Modeling Disease Impact of Vibrio-Phage Interactions

Since the work of John Snow, scientists and medical professionals have understood that individuals develop cholera by means of consuming contaminated water. Despite the knowledge of cholera\u27s route of infection, many countries have experienced and still experience endemic cholera. Cholera is caused by the Vibrio cholerae (V. cholerae) bacterium and presents with acute diarrhea and vomiting. If untreated, infected individuals may die due to dehydration. Cholera is a disease that most commonly affects countries with poor infrastructure and water sanitation. Despite efforts to control cholera in such countries, the disease persists. One such example is Haiti which has been experiencing a cholera outbreak since 2010. While there has been much research in the field of microbiology to understand V. cholerae, there has been comparably less research in the field of mathematical biology to understand the dynamics of V. cholerae in the environment. A mathematical model of V. cholerae incorporating a phage population is coupled with a SIRS disease model to examine the impact of vibrio and phage interaction. It is shown that there might exist two endemic equilibria, besides the disease free equilibrium: one in which phage persist in the environment and one in which the phage fail to persist. Existence and stability of these equilibria are established. Disease control strategies based on vibrio and phage interactions are discussed