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

The University of Notre Dame Australia, PO Box 944, Broadway, NSW, 2007, Australia, .
Acta Biotheoretica (Impact Factor: 0.7). 06/2012; 60(4). DOI: 10.1007/s10441-012-9161-5
Source: PubMed


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.

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    • "This has informed the incorporation of Iwao's model into linear differential equation models (Iwao, 1968; Waters, 2012). A unique feature of Iwao's linear model is that its intercept (a) and slope (b) parameters have been demonstrated to take on particular values when individuals are distributed according to the uniform, Poisson and negative binomial distributions (see Table 1) (Iwao, 1968; Kuno, 1988). "
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    ABSTRACT: Extended logistic and competitive Lotka–Volterra equations were developed by Eizi Kuno to understand the implications of population heterogeneity (especially spatial) for population growth. Population heterogeneity, defined as the presence of individuals in some patches of population and not others, is the resulting expression of a number of processes, including dispersal, habitat heterogeneity and searching behaviour. Kuno's models allow the effect of population heterogeneity (thus defined) on a population at equilibrium to be accounted for without using multi-patch models. This paper demonstrates this for the first time using numerical simulations and presents a more complete mathematical derivation of his models. An extension of Kuno's equations to model predator–prey scenarios with heterogeneity in the prey population is also developed. Analysis of this predator–prey case shows that a patchy distribution of prey facilitates their stable coexistence with predators. This paper has broad implications for ecological modelling because it shows how the effects of a number of population processes, including dispersal, are reflected in the density of populations at equilibrium. Therefore, by adjusting the equilibrium solutions of models, the effects of a number of processes are captured without representing the processes themselves in an explicit way.MSC92B05KeywordsPopulation dynamicsPredator–preyLotka–Volterra
    Ecological Modelling 02/2015; 297. DOI:10.1016/j.ecolmodel.2014.11.019 · 2.32 Impact Factor
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    • "A number of ways of assessing spatial heterogeneity are commonly used in ecological sampling studies, and one of these, Lloyd's index of mean concentration or mean demand (C * ) [14] [18], can be expressed as a linear function of the mean number of individuals in a population [13], enabling it to be easily incorporated in deterministic epidemic and ecological models to model heterogeneity. Whilst C * has been used in this way to account for spatial heterogeneity in the number of infected individuals in different areas when modelling sexually transmitted infections in animal and human populations [5] [26], the assumption that susceptible as well as infected individuals might be nonuniformly distributed in space has not been explicitly modelled. This paper uses C * together with Lloyd's index of interspecific mean crowding, m * xy [18], and Iwao's index of spatial overlap, γ [10] [15], to explicitly model the effect of heterogeneous distributions of infected and susceptible individuals on the dynamics of a simple SIR model. "
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    ABSTRACT: Patchy or divided populations can be important to infectious disease transmission. We first show that Lloyd's mean crowding index, an index of patchiness from ecology, appears as a term in simple deterministic epidemic models of the SIR type. Using these models, we demonstrate that the rate of movement between patches is crucial for epidemic dynamics. In particular, there is a relationship between epidemic final size and epidemic duration in patchy habitats: controlling inter-patch movement will reduce epidemic duration, but also final size. This suggests that a strategy of quarantining infected areas during the initial phases of a virulent epidemic might reduce epidemic duration, but leave the population vulnerable to future epidemics by inhibiting the development of herd immunity. 2010 Mathematics subject classification: 92B05.
    The ANZIAM Journal 10/2013; 54(1-2):23-36. DOI:10.1017/S1446181113000035 · 1.03 Impact Factor
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    ABSTRACT: Human Papillomavirus (HPV) is the most common sexually transmitted infection. In Italy, HPV vaccination is now offered free of charge to 12-year-old females. However, some regional health authorities have extended free vaccination to other age-groups, especially to girls under 18 years of age. We conducted a multicentre epidemiological study to ascertain the prevalence of different genotypes of HPV in young Italian women with normal cytology, with the aim of evaluating the possibility of extending vaccination to older females. The study was performed in 2010. Women aged 16-26 years with normal cytology were studied. Cervical samples were analyzed to identify the presence of HPV by PCR amplification of a segment of ORF L1 (450 bp). All positive HPV-DNA samples underwent viral genotype analysis by means of a restriction fragment length polymorphism assay. Positivity for at least one HPV genotype was found in 18.2% of the 566 women recruited: 48.1% in the 16-17 age-class, 15.4 in the 18-20 age-class, 21.9% in the 21-23 age-class, and 15.5% in the 24-26 age-class; 10.1% of women were infected by at least one high-risk HPV genotype. HPV-16 was the most prevalent genotype. Only 4 (0.7%), 4 (0.7%) and 3 (0.5%) women were infected by HPV-18, HPV-6 and HPV-11, respectively. Of the HPV-DNA-positive women, 64.1% presented only one viral genotype, while 24.3% had multiple infections. The HPV genotypes most often involved in multiple infections were high-risk. A high prevalence was noted in the first years of sexual activity (48.1% of HPV-DNA-positive women aged 16-17 years); HPV prevalence subsequently declined and stabilized.The estimate of cumulative proportions of young women free from any HPV infection at each age was evaluated; 93.3% and 97.1% of 26 year-old women proved free from HPV-16 and/or HPV-18 and from HPV-6 and/or HPV-11, respectively. Our findings confirm the crucial importance of conducting studies on women without cytological damage, in order to optimise and up-date preventive interventions against HPV infection, and suggest that vaccinating 26-year-old females at the time of their first pap-test is to be recommend, though this issue should be further explored.
    BMC Infectious Diseases 12/2013; 13(1):575. DOI:10.1186/1471-2334-13-575 · 2.61 Impact Factor

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