Acta Biotheoretica

, Volume 60, Issue 4, pp 333–356 | Cite as

Aggregation and Competitive Exclusion: Explaining the Coexistence of Human Papillomavirus Types and the Effectiveness of Limited Vaccine Conferred Cross-Immunity

Regular Article


Human Papillomavirus (HPV) types are sexually transmitted infections that cause a number of human cancers. According to the competitive exclusion principle in ecology, HPV types that have lower transmission probabilities and shorter durations of infection should be outcompeted by more virulent types. This, however, is not the case, as numerous HPV types co-exist, some which are less transmissible and more easily cleared than others. This paper examines whether this exception to the competitive exclusion principle can be explained by the aggregation of infection with HPV types, which results in patchy spatial distributions of infection, and what implications this has for the effect of vaccination on multiple HPV types. A deterministic transmission model is presented that models the patchy distribution of infected individuals using Lloyd’s mean crowding. It is first shown that higher aggregation can result in a reduced capacity for onward transmission and reduce the required efficacy of vaccination. It is shown that greater patchiness in the distribution of lower prevalence HPV types permits co-existence. This affirms the hypothesis that the aggregation of HPV types provides an explanation for the violation of the competitive exclusion principle. Greater aggregation of lower prevalence types has important implications where type-specific HPV vaccines also offer cross-protection against non-target types. It is demonstrated that the degree of cross-protection can be less than the degree of vaccine protection conferred against directly targeted types and still result in the elimination of non-target types when these non-target types are patchily distributed.


Human Papillomavirus vaccination Competitive exclusion Competitive coexistence Patchiness SIS model 


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© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.The University of Notre Dame AustraliaBroadwayAustralia

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