Conceived and designed the experiments: AL NMF. Performed the experiments: AL. Analyzed the data: AL. Wrote the paper: AL NMF.
The authors have declared that no competing interests exist.
Pathogens have evolved diverse strategies to maximize their transmission fitness. Here we investigate these strategies for directly transmitted pathogens using mathematical models of disease pathogenesis and transmission, modeling fitness as a function of within and betweenhost pathogen dynamics. The withinhost model includes realistic constraints on pathogen replication via resource depletion and crossimmunity between pathogen strains. We find three distinct types of infection emerge as maxima in the fitness landscape, each characterized by particular withinhost dynamics, host population contact network structure, and transmission mode. These three infection types are associated with distinct nonoverlapping ranges of levels of antigenic diversity, and welldefined patterns of withinhost dynamics and betweenhost transmissibility. Fitness, quantified by the basic reproduction number, also falls within distinct ranges for each infection type. Every type is optimal for certain contact structures over a range of contact rates. Sexually transmitted infections and childhood diseases are identified as exemplar types for low and high contact rates, respectively. This work generates a plausible mechanistic hypothesis for the observed tradeoff between pathogen transmissibility and antigenic diversity, and shows how different classes of pathogens arise evolutionarily as fitness optima for different contact network structures and host contact rates.
Infectious diseases vary widely in how they affect those who get infected and how they are transmitted. As an example, the duration of a single infection can range from days to years, while transmission can occur via the respiratory route, water or sexual contact. Measles and HIV are contrasting examples—both are caused by RNA viruses, but one is a genetically diverse, lethal sexually transmitted infection (STI) while the other is a relatively mild respiratory childhood disease with low antigenic diversity. We investigate why the most transmissible respiratory diseases such as measles and rubella are antigenically static, meaning immunity is lifelong, while other diseases—such as influenza, or the sexually transmitted diseases—seem to trade transmissibility for the ability to generate multiple diverse strains so as to evade host immunity. We use mathematical models of disease progression and evolution within the infected host coupled with models of transmission between hosts to explore how transmission modes, host contact rates and network structure determine antigenic diversity, infectiousness and duration of infection. In doing so, we classify infections into three types—measleslike (high transmissibility, but antigenically static), flulike (lower transmissibility, but more antigenically diverse), and STIlike (very antigenically diverse, long lived infection, but low overall transmissibility).
There are two major principles by which pathogens avoid their elimination: escaping the host immune response via antigenic variation or immune evasion, or transmission to a new immunologically naive host. Directly transmitted pathogens which cause chronic diseases, such as many sexually transmitted infections (STIs), tend to rely more on the former, while many acute infections, for instance measles, rely more on high transmissibility. Indeed pathogens such as measles show very little antigenic diversity, with immune responses being strongly crossreactive between strains. There are then those pathogens which have intermediate levels of both immune escape and transmissibility — such as influenza, rhinovirus and RSV (here referred to as FLIs — flulike infections).
The evolutionary success of directly transmitted pathogens can also be seen to depend on the nature, frequency and structure of contacts between hosts. Infections transmitted to a small number of hosts (per time unit and infected individual) via intense contact (e.g., via fluids) are usually caused by pathogens of high antigenic diversity and long duration of infection, while those transmitted via casual contact (e.g., via aerosol) with a large number of hosts may typically have lower diversity and much shorter durations of infection. While many of the evolutionary constraints are different
It is straightforward to explain the long duration of infection and consequent antigenic diversity of sexually transmitted or bloodborne infections: the frequency of relevant contacts between hosts is low, meaning infection needs to be extended to ensure the reproduction number (the number of secondary cases per primary case
The molecular genetic basis of transmissibility is still poorly understood for most pathogens. However, all other things being equal, the level of pathogen shedding by a host (whatever route is relevant) must be positively correlated with infectiousness. A firstpass analysis might therefore postulate that overall transmissibility (as quantified by the basic reproduction number,
However, the assumption that transmission fitness (as quantified by
The maximal risk, which corresponds to 11.8 per 100 personyears, is normalized to 1, and the viral load in 10 liters of plasma plotted. Data points (blue polygon) are compared with the leastsquares best fit of the infectiousness model given in the text (green); cf. (7). The viral load
A key insight (and assumption) of the work presented here is that while we might expect pathogens to be able to evolve to reduce (or increase)
We will show that there is a critical value of
Our approach is to construct a model of withinhost pathogen dynamics which incorporates adaptive host immunity and antigenic diversification. The key output from this model is how pathogen load varies through time during an infection. We then calculate the basic reproduction number,
The withinhost model developed here is an extension of a model studied earlier by one of us
We use
We do not explicitly consider how a pathogen could evolve its biological characteristics to maximize transmission fitness (i.e. the evolutionary trajectory a pathogen would take through parameter space). There are undoubtedly many constraints on the possible paths which pathogens can take
