Discrete and continuous mathematical investigation of juvenile mosquito dynamics

There are thousands of species of mosquitoes, but only a handful of these species carry pathogens that cause human diseases. Here, we study two species, Aedes albopictus and Aedes aegypti, which transmit infections such as dengue, Zika, Mayaro virus, and La Crosse virus. Curtailing these diseases is a good reason to consider control of mosquito populations. However, mosquitoes are quite hardy and spraying of pesticides is typically a short-term solution. Thus, more long-term solutions require careful thought about mosquito populations, including early juvenile aquatic stages: egg, larva, and pupa. In this dissertation, we examine the factors that affect the dynamics of aquatic stages by creating mathematical models. The goal is to assess what key biological features most impact the total population. Both Aedes albopictus and Aedes aegypti lay eggs in small containers, producing limitations on space and food. We investigate how restricting resources changes development time, survival to adulthood, and body mass at emergence. The interactions between these changes are complicated, so to disentangle their effects we create three different mathematical models. The first model is discrete in time and focuses on the best way to incorporate the influence of larval density. We compare the impact of larval density by inputting seven different functional forms altering survival and development time. Larval density used in the model is determined from the average of the population size over the past one to thirty-six days. The second model is also discrete in time but focuses on the interaction between survival, development time, and mass. This model considers three levels of mass. Here, we use the density-dependent function determined from our first model and fit the maximum value for development time from experimental data. Survival values are fit using constants and a density-dependent function. Finally, growth is built in as a function of food. Food decreases at each time point as a function of the total larvae in the environment. We compare between model formulations with Akaike information criterion. The third model examines the ramifications of constricting resources on growth verses death. We employ a partial differential equation that has three independent variables: time, age, and mass. We find that density dependence is highly influential in the maturation of mosquitoes, and it is more essential to include its impacts on development time than on survival. These findings can be incorporated into a larger framework of disease dynamics, and give insight into better control of mosquitoes and disease spread.