École Nationale Supérieure de
Techniques Avancées

Abstract

The aim of this study is to model the dynamics of a bacterium (Salmonella enterica Typhimurium) by using mathematical models in order to understand the immune response of the organism and create ecient vaccines. More precisely, we want to gure out how the bacteria spread and how many bacteria there are in the dierent organs of the organism. Many mathematical approaches have been already developed to model this phenomena. However, some approaches are very complex and can only be solved in some special cases. In addition, because of the diculty to collect data, it is important at least to know the mean and the variance to have an estimate of the number of bacteria in the organs. In fact, we will be interested in a moment-based approach which is less precise because we do not calculate exactly the number of bacteria in each organ but very informative and easier to solve.