A stochastic model for head lice infections

An SIS epidemic model with individual variation

We study an extension of the stochastic SIS (Susceptible-Infectious-Susceptible) model in continuous time that accounts for variation amongst individuals. By examining its limiting behaviour as the population size grows we are able to exhibit conditions for the infection to become endemic.

Measuring Infection Transmission in a Stochastic SIV Model with Infection Reintroduction and Imperfect Vaccine

An additional compartment of vaccinated individuals is considered in a SIS stochastic epidemic model with infection reintroduction. The quantification of the spread of the disease is modeled by a continuous time Markov chain. A well-known measure of the initial transmission potential is the basic reproduction number [Formula: see text], which determines the herd immunity threshold or the critical proportion of immune individuals required to stop the spread of a disease when a vaccine offers a complete protection. Due to repeated contacts between the typical infective and previously infected individuals, [Formula: see text] overestimates the average number of secondary infections and leads to, perhaps unnecessary, high immunization coverage. Assuming that the vaccine is imperfect, alternative measures to [Formula: see text] are defined in order to study the influence of the initial coverage and vaccine efficacy on the transmission of the epidemic.

Deterministic approaches for head lice infestations and treatments

Pediculus humanus capitis are human ectoparasites which cause infestations, mostly in children, worldwide. Understanding the life cycle of head lice is an important step in knowing how to treat lice infestations, as the parasite behavior depends considerably on its age and gender. In this work we propose a mathematical model for head lice population dynamics in hosts who could be or not quarantined and treated. Considering a lice population structured by age and gender we formulate the model as a system of hyperbolic PDEs, which can be reduced to compartmental systems of delay or ordinary differential equations. Besides studying fundamental properties of the model, such as existence, uniqueness and nonnegativity of solutions, we show the existence of (in certain cases multiple) equilibria at which the infestation persists on the host’s head. Aiming to assess the performance of treatments against head lice infestations, by mean of computer experiments and numerical simulations we investigate four possible treatment strategies. Our main results can be summarized as follows: (i) early detection is crucial for quick and efficient eradication of lice infestations; (ii) dimeticone-based products applied every 4 days effectively remove lice in at most three applications even in case of severe infestations and (iii) minimization of the reinfection risk, e.g. by mean of synchronized treatments in families/classrooms is recommended.

Head lice predictors and infestation dynamics among primary school children in Norway

BACKGROUND

Health providers need to know which measures to take and children to prioritize in order to decrease costs associated with head lice infestations.

OBJECTIVE

Our aim was to determine the most important predictors for head lice and identify the major drivers of an infestation outbreak in a low-prevalence area.

METHODS

The study was based on three datasets of head lice prevalence (retrospective, point prevalence and prospective approach) from primary school children (ages 6-12) at 12 schools in Oslo, Norway. The tested predictors were siblings with lice, individual and household characteristics as well as class and school affiliation. Self-reported monthly incidences (prospective approach) of head lice were used to evaluate infestation dynamics.

RESULTS

Infested siblings strongly increased the odds of head lice infestation of school children (odds ratio 36, 26 and 7 in the three datasets) whereas having short hair halved the odds. Household characteristics were of minor importance, and class affiliation proved more important than school affiliation. Having head lice in one school term increased the odds of an infestation in the next, but this effect diminished over time. About 97% of all self-reported infestations were noted in two consecutive months or less.

CONCLUSIONS

With the exception of hair length, we have found that individual and household characteristics are of minor importance to predict head lice infestations in a low-prevalence country and that unnoticed transmissions in school classes and families are likely to be the major driver upon outbreaks.

On the Markovian approach for modeling the dynamics of nosocomial infections

We analyze the dynamics of nosocomial infections in intensive care units (ICUs) by using a Markov chain model. Since population size in the ICU is small, in contrast to previous studies, we concentrate on the analytical solution rather than using simulation. We investigate how changes in the system parameters affect to some important behavioral indicators of the spread of the pathogen. We also present an exact measure of the number of secondary cases of infection produced by one colonized patient.

