Pathogen genetic variation in small-world host contact structures

We introduce a model for assessing the levels and patterns of genetic diversity in pathogen populations, whose epidemiology follows a susceptible–infected–susceptible model. We assume a population which is structured into many small subpopulations (hosts) that exchange migrants (transmission) between their neighbours. We consider that the hosts are connected according to a small-world network topology, and in this way our model interpolates between two classical population genetics models: the stepping-stone and the island model. We have observed that the level of diversity has a maximum at intermediate values of the basic reproductive number R0. This result is independent of the topology considered, but depends on the relation between parasite load and the rate at which the immune system clears the pathogen. We show that, for a given R0 of the pathogen, as the host contact structure changes, by increasing the rewiring probability p, the level of pathogen diversity decreases. Its level is higher in regular lattices and smaller in random graphs. The latter topology presents a similar diversity level to the island model (a fully connected network), but also presents a clear pattern of isolation by distance, which is observed in some pathogen populations.

[1]  Mark E. J. Newman,et al.  The Structure and Function of Complex Networks , 2003, SIAM Rev..

[2]  Manfred Kochen,et al.  Small World , 2002 .

[3]  Alessandro Vespignani,et al.  Velocity and hierarchical spread of epidemic outbreaks in scale-free networks. , 2003, Physical review letters.

[4]  B. Derrida,et al.  Evolution of the most recent common ancestor of a population with no selection , 2006, cond-mat/0601167.

[5]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[6]  D. Conway,et al.  A principal target of human immunity to malaria identified by molecular population genetic and immunological analyses , 2000, Nature Medicine.

[7]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[8]  S. Wright Evolution in mendelian populations , 1931 .

[9]  R. May,et al.  How Viruses Spread Among Computers and People , 2001, Science.

[10]  B. Charlesworth,et al.  Effects of metapopulation processes on measures of genetic diversity. , 2000, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[11]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[12]  A. E. Hirsh,et al.  The application of statistical physics to evolutionary biology. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[13]  M. Keeling,et al.  Networks and epidemic models , 2005, Journal of The Royal Society Interface.

[14]  Paulo R A Campos,et al.  Muller's ratchet in random graphs and scale-free networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[16]  O. Pybus,et al.  Unifying the Epidemiological and Evolutionary Dynamics of Pathogens , 2004, Science.

[17]  Eli Stahl,et al.  Unifying the spatial population dynamics and molecular evolution of epidemic rabies virus. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[18]  M. Stephens,et al.  Traces of Human Migrations in Helicobacter pylori Populations , 2003, Science.

[19]  B. McDonald,et al.  Pathogen population genetics, evolutionary potential, and durable resistance. , 2002, Annual review of phytopathology.