Title page for ETD etd-05112016-210816

Type of Document Master's Thesis
Author Gao, Guangyue
Author's Email Address gygao@vt.edu
URN etd-05112016-210816
Title A Stochastic Model for The Transmission Dynamics of Toxoplasma Gondii
Degree Master of Science
Department Computer Science
Advisory Committee
Advisor Name Title
Cao, Yang Committee Chair
Sandu, Adrian Committee Member
Sun, Shu-Ming Committee Member
  • Gillespie Algorithm
  • Toxoplasma Gondii
  • Finite Difference Method
  • Transmission Dynamics
  • Compartment-Based Model
  • Stochastic Simulation
Date of Defense 2016-05-05
Availability unrestricted
Toxoplasma gondii (T. gondii) is an intracellular protozoan parasite. The parasite can infect all warm-blooded vertebrates. Up to 30% of the world's human population carry a Toxoplasma infection. However, the transmission dynamics of T. gondii has not been well understood , although a lot of mathematical models have been built. In this thesis, we adopt a complex life cycle model developed by Turner et al. and extend their work to include diffusion of hosts. Most of researches focus on the deterministic models. However, some scientists have reported that deterministic models sometimes are inaccurate or even inapplicable to describe reaction-diffusion systems, such as gene expression. In this case stochastic models might have qualitatively different properties than its deterministic limit. Consequently, the transmission pathways of T. gondii and potential control mechanisms are investigated by both deterministic and stochastic model by us. A stochastic algorithm due to Gillespie, based on the chemical master equation, is introduced. A compartment-based model and a Smoluchowski equation model are described to simulate the diffusion of hosts. The parameter analyses are conducted based on the reproduction number. The analyses based on the deterministic model are verified by stochastic simulation near the thresholds of the parameters.
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