Mathematical modelling of infectious diseases of the humans, domestic and wild animals and plants is a rapidly expanding and a highly practically relevant area of research. This general area includes a number of directions of research such as an emergence and invasion of new pathogens, evolution of pathogens, the dynamics of infectious disease in a population, as well as dynamics of microparasites within a host. It is also dealing with mathematical description of immune response, as well as with its failure, as in the case of HIV infection. The most important direction is, however, assisting the epidemiologists and biologists in the developing of rational strategies for control of infectious diseases, at both a population and a single host levels.
At CRM, we employ the mathematical technique of the Dynamical System Theory to describe and study the dynamic of infectious diseases. Our particular interests are in the invasion of emerging infections, in the stability and persistence of a pathogen, as well as the stability of immune response. We also interested in viral and microbial evolution, which is probably the most important factor responsible for emergence of new infections, and in control of infectious diseases. One of the directions, which we are actively exploring, is application of the tools and methods of the Optimal Control Theory to the control of infectious diseases.