Feasibility of controlling hookworm infection through preventive chemotherapy: a simulation study using the individual-based WORMSIM modelling framework

Background Globally, hookworms infect 440 million people in developing countries. Especially children and women of childbearing age are at risk of developing anaemia as a result of infection. To control hookworm infection and disease (i.e. reduce the prevalence of medium and heavy infection to <1 %), the World Health Organization has set the target to provide annual or semi-annual preventive chemotherapy (PC) with albendazole (ALB) or mebendazole (MEB) to at least 75 % of all children and women of childbearing age in endemic areas by 2020. Here, we predict the feasibility of achieving <1 % prevalence of medium and heavy infection, based on simulations with an individual-based model. Methods We developed WORMSIM, a new generalized individual-based modelling framework for transmission and control of helminths, and quantified it for hookworm transmission based on published data. We simulated the impact of standard and more intense PC strategies on trends in hookworm infection, and explored the potential additional impact of interventions that improve access to water, sanitation, and hygiene (WASH). The individual-based framework allowed us to take account of inter-individual heterogeneities in exposure and contribution to transmission of infection, as well as in participation in successive PC rounds. Results We predict that in low and medium endemic areas, current PC strategies (including targeting of WCBA) will achieve control of hookworm infection (i.e. the parasitological target) within 2 years. In highly endemic areas, control can be achieved with semi-annual PC with ALB at 90 % coverage, combined with interventions that reduce host contributions to the environmental reservoir of infection by 50 %. More intense PC strategies (high frequency and coverage) can help speed up control of hookworm infection, and may be necessary in some extremely highly endemic settings, but are not a panacea against systematic non-participation to PC. Conclusions Control of hookworm infection by 2020 is feasible with current PC strategies (including targeting of WCBA). In highly endemic areas, PC should be combined with health education and/or WASH interventions. Electronic supplementary material The online version of this article (doi:10.1186/s13071-015-1151-4) contains supplementary material, which is available to authorized users.


This document
This document provides a description of the WORMSIM model structure and default parameter quantification as used in the simulations for the paper Feasibility of controlling hookworm infection through preventive chemotherapy: a simulation study using the individual-based WORMSIM modelling framework by Coffeng et al (Parasites and Vectors 2015). Given the many similarities between WORMSIM and ONCHOSIM, this document's contents are adapted from a previously published formal description of ONCHOSIM [1].

Introduction
WORMSIM is a generalised framework for modelling transmission and control of helminth infections in humans. It is based on previous individual-based models for onchocerciasis (ONCHOSIM), schistosomiasis (SCHISTOSIM), and lymphatic filariasis (LYMFASIM) [2][3][4]. WORSIM simulates the life histories of individual helminths and their transmission from person to person mediated by either a cloud of vectors or an environmental reservoir. In addition, WORMSIM can be used to evaluate the effects of different control strategies, such as vector control and chemotherapy. WORMSIM combines two simulation techniques; stochastic microsimulation is used to calculate the life events of individual persons and their inhabitant parasites, while the dynamics of infective material in the cloud (i.e. the vector population or environmental reservoir) is simulated deterministically.
The version of WORMSIM used in this study (v2.58Ap9) is originally based on the C++ code of ONCHOSIM, but has been redesigned and extended using object-oriented principles and has been programmed in Java. Individual people and mature worms are modelled as distinct objects. WORMSIM is event-driven, which means that time progresses as a result of events (although monthly events are used for most processes). The main advantages of the implementation in Java are improved code quality and therefore easier maintenance and extension. Model input parameters are specified in a structured XML-file, which is automatically validated using an XML Schema before the start of a set of simulations.
The WORMSIM framework is very flexible in that it allows the user to choose probability distributions for stochastic processes (Table A1-1) and functional relationships for deterministic processes (Table A1-2), and to change the associated parameter values. Table  A1-3 provides an overview of the probability distributions, functional relationships, and parameter values used in this study.
In section 3, we describe the general structure of the modelling framework. In footnotes we highlight details and alternative options that are not evident from the mathematical descriptions. In sections 0, we provide instructions for installing and running WORMSIM. In sections 5 and 6, we present annotated WORMSIM input and output files, respectively. Reference numbers (rightmost column) are used in the WORMSIM input file to define probability distributions for stochastic processes. Within WORMSIM, stochastic processes are pre-defined to follow either a continuous or discrete distribution, so each type has its own list of reference numbers.

