Over the past several years, we have been developing new network-based mathematical approaches for predicting the spread of infectious diseases. In collaboration with public health officials in the United States and Canada, we apply these methods to the design of optimal control measures for respiratory diseases including influenza and SARS. We are also collaborating with field ecologists to better understand the contact network structures of wildlife populations and their epidemiological consequences. Using mathematical modeling, we have addressed several fundamental questions about (a) the impact of environmental heterogeneity on evolutionary dynamics and (b) the structure of complex fitness landscapes. Our work in these areas have yielded important insights into the diversity of certain classes of biological molecules and the ability of some viruses to rapidly evolve as they spread through human populations.
Mathematical modeling has been used extensively to forecast emerging and re- emerging infectious disease epidemics because it allows to mechanistically represent the different factors determining disease transmission and their dynamics over time. We will develop a mathematical model of drug use in the United States which represents current patterns of drug use across the country and associated HIV, HCV and overdose incidence. It will explicitly represent heterogeneity in susceptibility to drug use disorders in the population, social networks and the influence of drug markets, law enforcement and healthcare services on drug use and associated health outcomes. This project will 1) systematically investigate the potential for emerging drug use epidemics; 2) identify the optimal allocation of resources towards combination of interventions to control them and limit associated harms; 3) pilot a targeted mass-media based intervention to increase access to appropriate prevention methods among a specific population at risk of an emerging drug use in real time as identified by the model.
Vector-borne diseases have more complex transmission routes than the most of infcectious diseases. This research utilizes the dynamic modeling and agent-based modeling to describe the disease transmission for ZIKA Virus and Zoonotic Visceral Leishmaniasis. Theortical analysis are used to figure out the most important part from the model. Based on the analysis result, this research uses optimal control theory to design the control strategies which can reduce the cost during the epidmeic. The simulation is used to verify the control strategies and predict the future disease transmission Since the traditional Pontryagin maximum principle-based optimal control algorithm can only solve the optimal control problem for with convex objective functions. The major contribution of this research is developing the new methodology of numerical epidemic control.An innovative heuristic algorithm based method is proposed to solve the optimal control problem with the highly nonlinear objective function. This project also introduces evidence data based optimal control method, which trained the neural network with epidemic data to control the current prevalence.