The multistrain model used extends past work
The dynamics of the model is characterized by an initial period of exponential growth of the pathogen load, which eventually slows due to immune responses and resource limitations. One observes a latency period and an initial peak. Pathogen load then declines exponentially. If the trough load of a pathogen strain drops below a threshold level we assume the pathogen is eliminated from the host (to avoid persistence at unrealistically low, fractional, loads). However if a novel strain emerges before the seed strain goes extinct, pathogen load can recover, so long as there is sufficient resource available and crossimmunity is not too strong — leading to a second, albeit lower peak in pathogen load. Further peaks in pathogen load can occur via the same mechanism. The rate at which new strains arise is the most important determinant of the number of pathogen load peaks seen and thus the overall duration of infection. Less intuitively, this rate also determines the size of the initial peak (discussed below).
Since mutation is modeled stochastically, we average over multiple realizations (e.g.
Graphs show pathogen load [red], specific immunity [blue], resource [green], number of strains [black] and corresponding mean values plotted over time — for individual hosts in (A,B,D) and average hosts in (C,E,F), respectively. (A) and (B) show two different model realizations for the same parameters of antigenic mutation proportion
We systematically calculate average pathogen load curves from the withinhost model for wide ranges of two biological parameters: the antigenic mutation rate
From the discussion in the introduction, we can immediately identify the cumulative pathogen load and duration of infection as epidemiologically relevant quantities.
(A) the cumulative pathogen load
The withinhost dynamics generate a tradeoff between initial peak pathogen load and antigenic diversity: high initial peak load corresponds to low diversity and viceversa (see
To calculate the reproduction number (i.e., the pathogen fitness), we model a dynamic contact network in the neighborhood of one initially infected host. The profiles of pathogen load over time obtained from the withinhost model then determine the infectiousness of the infected host to its neighbors. (We utilize the meanload profiles averaged over individual hosts.) Epidemiological dynamics are determined by 4 parameters. Two of these relate to properties of the transmission route: the infectiousness parameter
We build a model (cf.
Varying the 4 parameters of transmission and contact space, we obtain three different classes of fitness landscapes over pathogen space — as represented by
There are clear similarities between the three classes of fitness landscapes (
Varying the infectiousness parameter
Varying the transmission and contact space parameters more systematically, one can map out the regions of parameter space for which particular infection types are optimal (
Different plots show results for different choices of betweenhost contact network, as defined by the replacement rate of network neighbors
So far we have assumed only the pathogen space parameters (
For each value of
As expected, the evolutionary optimal value of the infectiousness parameter (
The evolutionarily optimal replication rate
Reexamining
(A) results for a lower bound on
As discussed already, the transmission route is likely to be the most important determinant of the lower bound on
The work in this paper was motivated by a desire to understand why the most transmissible human pathogens — archetypal childhood diseases such as measles and rubella — show remarkably little antigenic variation, while less transmissible diseases — such as influenza (and many other respiratory viruses) and sexually transmitted diseases show substantial diversity. Addressing this question requires consideration of how evolvable parameters governing the natural history of infection within a host affect the transmission characteristics of a pathogen in the host population.
We developed a relatively simple multistrain model of the withinhost dynamics of infection. Pathogen particle consume resource to replicate, and their replication is inhibited by a dynamically modeled immune response with two components: strainspecific immunity, and crossimmunity. Crossimmunity was assumed to be the key fitness cost of antigenic diversity within the host; the benefit is a much enhanced duration of infection (and thus transmission). Pathogens which have a low rate of generating new antigenic variants are cleared from the host much faster than those with a high rate of antigenic diversification, but also maximize the initial peak level of parasite load reached prior to clearance (cf.
The second evolvable withinhost parameter we considered was the withinhost pathogen replication rate. Given the resourcedependent model of replication assumed, this has a more limited effect than in some models, but can set the timescale for pathogen load to initially peak and thus determine the effective latent period of the disease.
At the betweenhost level, we assume a simple relationship between pathogen load and infectiousness which has been shown to be appropriate to model HIV transmissibility
The final element we incorporate into the framework developed is contact between hosts, assumed to occur at some rate
Putting these elements together, we found that optimizing reproductive fitness in this way leads to welldefined infection types A, B, C, as contact rates (and reproductive numbers) increase (cf.
Infection type C represents childhood diseases with the highest values of
The limited antigenic diversity and short infectious periods of type C pathogens are determined by the higher infectiousness threshold and the consequent need to maximize the peak pathogen load attained early in infection. When contact rates are high, the increase in duration of infection resulting from higher rates of antigenic diversity is insufficient to compensate for the reduction in peak pathogen load (and therefore infectiousness) caused by crossimmunity being generated against multiple pathogen strains simultaneously. A single strain pathogen generating a single immune response is able to generate a larger primary infection peak — though at the cost of being unable to sustain infection further.
