Systems biology is a comprehensive quantitative analysis of the manner in which all the components of a biological system interact functionally along with time. Mathematical modeling and computational methods are indispensable in such kind of studies, especially for interpreting and predicting the complex interactions among all the components so as to obtain some desirable system properties. System dynamics, system robustness and control method are three crucial properties in systems biology. In this thesis, the above properties are studied in four different biological systems. The outbreak and spread of infectious diseases have been questioned and studied for years. The spread mechanism and prediction about the disease could enable scientists to evaluate isolation plans to have significant effects on a particular epidemic. A differential equation model is proposed to study the dynamics of HIV spread in a network of prisons. In prisons, screening and quarantining are both efficient control manners. An optimization model is proposed to study optimal strategies for the control of HIV spread in a prison system. A primordium (plural: primordia) is an organ or tissue in its earliest recognizable stage of development. Primordial development in plants is critical to the proper positioning and development of plant organs. An optimization model and two control mechanisms are proposed to study the dynamics and robustness of primordial systems. Probabilistic Boolean Networks (PBNs) are mathematical models for studying the switching behavior in genetic regulatory networks. An algorithm is proposed to identify singleton and small attractors in PBNs which correspond to cell types and cell states. The captured problem is NP-hard in general. Our algorithm is theoretically and computationally demonstrated to be much more efficient than the naive algorithm that examines all the possible states. The goal of studying the long-term behavior of a genetic regulatory network is to study the control strategies such that the system can obtain desired properties. A control method is proposed to study multiple external interventions meanwhile minimizing the control cost. Robustness is a paramount property for living organisms. The impact degree is a measure of robustness of a metabolic system against the deletion of single or multiple reaction(s). An algorithm is proposed to study the impact degree in Escherichia coli metabolic system. Moreover, approximation method based on Branching process is proposed for estimating the impact degree of metabolic networks. The effectiveness of our method is assured by testing with real-world Escherichia coli, Bacillus subtilis, Saccharomyces cerevisiae and Homo Sapiens metabolic systems. / published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy