Date of Award
Master of Science
Dr. Xingfu Zou
More than one sub-type of HIVs have been identified. This raises an issue of co-infections by multiple strains of HIVs. In this thesis, we propose two mathematical models, one ignoring intracellular delay and the other incorporating the delay, to describe the interactions of the populations of CD4+cells and two HIV stains. By nature, the two strains compete for CD4+ cells to invade for their own replications. By analyzing the two models, we find that the models demonstrate threshold dynamics: if the overall basic reproduction number Ro < 1, then the infection free equilibrium is globally asymptotically stable; when R0 > 1, then the competition exclusion principle generically holds in the sense that, except for the critical case R\ = R2 > 1 where /?, is the individual basic reproduction number for strain i, all biologically meaningful solutions will converge to the single infection equilibrium representing the winning of the strain that has greater individual basic reproduction number. Numerical simulations are also performed to illustrate the theoretical results. The results on the model with delay also show that the basic reproduction number will be over calculated if the cellular delay is ignored.
Xu, Jin, "GLOBAL ANALYSIS OF CELL INFECTION AND VIRUS PRODUCTION ON HIV-1 DYNAMICS" (2011). Digitized Theses. 3384.