This book is dedicated to the computer models of microevolution and their applications in virology and biomedicine. Its content is based on courses taught by the author at Peter the Great St. Petersburg Polytechnic University.

Several viruses, including HIV, hepatitis C virus (HCV), influenza viruses, and coronaviruses, evolve rapidly within human populations and consequently exhibit extensive genetic diversity. In the case of HIV and HCV, viruses persisting in their hosts, substantial genetic variation can also arise within individual hosts. Rapid evolution enables viruses to evade immune responses, reduce vaccine effectiveness, and develop resistance to antiviral therapies. Mathematical models make it possible to predict viral evolutionary dynamics in a probabilistic framework, providing insights that are essential for optimizing vaccine design and antiviral treatment strategies.

The book is intended for undergraduate and graduate students in the biological and medical sciences, as well as for early-career researchers. Although it focuses on mathematical models, it avoids mathematical notation and instead relies on diagrams, graphs, and conceptual explanations, making the subject accessible to readers without an advanced mathematical background.

Igor M. Rouzine is the head of the Population Genetics and Virology group of the Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of Sciences, St Petersburg, Russia. Previously, he worked as a Research Professor or Researcher in the area of mathematical modeling of viral evolution and immune response at three American virological labs and in Sorbonne, France (grant "Hosting Researchers of a High Level"). His work resulted in 43 articles on mathematical biology in PNAS, Cell, Cell Host & Microbe, PLoS Comp Bio, PLoS Pathogens, Comm. Med., Scientific Reports, J. Virology, Viruses, AIDS, Genetics, J. of Theor. Bio., and Theor. Pop. Bio.. He trained numerous interns, PhD students, and postdocs, taught at UCLA, USF, Sorbonne, and reviewed for more than 40 journals. He has a Ph.D. degree in theoretical physics and a D.Sci. degree in mathematical biology and bioinformatics.