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Of lice and math: using models to understand and control populations of head lice.

Laguna MF, Laguna MF, Risau-Gusman S - PLoS ONE (2011)

Bottom Line: In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways.It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations.For both cases we assess the impact of several collective strategies of treatment.

View Article: PubMed Central - PubMed

Affiliation: Consejo Nacional de Investigaciones Cientficas y Técnicas and Centro Atómico Bariloche, Bariloche, Río Negro, Argentina. lagunaf@cab.cnea.gov.ar

ABSTRACT
In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations. We analyze two scenarios: One where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ("superspreader"). For both cases we assess the impact of several collective strategies of treatment.

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Intrinsic growth rate.Behaviour of the intrinsic growth rate for a lice population as a function of the average of daily eggs laid by a single female. The rest of the parameters that define the population are taken from [8] (Takano-Lee curve) and [23] (Evans/Smith curve). The vertical line shows the position of the critical value of daily eggs.
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pone-0021848-g002: Intrinsic growth rate.Behaviour of the intrinsic growth rate for a lice population as a function of the average of daily eggs laid by a single female. The rest of the parameters that define the population are taken from [8] (Takano-Lee curve) and [23] (Evans/Smith curve). The vertical line shows the position of the critical value of daily eggs.

Mentions: With our model it is possible to estimate how much certain vital parameters should change to achieve an effective control of population growth. Mathematically, the critical value for a given parameter is defined as the value for which the evolution matrix has . In other words, the critical value separates the parameter region for which the population increases exponentially () from the region of parameters for which it becomes extinct (). Applying this to fertility, we have found that the critical value for the number of daily eggs laid by each female is approximately 1 egg per week (both for TL and ES data), which is much less than the ‘natural’ value (see Table 1). Furthermore, Fig. 2 shows that, when considered as a function of the daily number of eggs, grows rapidly in the vicinity of the critical value. Thus, even a small increase on the critical number of daily eggs produces a significant intrinsic growth of the population. Studies carried out with lice fed on rabbit blood [31], [32] have shown that, even when rabbits are specifically immunized (which should have a stronger effect than an spontaneously triggered immune response), the effect on female lice is to diminish the number of eggs laid to 1 or 2 per day, which is far from the critical value. This suggests that it is unlikely that the control of the lice population is done through a lowering of the reproductive success of female lice.


Of lice and math: using models to understand and control populations of head lice.

Laguna MF, Laguna MF, Risau-Gusman S - PLoS ONE (2011)

Intrinsic growth rate.Behaviour of the intrinsic growth rate for a lice population as a function of the average of daily eggs laid by a single female. The rest of the parameters that define the population are taken from [8] (Takano-Lee curve) and [23] (Evans/Smith curve). The vertical line shows the position of the critical value of daily eggs.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3140471&req=5

pone-0021848-g002: Intrinsic growth rate.Behaviour of the intrinsic growth rate for a lice population as a function of the average of daily eggs laid by a single female. The rest of the parameters that define the population are taken from [8] (Takano-Lee curve) and [23] (Evans/Smith curve). The vertical line shows the position of the critical value of daily eggs.
Mentions: With our model it is possible to estimate how much certain vital parameters should change to achieve an effective control of population growth. Mathematically, the critical value for a given parameter is defined as the value for which the evolution matrix has . In other words, the critical value separates the parameter region for which the population increases exponentially () from the region of parameters for which it becomes extinct (). Applying this to fertility, we have found that the critical value for the number of daily eggs laid by each female is approximately 1 egg per week (both for TL and ES data), which is much less than the ‘natural’ value (see Table 1). Furthermore, Fig. 2 shows that, when considered as a function of the daily number of eggs, grows rapidly in the vicinity of the critical value. Thus, even a small increase on the critical number of daily eggs produces a significant intrinsic growth of the population. Studies carried out with lice fed on rabbit blood [31], [32] have shown that, even when rabbits are specifically immunized (which should have a stronger effect than an spontaneously triggered immune response), the effect on female lice is to diminish the number of eggs laid to 1 or 2 per day, which is far from the critical value. This suggests that it is unlikely that the control of the lice population is done through a lowering of the reproductive success of female lice.

Bottom Line: In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways.It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations.For both cases we assess the impact of several collective strategies of treatment.

View Article: PubMed Central - PubMed

Affiliation: Consejo Nacional de Investigaciones Cientficas y Técnicas and Centro Atómico Bariloche, Bariloche, Río Negro, Argentina. lagunaf@cab.cnea.gov.ar

ABSTRACT
In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations. We analyze two scenarios: One where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ("superspreader"). For both cases we assess the impact of several collective strategies of treatment.

Show MeSH
Related in: MedlinePlus