Fereshteh Nazari

(Department of Mathematics, University of Manitoba)

Backward Bifurcation In HCV Transmission Dynamics

Date Monday, June 16, 2014

Backward bifurcation, a dynamic phenomenon characterized by the co- existence of multiple stable attractors under certain conditions, has been observed in numerous disease transmission models. Its presence makes the e ective control of the disease being modelled dicult. This thesis is based on the use of mathematical modeling and dynamical systems analysis to establish, for the rst time, the pres- ence of backward bifurcation phenomenon in the transmission dynamics of hepatitis C virus (HCV) within an injection drug user population. Three new scenarios where such bifurcation can be removed have been identi ed. In particular, it is shown, using centre manifold theory and comparison theory, that the bifurcation can be re- moved if there is no di erential infectivity between re-infected and primary-infected individuals. The e ect of uncertainties in the estimates (and sensitivities) of the parameter values have been accounted for using appropriate statistical techniques, notably Latin Hypercube Sampling and Partial Rank Correlation Coecients. Nu- merical simulations of the model show that while the re-infection of recovered indi- viduals has marginal e ect on HVC dynamics, the treatment of chronically-infected IDUs (even at the current 4% rate) o ers signi cant population-wide bene t.