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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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Related in: MedlinePlus

Average durations and number of necessary applications of different treatments.Average durations are shown in panel A and the number of necessary applications to cure the infestation are shown in panel B. Results correspond to several treatments, when they are successful, and are shown as a function of the fraction of lice eliminated by each application. Squared symbols are systematic treatments, whereas the rest are non systematic ones. Full symbols correspond to daily applications that are stopped when less than  mobile lice remain in the population. Empty symbols correspond to an application every 3 days.
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pone-0021848-g006: Average durations and number of necessary applications of different treatments.Average durations are shown in panel A and the number of necessary applications to cure the infestation are shown in panel B. Results correspond to several treatments, when they are successful, and are shown as a function of the fraction of lice eliminated by each application. Squared symbols are systematic treatments, whereas the rest are non systematic ones. Full symbols correspond to daily applications that are stopped when less than mobile lice remain in the population. Empty symbols correspond to an application every 3 days.

Mentions: Turning now to non systematic treatments, we assume that the threshold refers exclusively to mobile lice, because eggs are not only difficult to detect, but it is usually not easy to distinguish between live and dead eggs. The effect of using different threshold values and several application frequencies are shown in Figs. 4, 5 and 6, which present the results of simulations of the model. In Figs. 4(B), 5(A) and 6(A) we plot the average duration of the treatments. It is interesting to compare these times for systematic and non systematic treatments: from Fig. 4(B) we see that if the applications have a reasonable efficacy (i.e. when the daily fraction of killed lice is larger than ), applying the treatment every day as long as there is at least one mobile lice () is less effective than applying it systematically every 4 days ().


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

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

Average durations and number of necessary applications of different treatments.Average durations are shown in panel A and the number of necessary applications to cure the infestation are shown in panel B. Results correspond to several treatments, when they are successful, and are shown as a function of the fraction of lice eliminated by each application. Squared symbols are systematic treatments, whereas the rest are non systematic ones. Full symbols correspond to daily applications that are stopped when less than  mobile lice remain in the population. Empty symbols correspond to an application every 3 days.
© Copyright Policy
Related In: Results  -  Collection

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

pone-0021848-g006: Average durations and number of necessary applications of different treatments.Average durations are shown in panel A and the number of necessary applications to cure the infestation are shown in panel B. Results correspond to several treatments, when they are successful, and are shown as a function of the fraction of lice eliminated by each application. Squared symbols are systematic treatments, whereas the rest are non systematic ones. Full symbols correspond to daily applications that are stopped when less than mobile lice remain in the population. Empty symbols correspond to an application every 3 days.
Mentions: Turning now to non systematic treatments, we assume that the threshold refers exclusively to mobile lice, because eggs are not only difficult to detect, but it is usually not easy to distinguish between live and dead eggs. The effect of using different threshold values and several application frequencies are shown in Figs. 4, 5 and 6, which present the results of simulations of the model. In Figs. 4(B), 5(A) and 6(A) we plot the average duration of the treatments. It is interesting to compare these times for systematic and non systematic treatments: from Fig. 4(B) we see that if the applications have a reasonable efficacy (i.e. when the daily fraction of killed lice is larger than ), applying the treatment every day as long as there is at least one mobile lice () is less effective than applying it systematically every 4 days ().

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