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Stochastic Models for the Control of Mosquito-borne Pathogens

  • Author(s): Wu, Sean Lawrence
  • Advisor(s): Marshall, John M
  • et al.
Abstract

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.

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