Elsevier

Mathematical Biosciences

Volume 309, March 2019, Pages 163-173
Mathematical Biosciences

A biological model of scabies infection dynamics and treatment informs mass drug administration strategies to increase the likelihood of elimination

https://doi.org/10.1016/j.mbs.2018.08.007Get rights and content

Highlights

  • A compartmental model for infection and treatment dynamics with Scabies Sarcoptei is proposed.

  • Optimisation of timing of mass drug administration (MDAs) is explored.

  • Model captures recrudescence of infection post-MDA that is observed in practice.

  • Eradication under MDAs is unlikely even under ideal conditions.

Abstract

Infections with Sarcoptes scabiei, or scabies, remain common in many disadvantaged populations. Mass drug administration (MDA) has been used in such settings to achieve a rapid reduction in infection and transmission, with the goal of eliminating the public health burden of scabies. While prevalence has been observed to fall substantially following such an intervention, in some instances resurgence of infection to baseline levels has occurred over several years. To explore the biology underpinning this phenomenon, we have developed a theoretical model of scabies life-cycle and transmission dynamics in a homogeneously mixing population, and simulate the impact of mass drug treatment strategies acting on egg and mite life cycle stages (ovicidal) or mites alone (non-ovicidal). In order to investigate the dynamics of the system, we first define and calculate the optimal interval between treatment doses. We calculate the probability of eradication as a function of the number of optimally-timed successive treatment doses and the number of years over which a program is run. For the non-ovicidal intervention, we first show that at least two optimally-timed doses are required to achieve eradication. We then demonstrate that while more doses over a small number of years provides the highest chance of eradication, a similar outcome can be achieved with fewer doses delivered annually over a longer period of time. For the ovicidal intervention, we find that doses should be delivered as close together as possible. This work provides a platform for further research into optimal treatment strategies which may incorporate heterogeneity of transmission, and the interplay between MDA and enhancement of continuing scabies surveillance and treatment strategies.

Introduction

Infections with the mite Sarcoptes scabiei, commonly known as scabies, remain common in many disadvantaged settings. In remote communities in northern Australia, for example, prevalence is as high as 49% while in the Solomon Islands and Fiji prevalence is 43% and 28% [26]. Scabies is highly contagious and causes intense itching on the host [22]. Besides the psychological impact due to the constant itching [14], the scratching leads to a break in the skin layer which creates a pathway for secondary skin infections such as Group A Streptococcus (GAS) to take hold [9]. It has been hypothesized that controlling scabies infections could lead to a reduction in the disease burden attributable to GAS and its sequelae [9]. However, despite multiple trials confirming the short term effectiveness of scabicidal therapies, follow up studies in several communities have shown recrudescence of infection within months to years of treatment cessation [2], [17], [20], [32].

Mathematical models provide useful frameworks in which to consider the drivers of infectious disease, with a view to optimising treatment approaches. To our knowledge, there exist only three models for scabies infection in humans [7], [13], [19], and none of these models attempts to capture the natural history of the mite’s life cycle in relation to the host. This omission is important in understanding intervention effects, as the parasite’s life state can interact critically with treatment success or failure, as we will demonstrate in this paper.

Here, we develop a model of scabies infection and use it to explore the likely impact of mass drug administration treatment strategies. The structure of this paper is as follows: In Section 2, we summarise the biology of the mite and the effect of ovicidal and non-ovicidal treatments. In Section 3, we develop and introduce a compartmental model for scabies, including the effects of different treatment mechanisms. In Section 4, the results of the investigation into the model are presented, and in Section 5, the implications of our investigation are discussed and summarised.

Section snippets

Scabies biology and treatment

The scabies mite progresses through three general life stages: egg, young mite and adult. The eggs are relatively well studied, and are believed to take approximately two days to hatch [5], [10], [31]. The young mite stage is more complex, comprising a number of developmental stages. Initially, mites are considered larvae, and are unlikely to emerge from the burrow in which the eggs were laid. Mites remain as larvae for approximately five days [5], [31], before developing into Protonymphs and

Model development

We introduce a compartmental mathematical model to characterise scabies transmission and treatment in a population with high endemic prevalence, and capture the potential differences between ovicidal and non-ovicidal treatments. First, we develop the model considering the non-ovicidal treatment regime which does not kill the eggs laid by the mite. Later we will consider the model including ovicidal treatment.

In addition to susceptible and infectious states, a population level model of scabies

Results

First, we establish the equilibrium dynamics in the absence of an MDA. Using the mean-field approximation, the model can be divided into three classes: susceptible, infected and latent. The susceptible class consists of the states S and S2, while the infected class consists of Ω{S,S2,G^}. Note that we make an important distinction between an infected and an infectious state. Only individuals who are harboring pregnant mites, and thus in states IA,I^A,I^,I2c,I^2c,I2 and I^2 are classified as

Discussion

We have developed a biologically informed mathematical model of scabies infestations in a population which explicitly accounts for the multiple life stages of the mite and the presence of eggs. While there have been other models of scabies proposed [7], [13], [19], they have not captured the critical features of the life-cycle of the mite. Our model provides a framework within which to explore the different consequences of ovicidal and non-ovicidal treatment strategies. Crucially, the model is

Acknowledgments

M.J. Lydeamore is supported by an Australian Postgraduate Award; J. McVernon is supported by an NHMRC Career Development Fellowship (CDF1061321); J. M. McCaw is supported by an ARC Future Fellowship (FT110100250). D.G. Regan is supported by an NHMRC Program Grant (APP1071269); S. Y. C. Tong is supported by an NHMRC Career Development Fellowship (CDF1145033); We thank the NHMRC Centre for Research Excellence in Infectious Diseases Modelling to Inform Public Health Policy (1078068). This work is

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