Domain
Probability density function Reference number

Continuous distributions
where !"#$% = / ! , = ! , and where !" = ln    that covers both STH and filariasis, certain parameters do not apply to  hookworm transmission but are listed anyway for the sake of completeness (indicated where applicable). Further, within the groups of model parameters for transmission and surveys, certain parameters are strongly correlated as indicated by "not identified". Where this is the case, set all but one parameter to arbitrary values, and then used the one parameter to tune the model, as indicated by "used as main parameter…".

General transmission parameters
Relative biting rate (rbr) = 1; applies only to filarial transmission; not identified.
Overall exposure rate of human hosts to central reservoir of infection ( ) Estimated from data (see main manuscript and Additional File 2); not identified, but used as main parameter to set level of transmission. [6] Seasonal variation in contribution to reservoir (mbr) Stable throughout the year. Assumption Transmission probability (v) = 1; not identified.

Individual relative exposure to cloud
Variation in by age and sex (Exa) Linearly increasing from 0 to 1 between ages 0-10 and stable thereafter; no difference between males and females.

Parameter Value Source
Variation due to personal factors (fixed through life) given age and sex ( !"# ) Estimated from data (see main manuscript and Additional File 2).

[6]
Individual relative contribution to cloud Variation by age and sex (Coa) Linearly increasing from 0 to 1 between ages 0-10 and stable thereafter; no difference between males and females.

Assumption
Variation due to personal factors (fixed through life) given age and sex ( !"# ) Assumed to be perfectly correlated with individual exposure to reservoir, given age and sex (i.e. = ).

Life history and productivity of the parasite in the human host
Average worm lifespan (Tl) 3 years [7][8][9] Variation in worm lifespan Weibull distribution with shape 2; i.e. the mortality rate is zero at age zero and then increases linearly with age.

Assumption
Prepatent period (pp) 7 weeks [10,7,8,11] Age-dependent reproductive capacity (R(a)) R(a) = 1 for patent female worms of any age. Assumption Longevity of infective material within host (Tm) 1 month; i.e. the minimum given that transmission is simulated in discrete time steps of one month.

Assumption
Mating cycle (rc) 1 month; i.e. the minimum given that transmission is simulated in discrete time steps of one month.

Density-dependent female worm reproductive capacity
Worm contribution to host load of infective material in absence of density dependence ( ! ) ! = 200 epg/worm; constant, i.e. no variation between human hosts. [12] Hyperbolic saturation: maximum total output of female worm population in a host ( ! ) Several alternative assumptions (see main text).
Exponential saturation of individual female worm productivity per worm present in host ( ! ) ! = 0, i.e. no exponential saturation; this type of saturation is too strong and causes a decline in total egg output once a certain number of worms is present in the host, such that we cannot reproduce distributions of infection intensities as observed in the field. [13][14][15][16][17][18][19]

Morbidity
Disease threshold (Elc) Not used.

Parameter Value Source
Reduction in remaining life expectancy due to disease (rl) Not used.

Infection dynamics in the cloud
Cloud uptake of infectious material ( . ) The identity function, meaning there is no densitydependence in uptake of infective material by the environmental reservoir.

Assumption
Monthly cumulative survival of infective material in the central reservoir ( ) 11.5%; , assuming that survival of infective material is exponential and the average lifespan is two weeks (95%-CI: 0.05-7.38 weeks), based on the notion that average survival is a matter of "weeks" according to literature. [10,11,20] Mass treatment coverage User-defined.

Vector control
Timing Not used.

Coverage
Not used.

Surveys
Dispersal factor for worm contribution to measured density of infective material (d) d = 1; constant, i.e. no additional variation; not identified.