On the exact measure of disease spread in stochastic epidemic models

The basic reproduction number, R₀, is probably the most important quantity in epidemiology. It is used to measure the transmission potential during the initial phase of an epidemic. In this paper, we are specifically concerned with the quantification of the spread of a disease modeled by a Markov chain. Due to the occurrence of repeated contacts taking place between a typical infective individual and other individuals already infected before, R₀ overestimates the average number of secondary infections. We present two alternative measures, namely, the exact reproduction number, Re0, and the population transmission number, Rp, that overcome this difficulty and provide valuable insight. The applicability of Re0 and Rp to control of disease spread is also examined.

The deterministic limit of a stochastic logistic model with individual variation

We consider a Markov chain model similar to the stochastic logistic model except that it allows for variation amongst individuals in the population. We prove that as the population size grows, the process can be approximated by a deterministic process. The equilibrium points of the limiting process and their stability are determined. Applications to modelling epidemics and metapopulations are discussed.

Head lice in Norwegian households: actions taken, costs and knowledge

INTRODUCTION

Head lice infestations cause distress in many families. A well-founded strategy to reduce head lice prevalence must shorten the infectious period of individual hosts. To develop such a strategy, information about the actions taken (inspection, treatment and informing others about own infestations), level of knowledge and costs is needed. The present study is the first to consider all these elements combined.

MATERIALS AND METHODS

A questionnaire was answered by 6203 households from five geographically separated municipalities in Norway.

RESULTS

94% of the households treated members with pediculicides when head lice were discovered. Nearly half of the households checked biannually or not at all. Previous occurrence of head lice and multiple children in a household improved both checking frequency and method. More than 90% of the households informed close contacts about their own pediculosis. Direct costs of pediculosis were low (less than €6.25 yearly) for 70% of the households, but the ability to pay for pediculicides decreased with the number of head lice infestations experienced. One in three households kept children from school because of pediculosis. Other widespread misconceptions, such as that excessive cleaning is necessary to fight head lice, may also add unnecessary burden to households. School affiliation had a significant effect on checking frequency and method, knowledge and willingness to inform others about own pediculosis.

CONCLUSIONS

Increased checking frequencies appear to be the most important element to reduce head lice prevalence in Norway and should be a primary focus of future strategies. National campaigns directed through schools to individual households, might be an important tool to achieve this goal. In addition to improving actions taken, such campaigns should also provide accurate information to reduce costs and enhance the level of knowledge about head lice in households.

Head lice prevalence among households in Norway: importance of spatial variables and individual and household characteristics

Head lice prevalence varies greatly between and within countries, and more knowledge is needed to approach causes of this variation. In the present study, we investigated head lice prevalence among elementary school students and their households in relation to individual and household characteristics as well as spatial variables. The investigation included households from 5 geographically separated municipalities. Present infestations among household members as well as previous infestations in the household were reported in a questionnaire. In elementary school students prevalence was low (1·63%), but more than one-third of the households (36·43%) had previously experienced pediculosis. Prevalence was higher in elementary school students than in other household members, and highest in third-grade children. Prevalence was also influenced by the school attended, which suggested that interactions between children in the same school are important for head lice transmission. Previous occurrence of head lice in homes also increased the risk of present infestation. Prevalence of previous infestations was higher in households with more children and in more densely populated municipalities, indicating that the density of hosts or groups of hosts influences transmission rates. These results demonstrate that information of hosts' spatial distribution as well as household and individual characteristics is needed to better understand head lice population dynamics.

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

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.

Stochastic epidemic models revisited: analysis of some continuous performance measures

We deal with stochastic epidemic models having a set of absorbing states. The aim of the paper is to study some continuous characteristics of the epidemic. In this sense, we first extend the classical study of the length of an outbreak by investigating the whole probability distribution of the extinction time via Laplace transforms. Moreover, we also study two almost new epidemic descriptors, namely, the time until a non-infected individual becomes infected and the time until the individual is removed from the infective group. The obtained results are illustrated by numerical examples including an application to a stochastic SIS model for head lice infections.

