*Virus Dynamics*. 2000, with Robert M. May*Evolutionary Dynamics*. 2006*Supercooperators*. 2011, with Roger Highfield

- Spatial games and evolution of cooperation. 1995. (In
*Advances in Artificial Life*)

The molecular structure of the human immunodeficiency virus (HIV) is known down to the tiniest details.
Yet despite this tremendous accomplishment, and other remarkable advances in our understanding of individual viruses and cells of the immune system,
there is still no clear model to explain the ultimate course and variability of the pathogenesis of AIDS.
Such gaps in our understanding prevent the development of effective therapies and vaccines.

In this accessible and well-written text, Martin Nowak and Robert May describe the emerging field of theoretical immunology. Using mathematical and computational models, the authors explore how populations of viruses and immune cells interact in various circumstances, and how infectious diseases spread within patients.

**Virus dynamics** is structured around the examples of HIV/AIDS and Hepatitis B virus,
although the approaches described are more widely applicable.
The authors use mathematical tools to uncover the detailed dynamics of viral infection and the effects of antiviral therapy.
Models are developed to describe the emergence of drug resistance,
and the dynamics of immune responses, viral evolution, and mutation.
The practical implications of this work for optimization of the design of therapy and vaccines are discussed.
The book concludes with future prospects of this fascinating and highly useful field of study.

**Evolution has become a mathematical theory**, Nowak suggests,
and any idea of an evolutionary process or mechanism should be studied
in the context of the mathematical equations of evolutionary dynamics.
His book presents a range of analytical tools that can be used to this end:
fitness landscapes, mutation matrices, genomic sequence space, random drift, quasispecies, replicators,
the Prisoner’s Dilemma, games in finite and infinite populations, evolutionary graph theory, games on grids,
evolutionary kaleidoscopes, fractals, and spatial chaos.

Nowak then shows how evolutionary dynamics applies to critical real-world problems, including the progression of viral diseases such as AIDS, the virulence of infectious agents, the unpredictable mutations that lead to cancer, the evolution of altruism, and even the evolution of human language. His book makes a clear and compelling case for understanding every living system—and everything that arises as a consequence of living systems—in terms of evolutionary dynamics.