Integrating life history and cross-immunity into the evolutionary dynamics of pathogens

Abstract

Models for the diversity and evolution of pathogens have branched into two main directions: the adaptive dynamics of quantitative life-history traits (notably virulence) and the maintenance and invasion of multiple, antigenically diverse strains that interact with the host's immune memory. In a first attempt to reconcile these two approaches, we developed a simple modelling framework where two strains of pathogens, defined by a pair of life-history traits (infectious period and infectivity), interfere through a given level of cross-immunity. We used whooping cough as a potential example, but the framework proposed here could be applied to other acute infectious diseases. Specifically, we analysed the effects of these parameters on the invasion dynamics of one strain into a population, where the second strain is endemic. Whereas the deterministic version of the model converges towards stable coexistence of the two strains in most cases, stochastic simulations showed that transient epidemic dynamics can cause the extinction of either strain. Thus ecological dynamics, modulated by the immune parameters, eventually determine the adaptive value of different pathogen genotypes. We advocate an integrative view of pathogen dynamics at the crossroads of immunology, epidemiology and evolution, as a way towards efficient control of infectious diseases.

Figure 1

Diagram of the compartmental model used in this paper. Expressions next to arrows show the per capita flow rates between compartments. Births and deaths are not shown. See main text for symbols.

Figure 2

Two examples of deterministic dynamics following introduction of strain 2. Immune period: 1/σ=20 years. For both strains: R₀=17, infectious period 1/γ=21 days. Life-expectancy: 1/μ=50 years. (a) Weak cross-immunity (φ=0.2). (b) Strong cross-immunity (φ=0.9).

Figure 3

Minimum prevalence (troughs) of strain 1 (upper row, a–c) or strain 2 (lower row, d–f) reached after introduction of strain 2, using the deterministic model. Horizontally: immune period (1/σ), where ‘Inf’ stands for life-long immunity. Vertically: cross-immunity (φ). Left-hand column (a and d): infectious period of strain 2 (1/γ₂) 14 days; middle column (b and e): 21 days; right-hand column (c and f): 28 days. Infectious period of strain 1 : 21 days. For both strains: R₀=17.

Figure 4

Distribution of outcomes for 48 series of 1000 stochastic simulations with different values of cross-immunity (vertical axis), infectious period of strain 2 and immune period (horizontal axis). Infectious period of strain 1 : 21 days. For both strains: R₀=17. Population size: 10⁶.