Date of Award:

5-2024

Document Type:

Dissertation

Degree Name:

Doctor of Philosophy (PhD)

Department:

Mathematics and Statistics

Committee Chair(s)

Luis Gordillo

Committee

Luis Gordillo

Committee

Jia Zhao

Committee

Nancy Huntly

Committee

Brynja Kohler

Committee

Yan Sun

Abstract

Mathematical models are useful tools in managing infectious disease. When designed appropriately, these models can provide insight into disease incidence patterns and transmission rates. In this work, we present several models that provide information that is useful in monitoring diseases spread by insects.

In the first part of this dissertation, we present two models that predict disease incidence patterns for Curly Top disease (CT) in tomato crops. CT affects a wide variety of plants and is spread through the bite of the Beet Leafhopper. This disease is particularly devastating to tomato crops. When infected, tomato plants present with stunted growth and the infected plants are unable to produce fruit. Any fruit that was already set fails to fully develop. There are no methods for treating CT in tomatoes, and the majority of control methods are aimed at prevention. The two models for CT presented in this dissertation allow for the estimation of disease transmission rates and the assessment of the severity of outbreaks. In addition, the models can be used to investigate the efficiency of different control methods.

The second part of this dissertation is focused on modeling the population dynamics of mosquitoes that transmit disease. Culex mosquitoes transmit several diseases to humans including West Nile Virus and Saint Louis Encephalitis. Control methods for these diseases are typically aimed at limiting transmission events which includes reducing and controlling mosquito populations. In this work, we present a model that predicts mosquito population dynamics and allows for the quantification of mosquitoes over a given season. This model is useful in that it provides information on the quantity of mosquitoes capable of transmitting disease. In addition, it can be used to inform control methods for mosquito populations, such as the application of insecticides, to better target the maximum number of susceptible mosquitoes. The model takes into consideration climate variables such as temperature and precipitation, which are known to influence mosquito populations. In addition to informing researchers on the size of mosquito populations, the model framework may be adapted to model other insect populations such as ticks which transmit disease to humans.

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