamics of infectious diseases within a population or within a host. They provide estimates that may not be otherwise available. We have developed a within-host mathematical model in order to understand how the pathophysiology of Salmonella Typhi contributes to its incubation period. The model describes the process of infection from ingestion to the onset of clinical illness using a set of ordinary differential equations. The model was parametrized using estimated values from human and mouse experimental studies and the incubation period was estimated as 9.6 days. A sensitivity analysis was also conducted to identify the parameters that most affect the derived incubation period. The migration of bacteria to the caecal lymph node was observed as a major bottle neck for infection. The sensitivity analysis indicated the growth rate of bacteria in late phase systemic infection and the net population of bacteria in the colon as parameters that most influence the incubation period. We have shown in this study how mathematical models aid in the understanding of biological processes and can be used in estimating parameters of infectious diseases.