Parameter Value Source
Variability in measured host load of infective material (eggs per gram faeces) Negative binomial distribution with mean and aggregation = 0.4 (estimated from data, see Additional File 2); not identified, but used as main parameter to quantify variation in observed egg counts. [24]

Human demography
The human population dynamics is governed by birth and death processes. We define F(a) as the probability to survive to age a (Table A1- The expected number of births (per year) at a given moment t is given by: number of women in age group a at time t ! annual birth rate in age-group a (Table A1-3).
! number of age-groups considered.
Each month, ! is adapted according to the number of women and their age-distribution.
Once every year, the total number of human individuals is checked; if the total number is larger than a user-defined value, a fraction (also user-defined) is randomly removed from the simulation.
The population distribution resulting from the aforementioned parameters is illustrated in Figure A1

Transmission of infection
In WORMSIM, transmission between individuals is mediated by a conceptual cloud, which either represents a vector population or an environmental reservoir of infection. Individual human hosts are exposed to the infective material in the cloud at varying rates, given their age, sex, and personal factors. Vice versa, individual hosts contribute infective material (larvae or eggs) to the cloud, the amount depending on the number and reproductive statues of worms in the individual, as well as an individual host's contribution rate (depending on age, sex, and personal factors). The amount of infective material in the cloud is updated in discrete monthly time steps. Below, we describe how WORMSIM simulates a full transmission cycle: human exposure to infection and acquisition of worms, dynamics of infection within humans, contribution of infective material to the cloud, and within-cloud dynamics of infective material.

Exposure to infection and acquisition of new worms
First, we define the overall force of infection acting on the human population in month t as a function of the current absolute amount of infective material in the cloud : Here, (zeta) is a scalar representing the overall exposure rate, and v is the probability that an infective particle in the reservoir successfully develops into a parasite life stage that is capable of infecting a human host. a Next, we define the force of infection acting upon individual i of age a and sex s as: Here, ! is the relative exposure of an individual, taking into account age a and sex s, as well as personal factors: with: ! , ! Relative exposure of person with age a and sex s, defined as a linearly interpolated function of user-defined exposure rates for a finite set of ages (for each sex).

!
Exposure index of person i, which captures personal factors related to e.g. behaviour and occupation. ! is assumed to follow a gamma distribution with mean 1.0 and shape and rate (or 1/scale) equal to !"# . The exposure index of a person remains constant throughout lifetime. b a is perfectly negatively correlated with transmission probability v, success ratio sr, relative biting rate rbr, and vector zoophily z. See also the section on contribution of infective material to reservoir. For filarial transmission, we set = 1, quantify v based on vector biology, set sr to a constant value, and calibrate transmission with rbr. For STH, we set = = = 1 , and calibrate transmission with , which has a more natural explanation in the STH context (exposure to the reservoir) than rbr.
b If desired, other continuous probability function can be chosen.
Finally, a person i is assumed to become infected in month m, according to a Poisson process with rate equal to Here, success ratio sr is a constant representing the probability that an inoculated infective particle will develop into a macroparasite. a Finally, ! ( ) represents the impact of the host's immune response in montht t on incoming infections [25]: Here, !"" is the effect of immunity and ! is an individual host's capacity to elicit an immune response, drawn from a positive bounded probability distribution with mean one (e.g. a gamma distribution with equal shape and rate (1/scale) parameters). !"#,! is the cumulatively experienced worm burden of host i in month t, ! is the worm burden of host i in month t, and !"" represents the immunological memory span ( !"" = ! !" ! /! !"" , where !"" is the desired half-life (in months) of the immunological response; vice vera !"" = − ln 2 ln !"" ).

