Two-strain competition in quasi-neutral stochastic disease dynamics

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.

References in corpus (2)

• Stochastic Models of Evolution in Genetics, Ecology and Linguistics
• Disease extinction in the presence of non-Gaussian noise

Cited by in corpus (14)

• Demographic noise can reverse the direction of deterministic selection
• Intrinsic noise in systems with switching environments
• Fisher-Wright model with deterministic seed bank and selection
• Virus spread versus contact tracing: two competing contagion processes
• Markovian approach to tackle the interaction of simultaneous diseases
• Population Genetics with Fluctuating Population Sizes
• Evolutionary Dynamics with Fluctuating Population Sizes and Strong Mutualism
• Stationary solutions for metapopulation Moran models with mutation and selection
• Anomalous diffusion and long-range memory in the scaled voter model
• Stochastic multi-scale models of competition within heterogeneous cellular populations: simulation methods and mean-field analysis
• Exploiting fast-variables to understand population dynamics and evolution
• Applications of WKB and Fokker-Planck methods in analyzing population extinction driven by weak demographic fluctuations
• The advantage of being slow: the quasi-neutral contact process
• Noise induces rare events in granular media