^{1}

^{1}

^{1}

^{2}

^{3}

^{1}

^{*}

The authors have declared that no competing interests exist.

Conducted the modelling: HCT. Advised on the modelling and commented on the manuscript for intellectual input: TSC MW MGB. Conceived the study: MGB. Read and approved the final, submitted version of the manuscript: HCT TSC MW MYOA RKP MGB. Wrote the paper: HCT TSC MW MGB.

Recent studies in Mali, Nigeria, and Senegal have indicated that annual (or biannual) ivermectin distribution may lead to local elimination of human onchocerciasis in certain African foci. Modelling-based projections have been used to estimate the required duration of ivermectin distribution to reach elimination. A crucial assumption has been that microfilarial production by

We modify a deterministic age- and sex-structured onchocerciasis transmission model, parameterised for savannah

There is substantial (biological and programmatic) uncertainty surrounding modelling projections of onchocerciasis elimination. These uncertainties need to be acknowledged for mathematical models to inform control policy reliably. Further research is needed to elucidate the effect of ivermectin on

Studies in Mali, Nigeria, and Senegal suggest that, in some settings, it is possible to eliminate onchocerciasis after 15–17 years of ivermectin distribution. Computer models have been used to estimate the required duration of ivermectin distribution to reach elimination. Some models assume that annual ivermectin treatment reduces the fertility of the causing parasite,

Human onchocerciasis, caused by

The Onchocerciasis Control Programme in West Africa (OCP) started in 1974. The programme was initially based on vector control until, in 1987, ivermectin was registered for human use against onchocerciasis. Thereupon, Merck & Co. Inc. took the unprecedented decision to donate ivermectin for as long as needed to eliminate onchocerciasis as a public health problem

In addition to OCP western extension areas that were treated twice-yearly (e.g. Senegal

Ivermectin is a potent microfilaricide, causing a greater than 90% reduction in skin microfilarial load within a few days, and a maximum reduction of 98–99% two months after treatment

Recent epidemiological and entomological evaluations conducted in Mali and Senegal suggest that 15–17 years of annual (or biannual) ivermectin distribution (in the absence of vector control) may be sufficient to lead to local onchocerciasis elimination in certain foci

Mathematical models such as

Whether or not ivermectin has a cumulative effect on female worm fertility

In this paper, we modify our current onchocerciasis transmission model

We modified our sex- and age-structured deterministic onchocerciasis transmission model

After each dose of ivermectin there is a microfilaricidal effect with 99% efficacy, and a reduction in microfilarial production (embryostatic effect) by fertile female worms

The schematic represents a closed population of adult worms (i.e., no incoming worms due to transmission or worm death).

Although the cumulative reduction proposed in

The model is stratified into four treatment compliance classes: a first group of individuals who take treatment every round; two groups who take treatment every other round alternately, and a fourth group who never take treatment. The latter class represents individuals in the community who are systematic non-compliers, as opposed to a situation in which a proportion of individuals miss some treatment rounds (e.g. because they are absent or pregnant at the time of treatment). The proportion of systematic non-compliers was set at 0.1%, 2%, and 5% to investigate its effect on model outputs. These values were chosen to explore potential variability in this parameter. A recent ivermectin compliance study reported that 6% had never taken the drug over the course of eight consecutive treatment rounds

Human age- and sex-structure reflects the demography in savannah areas of northern Cameroon

The overdispersion parameter for the distribution of adult worms among hosts was as estimated in

The model was used to explore the effect of 15 years of (annual or biannual) mass ivermectin distribution on: a) infection intensity defined as mean microfilarial load per mg of skin in those aged ≥20 years, and b) prevalence of microfilaridermia in the overall population. We choose 15 years as a suitable timescale to investigate the impact of long-term treatment of onchocerciasis with ivermectin, motivated by the epidemiological studies described in

The sensitivity of the above model outputs was explored regarding the following assumptions: 1) cumulative effect of ivermectin on female worm fertility (present vs. absent); 2) overall therapeutic coverage (proportion of the total population receiving ivermectin at each round: 60%, 70%, 80%); 3) proportion of systematic non-compliers (those who never take treatment: 0.1%, 2%, 5%); and 4) treatment frequency (annual vs. biannual). In order to explore the extent to which our results were sensitive to the assumption that biannual treatments each caused the same reduction in fertility of 30% per treatment; we also explored model outputs with a more conservative reduction of 16.5% per 6-monthly treatment (which gives an overall annual reduction of 30%).

