Abstract

The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquito-borne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting equilibria: a stable Wolbachia-free equilibrium, an unstable coexistence equilibrium, and a complete invasion equilibrium. We establish the conditions under which a population of Wolbachia infected mosquitoes may persist in the environment via the next generation number and determine when a natural mosquito population may experience a complete invasion of Wolbachia.

Thesis Completion

2018

Semester

Spring

Thesis Chair

Shuai, Zhisheng

Degree

Bachelor of Science (B.S.)

College

College of Sciences

Department

Mathematics

Degree Program

Mathematics

Location

Orlando (Main) Campus

Language

English

Access Status

Open Access

Release Date

5-1-2018

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Restricted to the UCF community until 5-1-2018; it will then be open access.

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