Contribution to the Mathematical Modelling and Analysis of Cholera Transmission with the Phage Therapy Perspective.

Résumé

A bacteriophage or phage is a virus that infects bacteria. This infection can either purifies a bacterial polluted environment as well as human small intestine or triggers virulent pathogenic bacterial disease outbreaks such as cholera. The aim of this dissertation is to study the impact of phages–bacteria infection on the transmission dynamics of cholera and assess on the use of phages to control the spread of disease and for therapeutic purpose. To this end, (i) we formulate a predator–prey model to describe and study the phages–bacteria interaction by taking into account both lytic and lysogenic life cycles of phages. A threshold called basic offspring number is computed. We derive using this ecological threshold conditions under which phages purify a bacterial polluted environment and the situations that phages trigger virulent pathogenic bacterial diseases outbreak. (ii) The coupled models of cholera dynamics and phages–bacteria interaction are used to study the influence of phages and bacteria on the spatiotemporal transmission of cholera. The epidemiological threshold called basic reproduction number which is actually the average number of secondary human infections by infectious vibrio cholerae in their entire lifespan is computed. It is shown through these models that whenever the phages–bacteria interaction is considered, the classical condition which consists to drop the basic reproduction number under unity even though necessary is not sufficient to eliminate cholera. We derive an ecological threshold needed for possible elimination of the disease. Our results predict that efforts should be made to drop both epidemiological and ecological thresholds under unity in order to stop the spread of cholera. For the control strategies that should be used to reduce the number of infected human population, we first propose the release of selected lytic/virulent phages into contaminated environment in order to infect and eliminate the population of vibrio cholerae. The second strategy is the ingestion of these selected phages to purify a polluted human small intestine. The latter is known as phage therapy. Using phages for therapeutic purpose has many potential applications in human medicine as well as veterinary science and agriculture.

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