The effect of disease life history on the evolutionary emergence of novel pathogens

Abstract

We present a general analytical result for the probability that a newly introduced pathogen will evolve adaptations that allow it to maintain itself within any novel host population, as a function of disease life-history parameters. We demonstrate that this probability of "evolutionary emergence" depends on two key properties of the disease life history: (i) the basic reproduction number and (ii) the expected duration of an infection. These parameters encapsulate all of the relevant information and can be combined in a very simple expression, with estimates for the rates of adaptive mutation, to predict the probability of emergence for any novel pathogen. In general, diseases that initially have a large reproductive number and/or that cause relatively long infections are the most prone to evolutionary adaptation.

Figure 1

Schematic of the transmission chain and emergence of an infectious disease. Introductions from the reservoir are followed by survival, transmission and death in the human population. In (a) and (c) the course of infections is symbolized by dotted lines; infections can reproduce at any time by transmission to susceptible hosts (right or left arrows), or die owing to immune clearance or host mortality (crosses). The introduced strain (open circles) is unable to spread because its reproduction rate, b, is lower than its death rate, d. (b) is a generation-based equivalent of (a), constructed in the same manner as fig. 1 of Antia et al. (2003). This is constructed by following the introduced infection of (a), and counting the total number of secondary infections that it generates (R₀ in expectation). These are then noted as offspring in the next generation and the procedure is repeated for each infection that is generated. The total number of reproduction events in the chain of transmission of the introduced pathogen, B, can be obtained graphically from (a), by considering one introduction event and counting the overall number of horizontal links in the arborescence generated. It can also be obtained from (b) by counting the number of links between two infections. The cumulative length of introduced infections, T, can be also obtained graphically from (a) by considering one introduction event and counting the overall length of vertical links in the transmission chain. T cannot be measured from (b) (nor from fig. 1 of Antia et al. 2003), because it lacks information relative to time. In (c) adaptation can occur; a single mutation (affecting b and/or d) is able to bring the pathogen above the epidemic threshold (b_a>d_a). The adaptive mutation can occur along two pathways: first, at each transmission event, the new infection can carry the mutation with a probability u (first adaptation pathway); second, the mutation can reach fixation during the course of an infection, at a rate μ per unit of time (second adaptation pathway). The infections caused by the evolved strain (filled circles) can go on to cause an epidemic (emergence).

Figure 2

Probability of emergence in the single-stage model, plotted as a function of the reproductive number (R₀=b/d) and expected length (L=1/d) of introduced infections (equation (A 3)). The probability for a secondary infection to carry an adaptive mutation (first adaptation pathway) is u=10⁻³; the rate of adaptation in the course of infection (second pathway) is μ=10⁻⁶; the probability of emergence of adapted strains is P_a=0.5 We could also estimate the probability of emergence of pathogens from Monte Carlo simulations, which confirmed the validity of our analytical model (not shown).

Figure 3

Probability of emergence in the two-stage model, plotted as a function of the expected length of the first and second stage (1/τ and 1/d₂, respectively), the overall pathogen fitness (R₀=b₂/d₂) being kept constant. The pathogen is transmitted and impacts host mortality only during the second stage (b₁=0 and d₁=0). All other parameters are as in figure 2.