A two-tiered model for simulating the ecological and evolutionary dynamics of rapidly evolving viruses, with an application to influenza
ABSTRACT Understanding the epidemiological and evolutionary dynamics of rapidly evolving pathogens is one of the most challenging problems facing disease ecologists today. To date, many mathematical and individual-based models have provided key insights into the factors that may regulate these dynamics. However, in many of these models, abstractions have been made to the simulated sequences that limit an effective interface with empirical data. This is especially the case for rapidly evolving viruses in which de novo mutations result in antigenically novel variants. With this focus, we present a simple two-tiered 'phylodynamic' model whose purpose is to simulate, along with case data, sequence data that will allow for a more quantitative interface with observed sequence data. The model differs from previous approaches in that it separates the simulation of the epidemiological dynamics (tier 1) from the molecular evolution of the virus's dominant antigenic protein (tier 2). This separation of phenotypic dynamics from genetic dynamics results in a modular model that is computationally simpler and allows sequences to be simulated with specifications such as sequence length, nucleotide composition and molecular constraints. To illustrate its use, we apply the model to influenza A (H3N2) dynamics in humans, influenza B dynamics in humans and influenza A (H3N8) dynamics in equine hosts. In all three of these illustrative examples, we show that the model can simulate sequences that are quantitatively similar in pattern to those empirically observed. Future work should focus on statistical estimation of model parameters for these examples as well as the possibility of applying this model, or variants thereof, to other host-virus systems.
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- "Additionally, they are not amenable to analytic treatment. In recent years, along with other contributions in agent-based modeling frameworks (Cobey and Pascual, 2011; Buckee et al., 2011; Zinder et al., 2013), the effort to deal with multistrain dynamics in a deterministic setting has been continued (Adams and Sasaki, 2007, 2009; Minayev and Ferguson, 2009a,b; Koelle et al., 2010; Kucharski and Gog, 2012). "
ABSTRACT: Starting from common assumptions, we build a rate equation model for multi-strain disease dynamics in terms of immune repertoire classes. We then move to a strain-level description where a low-order closure reminiscent of a pair approximation can be applied. We characterize the endemic equilibrium of the ensuing model in the absence of mutation and discuss the presence of degeneracy regarding the prevalence of the different strains. Finally we study the behavior of the system under the injection of mutant strains.Journal of Theoretical Biology 04/2014; 368. DOI:10.1016/j.jtbi.2014.12.001 · 2.30 Impact Factor
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- "duce a spurious signal of clonal interference in the frequency propagator statistics . This model describes neutral searches in epitope sequence space interspersed with selective sweeps triggered by beneficial escape mutants ( Ferguson et . al , 2003 ; Gog et al . , 2003 ; Tria et al . , 2005 ; Koelle et al . , 2006 ; Minayev and Ferguson , 2009 ; Koelle et al . , 2010 ) . Starting from an initial genotype with fitness F 0 , new epitope mutations are neutral with probability 1"
ABSTRACT: The seasonal influenza A virus undergoes rapid evolution to escape human immune response. Adaptive changes occur primarily in antigenic epitopes, the antibody-binding domains of the viral hemagglutinin. This process involves recurrent selective sweeps, in which clusters of simultaneous nucleotide fixations in the hemagglutinin coding sequence are observed about every 4 years. Here, we show that influenza A (H3N2) evolves by strong clonal interference. This mode of evolution is a red queen race between viral strains with different beneficial mutations. Clonal interference explains and quantifies the observed sweep pattern: we find an average of at least one strongly beneficial amino acid substitution per year, and a given selective sweep has three to four driving mutations on average. The inference of selection and clonal interference is based on frequency time series of single-nucleotide polymorphisms, which are obtained from a sample of influenza genome sequences over 39 years. Our results imply that mode and speed of influenza evolution are governed not only by positive selection within, but also by background selection outside antigenic epitopes: immune adaptation and conservation of other viral functions interfere with each other. Hence, adapting viral proteins are predicted to be particularly brittle. We conclude that a quantitative understanding of influenza's evolutionary and epidemiological dynamics must be based on all genomic domains and functions coupled by clonal interference.Genetics 07/2012; 192(2):671-82. DOI:10.1534/genetics.112.143396 · 4.87 Impact Factor
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ABSTRACT: Punctuated antigenic change is believed to be a key element in the evolution of influenza A; clusters of antigenically similar strains predominate worldwide for several years until an antigenically distant mutant emerges and instigates a selective sweep. It is thought that a region of East-Southeast Asia with year-round transmission acts as a source of antigenic diversity for influenza A and seasonal epidemics in temperate regions make little contribution to antigenic evolution. We use a mathematical model to examine how different transmission regimes affect the evolutionary dynamics of influenza over the lifespan of an antigenic cluster. Our model indicates that, in non-seasonal regions, mutants that cause significant outbreaks appear before the peak of the wild-type epidemic. A relatively large proportion of these mutants spread globally. In seasonal regions, mutants that cause significant local outbreaks appear each year before the seasonal peak of the wild-type epidemic, but only a small proportion spread globally. The potential for global spread is strongly influenced by the intensity of non-seasonal circulation and coupling between non-seasonal and seasonal regions. Results are similar if mutations are neutral, or confer a weak to moderate antigenic advantage. However, there is a threshold antigenic advantage, depending on the non-seasonal transmission intensity, beyond which mutants can escape herd immunity in the non-seasonal region and there is a global explosion in diversity. We conclude that non-seasonal transmission regions are fundamental to the generation and maintenance of influenza diversity owing to their epidemiology. More extensive sampling of viral diversity in such regions could facilitate earlier identification of antigenically novel strains and extend the critical window for vaccine development.Proceedings of the Royal Society B: Biological Sciences 12/2010; 278(1716):2249-56. DOI:10.1098/rspb.2010.2191 · 5.29 Impact Factor