Within-host dynamics of infection
For convenience, in this section we drop the subscript i for individual humans. The lifespan of male and female parasites within human hosts is a random variable: ~Weibull !" , !" , with mean !" years and shape !" . c Once parasites come of age (i.e. when they pass the prepatent age ), female worms can start producing larvae or eggs, and males can inseminate female worms. The reproductive capacity , of a patent female worm of age a at time t is calculated as follows (in absence of drug effects): with: ( ) Potential reproductive capacity of a female worm, A years after reaching patency, defined as a linearly interpolated function of user-defined values for a finite set of ages.
( ) Mating factor at time t The exponential fecundity coefficient at time t, defined as is the number of adult worms (males and females) in a given host at time t, and ! ∈ ℝ ! quantifies the amount of negative density dependence. If = 0, there is no exponential saturation in egg production ( = 1).
To produce larvae or eggs, a female worm must be inseminated each reproductive cycle , defined in terms of months. If insemination took place less than months ago, then = 1. Otherwise, the probability of insemination or reinsemination !"# in month t is given by: c For readers used to the other commonly used parameterization of the Weibull distribution in terms of shape k and scale λ, shape k is α Tl (as described in this document) and scale = !" Γ 1 + 1 !" . with: the number of male ( ! ) or female ( ! ) parasite in the human at time t the number of female worms that a male worm can inseminate per month d If no insemination takes place then = 0 and the female worm has a new opportunity to be inseminated in the next month t + 1. If insemination occurs in month t i then = 1 during t i ≤ t <t i + rc.
The density of larvae (e.g. per skin snip) or eggs (e.g. per gram faeces) in a host at time t is calculated by accumulating the production of all female parasites over the past Tm months within that host: with: the effective parasite load at time t. This intermediate variable describes the female parasite load obtained by weighting each worm according to the mfproductivity during the past Tm months. .
A function that returns the total amount of infective material produced by female parasites. For soil-transmitted helminths, we assume that . is the hyperbolic saturating function / 1 + / , where x is the number of worms, and and are shape parameters, and is a scale parameter. e ! dispersal factor of female parasite j. This is a random variable (mean 1.0) drawn for every "newborn" worm, and accounts for differences in the contribution of female worms to the density at the standard site of the body where samples are taken or vectors bite.
(fixed) lifespan of larvae or eggs within the host in terms of months. ! number of parasites alive during at least one of the months t-1,…,t-Tm.
Host contribution of infective material to the cloud Given the density of larvae or eggs ! in all host in month t, the total amount of infective material that is contributed to the cloud by the host is defined as d When the user specifies a negative value for male potential, female worms can produce larvae or eggs in the absence of male worms.
e Alternatively, a linear or other functional relationship between el and sl can be defined. Saturating functions should not be used when > 1, as this will cause partial saturation of female worm productivity in month t, given the output in months − 1 through − . This will be alleviated in a future version of WORMSIM by Here, is the average contribution rate in month t (monthly biting rate for filarial infections), allowing the user to define a seasonal pattern (in absence of vector control). The relative biting rate rbr is used to scale this seasonal pattern to some desired level. a The function . returns the amount of infective material taken up by the cloud given the density of eggs or larvae ! in a host, possibly in a density dependent manner to represent e.g. limited vectorial capacity to transmit infection. f Last, ! is the relative contribution of an individual, given age, sex, and personal factors: with: ! , ! Relative contribution of person with age a and sex s, defined as a linearly interpolated function of user-defined exposure rates for a finite set of ages (for each sex).
! Contribution index of person i, which captures personal factors related to e.g. behaviour and occupation. ! is assumed to follow a gamma distribution with mean 1.0 and shape and rate (or 1/scale) equal to !"# . The contribute index of a person remains constant throughout lifetime. In WORMSIM default assumption is that ! = ! , unless separate distributions are defined.

Dynamics of infective material in the cloud
For the dynamics of infective material in the cloud we define a deterministic, discrete model: Each month, new infective material !" is added to the cloud, and a fixed proportion of the infective material from the previous month is carried over, assuming exponential survival of infective material. The average life span of infective material in the cloud is then defined as −1 ln( ) months. To simulate filarial transmission, we set = 0, such that the cloud represents a vector population in which larvae survive for much shorter than a month. To simulate hookworm or other STH infections, we set 0 < < 1, such that the cloud represents an environmental reservoir of infection in which infective material survives for a nonnegligible time.

Morbidity
The event of a person developing symptoms at age a depends on the accumulated parasite load ( ) of a person: Each person has a threshold level (denoted as ) at which a person goes blind. follows a probability distribution: ~Weibull !"# , !"# , with mean !"# and shape !"# . Person i goes blind at age a when: f For filarial infection, . typically is a density-dependent function of ! ( ) to represent limited vectorial capacity to transmit infection, whereas for STH, we take . to be the identity function.
At that moment the remaining lifespan at age a is reduced by a factor rl which follows a userdefined distribution on [0,1]. g

