Modelling exposure heterogeneity and density dependence in onchocerciasis using a novel individual-based transmission model, EPIONCHO-IBM: Implications for elimination and data needs - Fig 4

The EPIONCHO-IBM density-dependent parasite establishment within-humans using the best-fit estimates of the parameters δH0, δH∞ and ch for each value of kE. In panel (a), solid lines show the population mean density dependence with age-, sex- and individual-specific heterogeneity in exposure to vector bites. Dashed lines show the density-dependent establishment function without heterogeneity in exposure using the same parameters. Panel (b) shows the density dependence for 100 individuals in the stochastic setting (each line is for one individual) for each value of kE. The mean of these lines (for each exposure heterogeneity value) gives the solids lines in panel (a). Density dependence parameter values for each value of kE are as in Fig 2. Note that the y-axis label has been abbreviated for presentational purposes; specifically for panel (b) this is ПH(i), in panel (a), we represent the value given by taking the mean output of this function for all individuals in the population with ПH (solid lines), and represent the function without exposure heterogeneity using ПH also (dashed lines).</p

Modelling exposure heterogeneity and density dependence in onchocerciasis using a novel individual-based transmission model, EPIONCHO-IBM: Implications for elimination and data needs - Fig 5

Microfilarial prevalence dynamics during 25 years of annual (a–d) and biannual (e–h) mass drug administration (MDA) with ivermectin for various levels of endemicity, heterogeneity in exposure to vector bites (measured by kE) and the associated density-dependent establishment parameters. The baseline microfilarial prevalence (30%, 50%, 60%, 70%, indicative of hypo-, meso-, hyper-, and high hyperendemicity, respectively) is modelled by increasing the annual biting rate. At each treatment round, 80% of the population receive treatment, excluding children aged kE = 0.3), thin light blue lines (kE = 0.2) and thin dark blue lines (kE = 0.4) are as in Fig 2.</p

Pre-intervention <i>Onchocerca volvulus</i> microfilarial prevalence and intensity vs. the annual biting rate of simuliid vectors.

The predicted microfilarial prevalence (percent) and microfilarial intensity (mean no. of microfilariae, mf, per mg of skin) (from 2 skin snips) for the annual vector biting rates reported in the combined epidemiological dataset (i.e. fitting and validation data, solid colour circles), using the estimated parameters, are represented by solid lines. The best-fit parameter values of the density-dependent parasite establishment within humans were δH0 = 0.186, δH∞ = 0.003 and cH = 0.005 for exposure heterogeneity parameter kE = 0.3 (thick red line); δH0 = 0.385, δH∞ = 0.003, cH = 0.008 for kE = 0.2 (thin light blue line), and δH0 = 0.118, δH∞ = 0.002, cH = 0.004 for kE = 0.4 (thin dark blue line). The EPIONCHO-IBM predictions are based on a host population size of 500 and 100 runs for 80 years to reach endemic equilibrium (human demography was simulated to equilibrium before simulating the epidemiology to equilibrium). The error bars are binomial (Clopper-Pearson) 95% confidence intervals for prevalence and bootstrapped 95% CIs for intensity (for which the raw individual microfilarial intensity data were available [44]). The main vectors in each setting are Simulium damnosum s.s./S. sirbanum (African savannah in Benin, Burkina Faso, Cameroon, Côte d’Ivoire, Ghana, Guinea, Mali, Togo); S. guianense s.l. (Amazonian focus in southern Venezuela) and S. exiguum s.l. (Cayapas focus in Ecuador), all species are without armed cibaria and have vector competence features similar to those of S. damnosum s.s. [7]. Fitting data are from [44, 45, 46]; validation data are from [9, 48, 49, 50]. The prevalence and intensity data points for an annual biting rate of 81,000 were excluded from the fitting of the model as according to [45] a large number of flies were nulliparous.</p

Density dependence in the establishment of adult <i>Onchocerca volvulus</i>.

(a) Density-dependent establishment of worms in the human host (, as described by [18] and using the parameterisation in [6]). The red points represent hypothetical values of δH before and after treatment. δH0 is the proportion of L3 larvae developing to the adult stage within the human host, per bite, when ATP → 0; δH∞ is the proportion of L3 larvae developing to the adult stage within the human host, per bite, when ATP(t) → ∞ and cH is the severity of transmission intensity-dependent parasite establishment. (b) The model and data in [9] are used to produce the equivalent of Dietz’s function [18], for the mean ATP values (black points), and their upper and lower confidence intervals (blue and red respectively) as reported in [9]. The O. volvulus nodule (onchocercoma) establishment rate per village is given by where NERi = ki/ai; ki is the number of nodules palpated in individual i at age ai; Z is the number of people across all villages entering the analysis for which nodulectomy (and paired ATP) data were available for 14 villages in the Onchocerciasis Control Programme in West Africa (OCP) database; n is the population size of the village under consideration; na is the number of people aged a, and za is the number of people aged a across all villages. The incidence of adult worms (parasite establishment rate, PER) in a village is then, , where p is the proportion of nodules accessible to palpation, and m is the average number of adult female worms in a nodule. We set m (which was multiplied by 2 to find the total number of adult worms, assuming a balanced sex ratio) and p to values proposed by [34].</p

Threshold biting rates for each endemic microfilarial prevalence varying the exposure heterogeneity parameter <i>k</i>_E and associated best-fit parameters of the density-dependent parasite establishment within humans.