It is encouraging to see that the classification of infection types our model predicts closely corresponds to many of the pathogen regimes identified in other work
Furthermore, it is interesting to note that in the context of our model only the concept of a minimal infectiousness threshold — introduced to characterize transmission modes — is necessary to explain the findings of
The key limitation of our analysis is our highly simplified treatment of betweenhost transmission — namely using a networkcorrected reproduction number as our measure of strain fitness. Doing so assumes evolutionary competition occurring in infinite (nonevolving) host populations in infinite timescales. It would clearly be substantially more realistic to explicitly simulate the transmission process in a large host population. The computational challenges are considerable — while largescale simulations of influenza A evolution and transmission have been undertaken
However, continuing advances in computing performance mean that it may now be feasible to explicit model multiple strains evolving within hosts and being transmitted independently in a large population. Such an approach would allow exploration of the relationship between antigenic diversity (and crossimmunity) within single hosts and strain dynamics at a population level. Perhaps even more importantly, it would allow extinction processes to be properly captured, while our current approach implicitly assumes fixation probabilities to be 1 even when fitness differences are marginal. Proper representation of finite population sizes and extinction will also allow the evolutionary emergence of childhood diseases (such as measles) as a function of early urbanization to be modeled.
A second limitation is that we only consider a single, highly simplified withinhost model. Future work to test the sensitivity of our results to the choice of withinhost model would be valuable (cf.
Also a conceptual simplification must be pointed out here: our model assumes that mutations, controlled by
Further, we have not attempted to capture specialized strategies pathogens have adopted for persistence within infected hosts, such as use of refuges from immune responses (HSV) or hijacking the immune system (HIV) — the model only reflects tradeoffs which may have contributed to pathogens adopting the range of persistence strategies seen in nature. An interesting addition to future work would also be the incorporation of pathogen virulence
A last area which is a clear priority for future research is the relationship between withinhost parasite load and infectiousness. We have assumed a relationship which has some support in data (
The withinhost dynamics are simulated by the following system of ordinary differential equations (see
Saturation effects, modifying linear dependency on
Guided by values for RNA viruses, random mutations are assumed to occur with probability
New antigenic variants
We assume 5 loci with 3 alleles at each. (These numbers are small but sufficient for our analyses, cf.
Independent of immunity, pathogen is cleared at a rate
The differential equations are solved using a RungeKutta algorithm with the initial values
The parameter values (essentially
This model is minimally complex, incorporating only the features essential to explain the tradeoff between transmissibility and antigenic diversity. A more realistic model is examined in
The essential withinhost dynamics of our combined within/betweenhost model is given by Eq. (1), which links pathogen replication to two inhibitors — host immunity and resource limitation. This equation quantifies the tradeoff for increasing antigenic diversity (the pathogen's survival strategy within the host) — namely the smaller initial pathogen load peak seen in
Let us consider the pathogen load dynamics soon after infection with one initial strain. Our numerical simulations have shown that the initial strain
This verbal argument can be formalized. For simplicity we assume the load of the initial strain is a good approximation of the total pathogen load at the initial peak,
As a consequence of resource limitation (i.e., the reduced growth
Finally, we examine what would happen if crossimmunity or resource limitation were not implemented in the model. Without crossimmunity,
As discussed in the text, we use the basic reproductive number
It should be noted that the network dynamics are invariant for
Here we derive Eqn. (8) of our betweenhost model, which also illustrates how the two parameters,
The transmission dynamic in an initially entire susceptible contact neighborhood of one index case and fixed size,
Written exclusively in terms of susceptibles (while utilizing the notion of convolution), (9) reads
Parameter  Description 
resource  
initial/max resource  
duration of infection  
Hill function, 

infectives  
neighborhood size  
number of mutant strains  
transmission rate  
reproduction number  
susceptibles  
total pathogen load  
initial/min pathogen load  
pathogen units per resource unit  
load of strain 

saturated growth of pathogen, 

infectiousness threshold (transmission space)  
initial/min immunity  
specific immunity to strain 

saturated growth of immunity, 

crossweight (over antigenic distance between strains 

crossreactive immunity to strain 

contact rate (transmission space)  
transmission coefficient  
probability of transmission  
antigenic variation (pathogen space)  
growth of immunity  
critical load for saturated immune response  
replenishment of resource  
mutation rate  
decline of immunity  
replication rate (pathogen space)  
clearance rate of pathogen induced by immunity  
cumulative pathogen load  
cliquishness (contact space)  
degree of crossimmunity  
clearance rate of pathogen  
replacement rate (contact space) 
In this appendix we present an extension of our withinhost model regarding the implementation of crossimmunity. We include the acquisition of immunity from antigenically similar strains and recalculate
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We thank the anonymous reviewers and the editor for their useful comments on the manuscript.