Mass treatment coverage and compliance
The primary characteristic of a certain ivermectin mass treatment w is the coverage ! (fraction of the population treated). However, a difficulty in calculating individual chances of participation is that there are several exclusion criteria for the drug. Moreover, compliance to treatment differs from person to person. Exclusion criteria can be either permanent (chronic illness) or transient (e.g. related to age or pregnancy). We define the population that potentially participates as the total population minus a fraction ! that never participates in mass drug administration. The coverage among the potentially participating population ′ ! is now given by: Here, ′ ! cannot be larger be than one (i.e. is capped off at one).
To capture transient contra-indications and other age-and sex-related factors for participation in mass treatment, we define the age-and sex-specific relative compliance ! , (Table A1-3). Note that in ! , only the ratio between the values for the different groups is relevant. Now, the coverage , , in each of the age-and sex-groups (among people that potentially participate) at treatment round w is calculated as: with: , , Number of individuals eligible to treatment in age-group k and sex s at treatment round w.
Total number of eligible individuals at treatment round w.
Finally, the probability to participate in treatment round w for an person i of age-group k and sex s is given by: with: ! Personal compliance index. This is considered as a lifelong property and is generated by a uniform distribution on [0,1] Note that for all k and s the average value of !,! equals , , . Now, in WORMSIM we define 3 coverage models. In model 0, the probability to be treated is as given in equation (17). In model 1, the probability is equal to , , and the compliance index is ignored. The simplest model is model 2 in which the treatment probability simply equals C' w . All models take account of a fraction ! of permanently excluded persons. Figure A1-2 illustrates the impact of different assumptions about compliance patterns on the proportion of the population that has never been treated after a certain number of treatment rounds. Figure A1-2. Relation between compliance patterns and proportion of population that has never been treated. For simplicity, here we assume that compliance is independent of age and sex. Random compliance (solid line) means that eligible individuals participate completely at random (compliance model 1 or 2 in WORMSIM, depending on whether age and sex-patterns are required). Systematic compliance (dotted line) means that an individual either always participates (if eligible) or never (compliance model 1 or 2 in WORMSIM, combined with a fraction of excluded people equal to one minus the target coverage). The mixed compliance pattern (dashed line) means that some individuals are systematically more likely to participate than others (but everyone will participate at some point; compliance model 0 in WORMSIM).

Parasitological effects of treatment
In WORMSIM, drug treatment affects parasites in three main ways. First, a drug may instantly kill a proportion of larvae or eggs present in a host. This proportion is either fixed or a randomly drawn from a user-defined probability distribution for each host and treatment.
Second, a drug may instantly kill pre-patent and adult worms with probability ! in host i. A worm j dies when a random variate ! on [0,1] (redrawn for every new treatment) is smaller than or equal to ! .
Third, a drug may temporarily and/or permanently (and cumulatively) reduce the reproductive capacity of female worm by a proportion ! in host i. In case of a temporary effect, the reproductive capacity will restore within a period ! to its maximum value (in case of any concomitant permanent reductions, reproductive capacity will regenerate to the new, permanently reduced maximum value. The second and third effect are jointly defined as follows:  Shape parameter of the recovery function. In addition to this, we explicitly consider that some persons (a user-defined random fraction of the treated population) do not at all react to the drug during a certain treatment due to malabsorption (e.g. due to vomiting or diarrhoea).

Vector control
Vector control is modelled as a reduction of the monthly biting rates during a given period of time. A period of vector control h is specified as the year + month of the beginning of the strategy and the year + month of the end of a strategy. If a certain month during a period of d days larvicides have been applied, then the reduction in in that month equals d/30 x 100%.

Surveys
During the simulation, user-defined surveys will take place. During a survey, for all simulated individuals the actual number of male and female worms is recorded, and a diagnostic test is simulated to detect infective material (larvae, eggs). For the diagnostic test, the expected amount of infective material per sample (e.g. microfilariae per skin snip, or eggs per gram faeces) for an individual is given by ! ( ).
The actual number of infective particles (microfilariae, eggs, etc.) in the sample is assumed to follow a discrete distribution like a Poisson or negative binomial distribution, with mean h Multiple periods of vector control can be specified, each with its own effectiveness. equal to ! ( ). i At each epidemiological survey a user-defined number of samples are taken from all simulated persons, for which the results are averaged (per simulated person). The results of such a survey are post-processed to arrive at age and sex-specific prevalences and intensities of infection.

