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J Theor Biol. 2014 Nov 7;360:149-62. doi: 10.1016/j.jtbi.2014.06.039. Epub 2014 Jul 10.

Evolutionary dynamics of infectious diseases in finite populations.

Author information

1
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA; Institute of Science and Technology Austria, Am Campus 1, 3400 Klosterneuburg, Austria; Faculty of Mathematics and Physics, Charles University in Prague, Czech Republic. Electronic address: jhumplik@ist.ac.at.
2
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA; Biophysics Program and Harvard-MIT Division of Health Sciences and Technology, Harvard University, Cambridge, MA 02138, USA. Electronic address: alhill@fas.harvard.edu.
3
Program for Evolutionary Dynamics, Harvard University, One Brattle Square, Cambridge, MA 02138, USA; Department of Organismic and Evolutionary Biology, Department of Mathematics, Harvard University, Cambridge, MA 02138, USA.

Abstract

In infectious disease epidemiology the basic reproductive ratio, R0, is defined as the average number of new infections caused by a single infected individual in a fully susceptible population. Many models describing competition for hosts between non-interacting pathogen strains in an infinite population lead to the conclusion that selection favors invasion of new strains if and only if they have higher R0 values than the resident. Here we demonstrate that this picture fails in finite populations. Using a simple stochastic SIS model, we show that in general there is no analogous optimization principle. We find that successive invasions may in some cases lead to strains that infect a smaller fraction of the host population, and that mutually invasible pathogen strains exist. In the limit of weak selection we demonstrate that an optimization principle does exist, although it differs from R0 maximization. For strains with very large R0, we derive an expression for this local fitness function and use it to establish a lower bound for the error caused by neglecting stochastic effects. Furthermore, we apply this weak selection limit to investigate the selection dynamics in the presence of a trade-off between the virulence and the transmission rate of a pathogen.

KEYWORDS:

Basic reproductive ratio; SIS model; Stochastic logistic model; Virulence

PMID:
25016046
DOI:
10.1016/j.jtbi.2014.06.039
[Indexed for MEDLINE]
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