Two-strain competition in quasineutral stochastic disease dynamics.
We develop a perturbation method for studying quasineutral competition in a broad class of stochastic competition models and apply it to the analysis of fixation of competing strains in two epidemic models. The first model is a two-strain generalization of the stochastic susceptible-infected-susceptible (SIS) model. Here we extend previous results due to Parsons and Quince [Theor. Popul. Biol. 72, 468 (2007)], Parsons et al. [Theor. Popul. Biol. 74, 302 (2008)], and Lin, Kim, and Doering [J. Stat. Phys. 148, 646 (2012)]. The second model, a two-strain generalization of the stochastic susceptible-infected-recovered (SIR) model with population turnover, has not been studied previously. In each of the two models, when the basic reproduction numbers of the two strains are identical, a system with an infinite population size approaches a point on the deterministic coexistence line (CL): a straight line of fixed points in the phase space of subpopulation sizes. Shot noise drives one of the strain populations to fixation, and the other to extinction, on a time scale proportional to the total population size. Our perturbation method explicitly tracks the dynamics of the probability distribution of the subpopulations in the vicinity of the CL. We argue that, whereas the slow strain has a competitive advantage for mathematically "typical" initial conditions, it is the fast strain that is more likely to win in the important situation when a few infectives of both strains are introduced into a susceptible population.
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
Oleg
O
Kogan
SGT Inc., NASA Ames Research Center, Moffett Field, Mountain View, California 94035, USA.
Michael
M
Khasin
Racah Institute of Physics, Hebrew University of Jerusalem, Jerusalem 91904, Israel.
Baruch
B
Meerson
Robert W. Holley Center for Agriculture and Health, Agricultural Research Service, United States Department of Agriculture, and Department of Plant Pathology and Plant-Microbe Biology, Cornell University, Ithaca, New York 14853, USA.
David
D
Schneider
Laboratory of Atomic and Solid State Physics, and Institute of Biotechnology, Cornell University, Ithaca, New York 14853, USA.
Christopher R
CR
Myers
D003198:Computer Simulation; D058872:Epidemics; D008954:Models, Biological; D011336:Probability; D013269:Stochastic Processes; D013997:Time Factors