Simulation warm-up
In general, before starting simulation of interventions in ONCHOSIM, a 200-year warm-up period is simulated, such as to allow the human and worm population to establish equilibrium levels, given the parameters for average fly biting rate and inter-individual variation in exposure to infection. At the start of the warm-up period, an artificial force of infection is simulated for a user-defined number of years, allowing worms to establish themselves in the human population (here: 5 worms per person per year for 5 years). After the 200 warm-up years, the simulated infection levels are no longer correlated with the initial conditions at the start of the warm-up period. and run your shell script with:

Instructions for installing and running WORMSIM
.\my_test to do 100 runs and aggregate the output of these runs. and run your shell script with:

Mac OS X or Linux
./my_test.sh to do 100 runs and aggregate the output of these runs

Output options
The -d output option will make WORMSIM produce additional detailed output. This output is found in *X.txt and *Y.txt (for instance example_STHX.txt and example_STHY.txt).
The -n output option suppresses all output except the *.log output (e.g. example_STH.log). Either output option can be added to the run command as follows: ./run.sh my_STH.xml 0 99 -d or ./run.sh my_STH.xml 0 99 -n

Annotated input file
The WORMSIM inputfile is an XML file that can be edited with any text editor or alternatively, with an XML editor (such as Oxygen XML Editor). The advantage of using the XML format is that any input file can be validated against an XML Schema (a formal specification of the grammar used in the specific XML dialect used for the WORMSIM input file).
The Wormsim input file is document with an annotated example (annotated-example.xml) and by the overview below. The XML Schema (wormsim.xsd) is documented in great detail in schema-documentation-wormsim.pdf (provided within Additional File 4). The main elements of the Wormsim inputfile are: We will cover each of these elements in more detail below.

<simulation>
The <simulation> element specifies the start year of the simulation, the timing of surveys (i.e. output moments), the number of skin snips taken at each survey and the age classes for output.

<mass.treatment>
The <mass.treatment> element defines parameters for the timing of mass treatment rounds, individual compliance (permanent, temporary and age dependent), and effects of ivermectin on mature worms, mf production by F worms and on mf.

Annotated output files
The WORMSIM standard output (e.g example_STH.txt) is a tab delimited text file with the following columns: year : time (years) N : nr examined N20 : nr examined > 20 yrs old mf+ : percentage with positive skin snip mf+20 : percentage with positive skin snip (> 20 yrs) mfPr : age/sex standardized mf prevalence aNmf : arithmetic mean nr mf per skin snip aNmf20 : arithmetic mean nr mf per skin snip (> 20 yrs) gNmf : geometric meain nr mf per skin snip CMFL : geometric meain nr mf per skin snip (> 20 yrs) bl : percentage blind bl20 : percentage blind (> 20 yrs) blPr : age/sex standardized prevalence of blindness w+ : percentage with at least one adult female worm w+20 : percentage with at least one adult female worm (> 20 yrs) aNw : arithmetic mean nr of adult female worms per person aNw20 : arithmetic mean nr of adult female worms per person (>20 yrs) mbr : monthly fly biting rate in previous month mtp : monthly transmission potential in previous month L1 : mean nr of L1 larvae per 1000 biting flies in previous month L3 : mean nr of L3 larvae per 1000 biting flies in previous month foi : mean force of infection (nr of new adult worms per person) in prev. month The WORMSIM log output (e.g example_STH.log) is a tab delimited text file with output for each simulation run in the following columns: seed : the seed of the random number generator (i.e. run nr) of that specific run year : time (years) mf+ : fraction with positive skin snip mf5+ : fraction with positive skin snip > 5 yrs w+ : fraction with at least one adult female worm N : nr examined aNmf : arithmetic mean nr mf per skin snip aNmf20 : arithmetic mean nr mf per skin snip (> 20 yrs) N20 : nr examined > 20 yrs old CMFL : geometric meain nr mf per skin snip (> 20 yrs) The detailed *X.txt output (e.g example_STHX.txt) contains sex and age specific output with the following columns: year : time (years which results in the following output columns: --1 : percentage of M in that age group with average skin snip count < 0.5 --1 : percentage of M in that age group with 0.5 <= average skin snip count < 1 --2 : percentage of M in that age group with 1 <= average skin snip count < 2 --4 : percentage of M in that age group with 2 <= average skin snip count < 4 --8 : percentage of M in that age group with 4 <= average skin snip count < 8 -- 16 : percentage of M in that age group with 8 <= average skin snip count < 16 --32 : percentage of M in that age group with 16 <= average skin snip count < 32 --64 : percentage of M in that age group with 32 <= average skin snip count < 64 --128 : percentage of M in that age group with 64 <= average skin snip count < 128 --256 : percentage of M in that age group with 128 <= average skin snip count < 256 --512 : percentage of M in that age group with 256 <= average skin snip count < 512 --1e9 : percentage of M in that age group with 512 <= average skin snip count < 1e9 followed by the same categories for F.