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
Recommended Citation
Reed, Hanna, "Mathematical Models of Mosquito Populations" (2018). Honors in the Major Theses. 299.
https://stars.library.ucf.edu/honorstheses/299