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ARS Home » Northeast Area » Ithaca, New York » Robert W. Holley Center for Agriculture & Health » Emerging Pests and Pathogens Research » Research » Publications at this Location » Publication #310943

Title: Two-strain competition in quasi-neutral stochastic disease dynamics

item KOGAN, OLEG - Cornell University - New York
item KHASIN, MICHAEL - Stinger Ghaffarian Technologies, Inc (SGT, INC)
item MEERSON, BARUCH - Hebrew University
item Schneider, David
item MYERS, CHRISTOPHER - Cornell University - New York

Submitted to: Physical Review E (PRE) - Statistical, Nonlinear, and Soft Matter Physics
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: 10/31/2014
Publication Date: 10/31/2014
Citation: Kogan, O., Khasin, M., Meerson, B., Schneider, D.J., Myers, C.R. 2014. Two-strain competition in quasi-neutral stochastic disease dynamics. Physical Review E (PRE) - Statistical, Nonlinear, and Soft Matter Physics. DOI: 10.1103/PhysRevE.90.042149.

Interpretive Summary: Many common infectious diseases are caused by one of several strains of a given pathogen circulating in a host population. While these strains may cause the same symptoms, they may be distinguishable by defense mechanisms of individual hosts and have different growth rates. So, it is natural to ask how the presence of one strain affects the prevalence of the other strains. Does one strain always eventually dominate and the others go extinct? To answer this question we performed a detailed analysis of a mathematical model for the progression of an epidemic involving two strains with the same basic reproduction numbers, but different growth rates. We show that the slower growing strain typically has a fitness advantage over the faster growing strain, except in the special case where small numbers of infected individuals are introduced into a large population of susceptibles. Under these “colonization” conditions, the faster growing strain has an advantage. In addition, this model suggests that the less fit strain will eventually die out. These results provide a framework for understanding why it is so common to find only a handful of dominant strains for any given disease, despite the fact that random mutations are constantly generating new strains. The slightly less fit strains arising from random mutations are statistically very likely to disappear before they infect a significant fraction of the population.

Technical Abstract: We develop a new perturbation method for studying quasi-neutral 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 (2007), Parsons et al (2008) and Lin, Kim and Doering (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 sub population 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 sub-populations 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.