Endemic prevalence values of 0 indicate annual biting rates (number of bites per person per year) that are below the so-called threshold biting rate (TBR) for transmission (indicating that the basic reproduction number R0 55]. Density dependence parameter values for each value of kE are as in Fig 2 TBR values are 97, 239 and 429 for kE = 0.2, 0.3 and 0.4, respectively.</p

Long-term impact of vaccination on microfilarial load in the absence of ivermectin treatment.

<p>The green <b>(A)</b>, blue <b>(B)</b> and red <b>(C)</b> lines correspond to, respectively, a pre-control endemicity of 40%, 60%, and 80% microfilarial prevalence. The solid lines indicate the pre-control contribution of each group to the overall microfilarial load, which is the product of multiplying the microfilarial age- and sex specific profiles (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3B</a>) times the proportion of hosts in each demographic stratum, i.e. the proportion of hosts in each age and sex group (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2</a>). The sum total of the age- and sex-specific contributions yields the overall mean microfilarial load. The dotted lines correspond to the values after 15 years of vaccination. The shaded area illustrates the reduction in microfilarial load in those aged less than 20 years. Modelling assumptions are as follows: a vaccination programme targeting initially 1–5 year olds with continuous vaccination of one year olds after the first year of the programme; an initial prophylactic efficacy against the development of incoming worms of 50%; an initial therapeutic efficacy against skin microfilarial load of 90%; a mean duration of protective and therapeutic effects of 20 years (rate of decay = 0.05 per year) and an 80% coverage of vaccination.</p

EPIONCHO’s underlying age- and sex-specific exposure and baseline microfilarial load profiles.

<p><b>(A)</b> The age- and sex-specific exposure profiles to blackfly bites calibrated to reproduce the observed pre-control age-dependent microfilarial loads. <b>(B)</b> The age- and sex-specific microfilarial loads in African savannah settings of northern Cameroon [<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.ref032" target="_blank">32</a>]. Note that the fitting was performed using the individual data, not the binned data shown in <a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2B</a>. Note also that the legend on panel <b>(B)</b> applies to both panels <b>(A)</b> and <b>(B)</b>.</p

Performance of M06, M06-2X, and M06-HF Density Functionals for Conformationally Flexible Anionic Clusters: M06 Functionals Perform Better than B3LYP for a Model System with Dispersion and Ionic Hydrogen-Bonding Interactions

We present a comparative assessment of the performance of the M06 suite of density functionals (M06, M06-2X, and M06-HF) against an MP2 benchmark for calculating the relative energies and geometric structures of the Cl^–·arginine and Br^–·arginine halide ion–amino acid clusters. Additional results are presented for the popular B3LYP density functional. The Cl^–·arginine and Br^–·arginine complexes are important prototypes for the phenomenon of anion-induced zwitterion formation. Results are presented for the canonical (noncharge separated) and zwitterionic (charge separated) tautomers of the clusters, as well as the numerous conformational isomers of the clusters. We find that all of the M06 functions perform well in terms of predicting the general trends in the conformer relative energies and identifying the global minimum conformer. This is in contrast to the B3LYP functional, which performed significantly less well for the canonical tautomers of the clusters where dispersion interactions contribute more significantly to the conformer energetics. We find that the M06 functional gave the lowest mean unsigned error for the relative energies of the canonical conformers (2.10 and 2.36 kJ/mol for Br^–·arginine and Cl^–·arginine), while M06-2X gave the lowest mean unsigned error for the zwitterionic conformers (0.85 and 1.23 kJ/mol for Br^–·arginine and Cl^–·arginine), thus providing insight into the types of physical systems where each of these functionals should perform best

Model-predicted proportion of bites taken on each age group.

<p>The product of multiplying the age-and sex-specific exposure profiles to blackfly bites (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g003" target="_blank">Fig 3A</a>) times the proportion of hosts in each age and sex group according to the demographic characteristics of the population (<a href="http://www.plosntds.org/article/info:doi/10.1371/journal.pntd.0003938#pntd.0003938.g002" target="_blank">Fig 2</a>).</p

Additional file 2: of Required duration of mass ivermectin treatment for onchocerciasis elimination in Africa: a comparative modelling analysis

A zip-file, which includes the computer simulation program itself (with the JAVA program code embedded in it), batch files used to run the model, PDF documentation of the XML input, and example input and output files. Instructions on how to run the model are provided in Additional file 1 (ONCHOSIM simulation program.zip). (DOCX 15 kb