Analytics and theoretical studies of complex systems and their applications in epidemic models

Abstract

Through human history, infectious diseases are among the top of the unintentional causes of human death worldwide. In the near several centuries, massive efforts have been done to control and prevent the spreading of infectious diseases. However, infectious disease is still one of the top 10 killers that seriously threaten the health of people in the 21st century. On the other hand, the development of computer hardware, big data, and algorithms science provides a new approach to research infectious diseases. Computer-based simulation can validate the epidemic control using mathematical models instead of the real-world experiment. Big data technology can benefit the epidemic modeling by providing more disease information. Algorithms are able to design the control strategies by scientific calculation rather than empiricism. Hence, the goal of this research is to study the epidemic control strategies by using the modeling, analysis, simulation, and optimization technics. To better discussing the epidemic control strategies, this research studies the modeling of vector-borne diseases. A partial differential equation model with age structure in human infections is introduced to describe the transmission of Zoonotic Visceral Leishmaniasis. A closed population dynamic system is introduced to study the prevention of Zika Virus. An agent-based model is presented to study emotion transmission during the epidemic like the 2009 flu pandemic. In this dissertation, analysis methods like sensitivity, stability and time series analysis are widely applied to further research the established models. The major contribution of this research is developing the new methodology of numerical epidemic control. The Pontryagin maximum principle-based optimal control algorithm is studied to control the Zika Virus. Moreover, an innovative heuristic algorithm based method is proposed to solve the optimal control problem with the highly nonlinear objective function. This dissertation also introduces evidence data based optimal control method, which trained the neural network with epidemic data to control the current prevalence. The last but not least, the simulation is used to predict the future epidemic and verify the designed control strategies.