I will present and/or derive fundamental mathematical models for the spread and control of infectious diseases and discuss their applications to diseases of interest (from a biothreat preparedness point of view). Specific examples include smallpox, plague and West Nile Virus. The simplest models consist of systems of nonlinear differential equations. I will briefly discuss methods for analyzing such system, and I will present results of numerical simulations of the models we have developed at Dynamics Technology, Inc.