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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.

This research demonstrates the use of two novel methodologies to evaluate energy autarky status of wastewater treatment plants (WWTPs) in two steps. Step I (analysis 1 and 2) focuses on overall energy performance evaluation of a conventional activated sludge process (CAS) using a quantitative mass balance model. Step II involves development of a dynamic model that simulates a future wastewater resource recovery facility (WRRF). The step I (analysis 1) focused on small WWTPs with treatment capacities less than 5 MGD. The results revealed that a CAS process can achieve energy autarky or energy-positive status when old technology equipment is replaced with new, high efficiency equipment to save 10-12% energy; aeration energy is reduced by installing nitritation/anammox nitrogen removal process; and energy production is enhanced with the addition of FOG for co-digestion. Analysis 2 of step I focusing on large plant capacities (i.e., > 20 MGD) evaluated the effect of influent wastewater strength (IWWS), primary treatment COD removal efficiency (PT-COD), and proper design of combined heat and power (CHP) systems on the overall energy performance. The results showed that energy autarky is feasible when PT-COD is 60% for low IWWS, 40% or greater for medium IWWS, and 30% or greater for high IWWS. In step II analysis, a new and dynamic model was developed by integrating high rate algal pond (HRAP) and anaerobic digester (AD) systems. The model was calibrated using the experimental data from recent studies. The results showed that this system can achieve energy autarky when advanced solids separation and co-digestion systems are included. Solids separation efficiency was increased from 75 to 90% to reduce the winter effluent COD concentrations from HRAP (by 20%). Similarly, nitrogen effluent concentrations were reduced by increasing the solids retention time. Future studies should focus on techno-economic and environmental life cycle impact analysis of these novel process configurations.

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