This dissertation presents computational approaches to understand the entomological and epidemiological dynamics associated with malaria transmission and genetic vector control. From both mechanistic and deep learning perspectives, this work provides a computational toolkit to i) estimate the entomological and epidemiological impacts of novel genetic vector control tools, ii) understand the relationship between genetic parameters and outcomes of interest, and iii) emulate and calibrate complex mechanistic models of malaria transmission to external data.

Chapter 1 surveys the current landscape of vector control interventions and provides historical context to this work. Chapter 2 proposes a ``decoupled'' vector-human mechanistic model to estimate the impacts on prevalence and clinical incidence of malaria associated with the deployment of genetic vector control tools in \textit{Anopheles} mosquitoes. Combining an entomological model of gene inheritance with an epidemiological model of malaria transmission via a novel sampling algorithm, this framework provides a modular way to simulate the impacts of genetic vector control interventions. Chapter 3 uses this framework to quantify the relative importance of various genetic parameters in a CRISPR-Cas9-based homing gene drive on epidemiological outcomes of interest, parameterized to two African locations of interest across varying transmission intensities. Finally, Chapter 4 provides a deep learning framework to emulate a complex model of malaria transmission and use this approach in conjunction with approaches from numerical optimization to calibrate the model to external data. Taken together, this work contributes to the advancement of computational modeling in epidemiology and holds potential for the design and implementation of urgently-needed novel interventions for vector control. Chapter 5 concludes this work by considering its implications and potential future directions.

In this dissertation mechanistic stochastic models of mosquito population dynamics rel- evant for the control of mosquito borne pathogens are discussed. The first chapter re- examines the classical theory of vector control, which has been developed since its in- ception over a century ago and has produced a set of quantitative metrics that are the basis for measuring pathogen transmission. One metric is vectorial capacity, which de- scribes the ability of a local mosquito population to transmit pathogens, expressed in a single equation. Despite its appealing simplicity, the formula is too coarse a description to describe mosquitoes in any particular place. Vectorial capacity is reevaluated as an emergent property arising from how mosquitoes use resources on a landscape accord- ing to biological imperatives, using a stochastic model based on behavioral state transi- tions. The second chapter builds a simulation modeling framework to evaluate the effects of gene drive and other genetic control strategies on epidemiological and entomological outcomes. The simulation modeling framework is constructed using stochastic Petri nets (SPN), a mathematical modeling language that succinctly expresses state and events in a bipartite network. The SPN can be interpreted as describing either a deterministic or stochastic system, and associated software is developed to numerically solve the resulting system of ordinary differential equations or continuous-time Markov chain. In the final chapter, an algorithm is developed to simulate stochastic jump processes as disaggregated agent-based models (ABM). To speed up simulation times, the algorithm approximates a subset of hazard rates used to specify the model, but also converges upon the true process as the time step goes to zero. The simulation technique is relevant to a wide variety of contagion processes of interest to epidemiology, and also related fields such as ecology and the quantitative social sciences.

Malaria, dengue, Zika, and other mosquito-borne diseases continue to pose a major global health burden through much of the world, despite decades of work combating the mosquito vector and the virus or parasite responsible for each disease. The advent of CRISPR/Cas9-based gene editing greatly simplifies design and implementation of novel genetic-based approaches for vector control. This has reignited interest in gene drive technologies, requiring an understanding of the population and spatial dynamics of the wide range of novel gene drive architectures in development.

This thesis traverses the path from design, to understanding, to prediction of the dynamics for novel gene drive constructs. Chapter 1 develops and extends simulation frameworks for exploring the dynamics of gene drives. The first half enhances the field's genetic and geo-spatial simulation capabilities, while the second half builds upon that to utilize time-varying properties applied with a continuous-time framework. The outcome of this chapter is two expansive and computationally-efficient software packages freely available in the R ecosystem.

Chapter 2 acknowledges our limited knowledge of factors that impact the success of different gene drive constructs, and in conjunction with the biological design and testing of novel constructs, develops a robust inference methodology to understand and quantify the mechanisms underpinning gene drive behavior. Chapter 2 begins with a standard MCR design targeting a non-essential gene. We then expand our approach for treatment of split-gene designs that target essential genes with different (pre or post-zygotic) fertility impacts. All of this work is done in a manner consistent with the simulation frameworks from chapter 1.

Finally, chapter 3 applies the models developed in chapter 1, while integrating knowledge gained in chapter 2, to forecast the dynamics of innovative gene drive constructs in realistic settings. The chapter begins with a large-scale exploration of two classic designs, now generated using a CRISPR-based approach, to query the chance of ``success", any dangers of ``success", and repercussions if ``success" was not the correct goal. The chapter finishes with a recent design that seeks to bridge the space between linked and split-gene drive designs, seeking to combine the benefits of both ideas. It is a fitting conclusion to a project that spans math and biology to generate a mechanistic and predictive understanding of modern gene drives.