On the number of recovered individuals in the SIS and SIR stochastic epidemic models

The basic models of infectious disease dynamics (the SIS and SIR models) are considered. Particular attention is paid to the number of infected individuals that recovered and its relationship with the final epidemic size. We investigate this descriptor both until the extinction of the epidemic and in transient regime. Simple and efficient methods to obtain the distribution of the number of recovered individuals and its moments are proposed and discussed with respect to the previous work. The methodology could also be extended to other stochastic epidemic models. The theory is illustrated by numerical experiments, which demonstrate that the proposed computational methods can be applied efficiently. In particular, we use the distribution of the number of individuals removed in the SIR model in conjunction with data of outbreaks of ESBL observed in the intensive care unit of a Spanish hospital.

Using dynamic stochastic modelling to estimate population risk factors in infectious disease: the example of FIV in 15 cat populations

BACKGROUND

In natural cat populations, Feline Immunodeficiency Virus (FIV) is transmitted through bites between individuals. Factors such as the density of cats within the population or the sex-ratio can have potentially strong effects on the frequency of fight between individuals and hence appear as important population risk factors for FIV.

METHODOLOGY/PRINCIPAL FINDINGS

To study such population risk factors, we present data on FIV prevalence in 15 cat populations in northeastern France. We investigate five key social factors of cat populations; the density of cats, the sex-ratio, the number of males and the mean age of males and females within the population. We overcome the problem of dependence in the infective status data using sexually-structured dynamic stochastic models. Only the age of males and females had an effect (p = 0.043 and p = 0.02, respectively) on the male-to-female transmission rate. Due to multiple tests, it is even likely that these effects are, in reality, not significant. Finally we show that, in our study area, the data can be explained by a very simple model that does not invoke any risk factor.

CONCLUSION

Our conclusion is that, in host-parasite systems in general, fluctuations due to stochasticity in the transmission process are naturally very large and may alone explain a larger part of the variability in observed disease prevalence between populations than previously expected. Finally, we determined confidence intervals for the simple model parameters that can be used to further aid in management of the disease.

Epidemiology of Pediculosis capitis in elementary schools of Buenos Aires, Argentina

The infestation with the human obligate ectoparasite Pediculus humanus capitis De Geer is a common public health problem affecting mainly schoolchildren worldwide. The aim of the present study was to investigate the infestation levels of head lice in elementary schools from Buenos Aires with resistant levels to permethrin >100. A total of 1,856 children aged 3-13 years old from eight selected elementary schools were examined for head lice. Pediculosis was observed in all the studied schools. The overall infestation rate was 29.7%. Girls were statistically significant more infested than boys, with infestation rate values of 36.1% and 26.7%, respectively (P < 0.0001). Only 42 of the infested girls (12%) and 23 of the infested boys (11.4%) had >10 lice on their hair. The proportions of infested children-both girls and boys-in each age group were not found to differ significantly from one another. The infestation rate among schools varied from 19.12% to 42.74%. This indicated that pediculosis is relatively common in elementary schools from Buenos Aires, and those levels are of epidemic importance. The differences of pediculosis among the studied schools could be explained by the different control strategies applied by parents or advisors to eradicate head lice.

Integrating stochasticity and network structure into an epidemic model

While the foundations of modern epidemiology are based upon deterministic models with homogeneous mixing, it is being increasingly realized that both spatial structure and stochasticity play major roles in shaping epidemic dynamics. The integration of these two confounding elements is generally ascertained through numerical simulation. Here, for the first time, we develop a more rigorous analytical understanding based on pairwise approximations to incorporate localized spatial structure and diffusion approximations to capture the impact of stochasticity. Our results allow us to quantify, analytically, the impact of network structure on the variability of an epidemic. Using the susceptible–infectious–susceptible framework for the infection dynamics, the pairwise stochastic model is compared with the stochastic homogeneous-mixing (mean-field) model—although to enable a fair comparison the homogeneous-mixing parameters are scaled to give agreement with the pairwise dynamics. At equilibrium, we show that the pairwise model always displays greater variation about the mean, although the differences are generally small unless the prevalence of infection is low. By contrast, during the early epidemic growth phase when the level of infection is increasing exponentially, the pairwise model generally shows less variation.