The effects of host contact network structure on pathogen diversity and strain structure Caroline O’F. Buckee*†‡, Katia Koelle†§, Matthew J. Mustard†¶ʈ, and Sunetra Gupta* *Department of Zoology, University of Oxford, Oxford OX1 3PS, United Kingdom; ¶Royal Botanic Gardens, Kew, Richmond, Surrey TW9 3AE, United Kingdom; ʈDepartment of Plant and Soil Science, St. Machar Drive, University of Aberdeen, Aberdeen AB24 3UU, United Kingdom; and §Department of Ecology and Evolutionary Biology, University of Michigan, Ann Arbor, MI 48104 Edited by Kenneth W. Wachter, University of California, Berkeley, CA, and approved May 28, 2004 (received for review March 22, 2004) For many important pathogens, mechanisms promoting antigenic al. (8) defined antigenic distance between strains in continuous variation, such as mutation and recombination, facilitate immune strain space, showing analogous dynamical results for varying evasion and promote strain diversity. However, mathematical levels of cross-immunity, stable homogeneous and heteroge- models have shown that host immune responses to polymorphic neous pathogen populations at low and high levels of cross- antigens can structure pathogen populations into discrete strains immunity, respectively, and traveling wave patterns through with nonoverlapping antigenic repertoires, despite recombination. strain space at intermediate levels. A different approach has Until now, models of strain evolution incorporating host immunity been taken to keep track of multiple strains (9), where the have assumed a randomly mixed host population. Here, we illus- immune status of the hosts at any point in time is taken into trate the effects of different host contact networks on strain account rather than the history of infection for each individual. diversity and dynamics by using a stochastic, spatially heteroge- Although sustained oscillations were not observed, the struc- neous analogue of this model. For randomly mixed populations, turing of the pathogen population was still dependent on mech- our model confirms that cross-immunity to strains sharing alleles at anisms of host immunity. antigenic loci may structure the pathogen population into discrete, Despite differences in the formulation of these deterministic nonoverlapping strains. However, this structure breaks down once models, they produce similar outcomes in terms of the polar- the assumption of random mixing is relaxed, and an increasingly ization of strains in strain space for higher levels of cross- diverse pathogen population emerges as contacts between hosts immunity. However, they all assume that host populations are become more localized. These results imply that host contact well mixed, and do not take stochastic effects and spatial network structure plays a significant role in mediating the emer- heterogeneities into account. Studies have shown that network gence of pathogen strain structure and dynamics. structure can significantly affect the processes occurring on social networks, including the dynamics and evolution of infec- tious diseases (10–13). For example, some have investigated the any important pathogens, such as Neisseria meningitidis effect of network structure on the evolution of disease traits such and Plasmodium falciparum, display structured strain di- M as infectious period and transmission rates (10), as well as versity: highly diverse genotypes are organized into distinct, invasion thresholds for epidemics (11). Others have explored the persisting strains, which can be detected as linkage disequilib- role of spatial contact structure in the evolution of virulence rium between particular genes (for example, see refs. 1 and 2). (12). To date, there have been no studies explicitly investigating Strains can often show cyclical temporal dynamics, with succes- the effects of host contact networks on the interaction of sive types dominating in prevalence within the host population. multiple strains incorporating host cross-immunity, however. Understanding the maintenance of diversity within pathogen Many important multistrain pathogens exist in diverse geograph- populations, and the dynamics of multiple strains, has been a ical environments and in different types of host populations. It focus for many theoretical studies. Previous studies have shown therefore follows that, for directly transmitted diseases, the that interference between strains, either through the prevention social network structure of the host population may impact the of superinfection (3) or from cross-immunity gained by exposure pathogen population by affecting the extent of strain mixing, and to ‘similar’ strains (4, 5), can allow for the stable coexistence of therefore the level of competition and recombination between different strains, as well as sustained oscillations, under certain different strains. In communities where local contacts are the conditions. The latter studies emphasized the importance of primary means of transmission, the population genetics of the cross-immunity as a mechanism for structuring pathogen pop- pathogen may be very different from in large cities where ulations, but assumed that the ‘‘similarity’’ between strains was individuals mix with large numbers of random contacts. based on a single genetic locus. Here we use a stochastic individual-based model (IBM), based For pathogens that undergo antigenic variation, such as on the framework of Gupta et al. (6) described above, to malaria, trypanosomes, and meningitis, multiple genetic loci are investigate the effects of social network structure on the evolu- often important in generating host immune responses. Gupta et tion of pathogen diversity and strain structure. We first restrict al. (6, 7) explicitly accounted for multiple, polymorphic immu- our analyses to regular and random host contact networks, as nogenic loci, by using the overlap between allelic profiles of caricatures of two extreme social network scenarios, and com- different strains to determine the extent of host cross-immunity. pare these networks to each other as well as to stochastic They showed that even high levels of cross-immunity can result mean-field approximations of the IBM to analyze the effect of in stable, diverse pathogen populations. For very low levels, no structured host contact networks on the dynamics of the strains. strain structure is observed. As it increases, unstable structure We then further analyze several small-world host contact net- can emerge, displaying cyclic or chaotic patterns of strain dominance. At sufficiently high levels of cross-immunity, selec- tion by the immune system will result in the dominance of a set This paper was submitted directly (Track II) to the PNAS office. of strains with nonoverlapping antigenic repertoires (which will Abbreviations: IBM, individual-based model; LHS, Latin hypercube sampling; ODE, ordinary not be competing for susceptible hosts). This structure will differential equation. †C.O’F.B., M.J.M., and K.K. contributed equally to this work. persist despite recombination events that generate different BIOLOGY variants, because immune selection against strains that share ‡To whom correspondence should be addressed. E-mail: [email protected]. POPULATION alleles at antigenic loci will suppress their prevalence. Gomes et © 2004 by The National Academy of Sciences of the USA www.pnas.org͞cgi͞doi͞10.1073͞pnas.0402000101 PNAS ͉ July 20, 2004 ͉ vol. 101 ͉ no. 29 ͉ 10839–10844 Downloaded by guest on September 29, 2021 works and argue that the extent of host clustering is the primary network characteristic affecting pathogen strain structure and diversity. The results highlight the importance of considering social network structure in the analysis of pathogen population structuring and dynamics. The Model Hosts. The individual-based model simulates each potential host as a separate entity including its contacts, the strains it is infected with, and its immune response (memory of infection). Each individual has a position in a ring lattice. A host contact network is created at the beginning of a simulation, with every individual in contact with a fixed number of other individuals. This contact network remains constant throughout the simulation for all host contact networks modeled, except the mean-field approximation host network (described below). The structure of the contact network, ranging from regular through small-world to random, is determined by the ␳ parameter, as in Watts and Strogatz (14). ␳ is the probability that an individual will come into contact with a randomly chosen individual rather than a local neighbor in the ␳ ring lattice. Hence, a of 0 means that an individual will only Fig. 1. Strain histograms illustrating diversity and discordance metrics. In this interact with its immediate neighbors, whereas a ␳ of 1 means example, with a three-allele pathogen, eight possible strains can exist in a that the host contact network is a random network, wherein population at any point in time (each consisting of a unique combination of every fixed interaction is with a randomly chosen individual. To three immunodominant loci). Populations in A and B both have the same approximate the mean-field ordinary differential equation discordance value (H ϭ 0.5), but population in A has a more diverse distribu- ϭ ϭ (ODE) model, the stochastic IBM model uses a host contact tion of strains present (D 1.0) than population in B (D 0.33). Populations ␳ ϭ in C and D, although having identical diversity levels (D ϭ 0.79), differ in the network that is random