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Chapter 7 : Effects of Immune Selection on Population Structure of Bacteria
Category: Fungi and Fungal Pathogenesis; Bacterial Pathogenesis
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Bacterial pathogens, the subject of this chapter, exhibit antigenic diversity both at the level of the pathogen population through allelic polymorphism and within individual bacteria, where the expression of antigenic loci may be switched on and off. The balance between the different effects of immune selection leads to the various patterns of antigenic diversity observed among bacterial pathogen populations. The chapter discusses some of these patterns and the theoretical frameworks that have been developed to try to understand them. The different population structures of meningococcal serogroups can be explained using simple mathematical models of immune selection. It introduces the basic frameworks used to understand the population dynamics of infectious diseases before describing models that incorporate pathogen population structure and the role of immune selection. For many bacterial pathogens, however, the immune response is generated to more than one antigen. Despite the complexity of the biological and epidemiological factors that affect the evolution of bacterial pathogens, a wide range of population structures can be accounted for using the simple theoretical models of immune selection. Understanding the role of immune selection for other bacterial pathogens will require similar large-scale projects that examine the structuring of antigenic determinants at a population level. As sequencing methods and other technological tools advance, examining pathogen population structures should become increasingly straightforward, enabling a deeper examination of the effects of immune selection on pathogen populations.
A simple SIR model of disease dynamics. The compartments represent proportions of the host population of each class, with arrows showing the inputs and outputs from each compartment. Below are the associated equations. The parameters are as follows: S, proportion of the host population susceptible; I, proportion infectious; R, proportion recovered/immune; μ, the birth and death rate; β, the transmission coefficient; σ, the recovery rate.
A modified SIR model incorporating two pathogen strains. Hosts move from the susceptible compartment to the immune compartments dependent on the force of infection (λ) of each strain. It is assumed that hosts become immune immediately upon infection. After immunity is gained by one strain, the host can become infected with and immune to the other strain depending on the level of cross-immunity (c).
Equations for Fig. 2. The differential equations describing the modified SIR model. Strains are denoted either i or i′, with i′ representing the “other” strain (strain B if strain A is denoted i, and vice versa. Susceptible hosts (those in the S compartment) are first infected by a particular strain i. Here, the force of infection for strain i, λ i , is given by β i I i , where β i is the transmission coefficient of strain i, and Ii is the proportion of the population infected with strain i. Once hosts are immune to strain i (Ri ), they can become infected by the other strain, i′, entering the Ii compartment at a rate dependent on the level of cross-immunity, c. As in the previous SIR model, σ is the recovery rate, which is the same for both strains. Following infection by the second strain, hosts become immune to both (Rboth ).
The equations governing the dynamics of the pathogen population depending on the level of cross-immunity. Here, zi is the proportion of the population that is immune to strain i; wi is the proportion exposed to strains sharing alleles with strain i (given by the subset i′, which includes strain i), and yi is the proportion infected. Each strain has the same transmission coefficient, β, such that the force of infection for strain i is βyi . The death rate is μ, and the rate of loss of infectiousness is σ. It is assumed that hosts gain immunity instantaneously upon infection. Cross-immunity is incorporated as γ, which determines whether exposure gives complete protection against strains that share alleles with strain i (γ = 1), no protection at all (γ = 0), or some intermediate level of protection (0 < γ < 1).
The effects of transitioning from regular to random networks on strain diversity and discordance. (A) The effect of ρ (the degree of host mixing) on mean discordance (dashed line) and mean diversity (solid line) for two simulations. (B) The degree of host clustering, measured by the clustering coefficient, as a function of ρ. The clustering coefficient is defined and computed as in Watts and Strogatz (1998). (C) The average size of the largest strain cluster as a function of ρ. The decrease in discordance and the increase in diversity with more localized interactions (lower ρ) is strongly correlated to the degree of host clustering and the growth in the size of the largest strain cluster. Both simulations were run for 5,000 time steps for each of the 14 ρ values, ranging from 0.0001 to 1. The first 2,000 time steps were discarded to remove the effect of transients. Note the logarithmic scale on the x-axis. For complete parameter values see Buckee et al. (2004).