Dr. Song's primary research interests lie in mathematical modeling, dynamical systems, dynamics of infectious diseases, population dynamics, and mathematical ecology. For an interest real world problem, he intends to use a mathematical model to describe it. Following the construction of the model, he analyzes the model, such as what the long-term behavior of the model is, how the dynamics changes with varying parameters, which parameter is most sensitive to the outcomes, etc. Based on parameter estimations according to availability of data, computer simulations are also utilized to get insights into the problem. Specifically, he has studied the transmission dynamics of tuberculosis and control strategies for the USA. For instance, he modeled the co-infection tuberculosis with HIV/AIDS and concluded that if the USA could successfully treat 20% of latently-infected tuberculosis, then it would be possible to eliminate the disease in 2020. He also modeled issues relevant to anti-bioterrism. The spread of smallpox deliberately released through public transportation system, like subway system, is studied in his recent work. Drug abuse among young adults was another aspect of Dr Song’s research interest. Using mathematical models, he studied the use of ecstasy and rave of the teenagers and young adults. From modeling, it was emphasized that education plays a crucial rule in battling the ecstasy user and the peer pressure.
Dr. Song has guided over 3 dozens of undergraduate research projects (half of them with MSU students). These projects resulted in more than 40 presentations. A dozen of the presentations won national or regional poster awards.
Mathematical modeling, dynamical systems, dynamics of infectious diseases, population dynamics, bifurcation analysis, numerical simulations, and mathematical ecology.