Model outputs indicate that the assumption of a cumulative impact of ivermectin on microfilarial production by female

Intensity of infection is quantified as microfilarial load per mg of skin in those aged ≥20 years. The red and blue solid lines represent, respectively, model outputs assuming the operation of a cumulative impact on the fertility of

Assumptions regarding the operation or absence of a cumulative effect of ivermectin on parasite fertility can also influence the expected relative benefits of annual vs. biannual treatment frequency regarding reductions in infection intensity, prevalence, and transmission. In the presence of a cumulative reduction with each treatment round, there is initially a very marked benefit of the biannual distribution on the reduction of parasitological indicators (as the rate of microfilarial production is rapidly reduced). However, after repeated treatments, there would be much less difference in the long-term impact of ivermectin treatment on microfilarial prevalence compared to an annual treatment strategy (

Solid and dashed lines represent, respectively, annual and biannual treatment frequency.

Varying the therapeutic coverage in the overall population, and the proportion of systematic non-compliers had a large influence on the infection intensity achieved at the end of the 15th year of ivermectin distribution. An increased overall coverage, or a decreased proportion of systematic non-compliers lead to lower microfilarial loads 12 months after the 15th year of intervention (

Intensity of infection is quantified as microfilarial load per mg of skin in those aged ≥20 years. The values presented correspond to one year after the 15^{th} treatment (for annual frequency, ^{th} treatment (for biannual frequency,

Mathematical models can play a fundamental role in informing control programmes and strategies, but crucially, policy makers must realise that model outputs are highly dependent on implicit and explicit model assumptions

The data that informed the model in

Since our current model is deterministic, we cannot presently explore the probability of elimination. However, comparison of our projections with those of other models is informative. ONCHOSIM projections indicate that with a coverage of 80%, and an initial intensity of 70 mf/ss (in those aged 20 years and older), a minimum of 25 years of annual ivermectin distribution would be necessary to achieve a 99% probability of elimination

Comparison with provisional thresholds for elimination is also interesting. Operational thresholds based on

Our results are compatible with those of other modelling studies

Biannual ivermectin treatment was found to have a large additional benefit in both reducing microfilarial prevalence and intensity compared to annual treatment when no cumulative reduction in parasite fertility was assumed. When such effect was assumed, the model indicated that there would be an initial substantial benefit (as rates of microfilarial production are reduced quickly) of the biannual strategy, but that there would be relatively little difference in microfilarial prevalence at the end of the 15^{th} year compared to annual treatment (

Varying therapeutic coverage (for fixed non-compliance) had less effect on the impact achieved with a biannual treatment frequency than it had for annual distribution. This can be explained as the model accounts for the fact that if someone misses a treatment round, there is another chance to get treated during that year, ensuring that at least one annual treatment is received. In annual frequency, a missed treatment would result in a gap of at least two years between treatments, allowing microfilaridermia levels to build-up and contribute to transmission in the between-treatments period. This has implications regarding policy decisions in areas that have been found to have low coverage in the past, and highlights the potential benefit of switching to a biannual treatment strategy. In any case, a higher therapeutic coverage would prevent more disease during the intervention as the intensity of infection would decrease more rapidly. Incidence of blindness

Assumptions regarding the proportion of systematic non-compliers were found to be just as important as those for overall coverage when projecting the long-term impact of ivermectin distribution. The proportion of systematic non-compliance (for a fixed level of therapeutic coverage) was also found to have a marked influence on the impact achieved by a biannual strategy, particularly when assuming a cumulative effect of ivermectin; the higher the non-compliance rate, the smaller the benefit of biannual treatment. This indicates that the effect of systematic non-compliance may not simply be overcome by increasing treatment frequency and has implications when considering switching to a biannual treatment strategy, as two areas with the same overall coverage but different proportion of systematic non-compliers may lead to very different results regarding the feasibility of elimination

As control programmes move towards elimination goals, the proportion of systematic non-compliers in the population becomes increasingly important. Studies of coverage and compliance for lymphatic filariasis treatment have indicated that, in addition to heterogeneity in transmission and vector density, and missed rounds of MDA, continuing transmission seems to be linked to rates of systematic non-compliance

Modelling studies should also routinely vary the proportion of systematic non-compliers in addition to levels of treatment coverage as part of their sensitivity analysis to help understand the impact of prolonged treatment in populations. Although there are some data indicating that treatment compliance may depend on host age and sex (Brieger

There is substantially more uncertainty surrounding model-derived projections of the long-term impact of, and feasibility of onchocerciasis elimination with ivermectin distribution than previously recognised. This uncertainty arises from an incomplete understanding of the effects of ivermectin on parasite survival, population structure, and reproductive biology, when the drug is administered at the standard dose annually, biannually (or more frequently, e.g. quarterly). Although the results presented in

Our results indicate that in areas with high baseline endemicity and perennial transmission, 15 years of annual or biannual treatment with ivermectin may not be sufficient to bring infection levels below potential elimination thresholds. Further incorporation of ivermectin effects into models; comparison of perennial vs. seasonal patterns of transmission; consideration of other

(PDF)

(PDF)

(DOC)

We thank all members of the Helminth Ecology Research Group at Imperial College London for valuable comments on preliminary versions of the results presented in this paper.