transmission intensity and the patterns of onchocerca volvulus ...

Am. J. Trop. Med. Hyg., 67(6), 2002, pp. 669–679 Copyright © 2002 by The American Society of Tropical Medicine and Hygiene

TRANSMISSION INTENSITY AND THE PATTERNS OF ONCHOCERCA VOLVULUS INFECTION IN HUMAN COMMUNITIES Ń ˜ EZ, RICHARD C. COLLINS, CHARLES H. PORTER, MARK P. LITTLE, AND MARIÁ-GLORIA BASA DAVID BRANDLING-BENNETT Department of Infectious Disease Epidemiology, and Department of Epidemiology and Public Health, Imperial College School of Medicine, St. Mary’s Campus, London, United Kingdom; Centro Amazónico para Investigación y Control de Enfermedades Tropicales, Estado Amazonas, Venezuela; Departments of Entomology and Veterinary Science, College of Agriculture, University of Arizona, Tucson, Arizona; Division of Parasitic Diseases, National Center of Infectious Diseases, Centers for Disease Control and Prevention, Atlanta Georgia; Pan American Health Organization, Washington, District of Columbia

Abstract. We focus on possible constraints upon Onchocerca volvulus establishment in humans in relation to exposure rates to infective larvae (L3) as measured by the annual transmission potential (ATP). We use mathematical and statistical modeling of pre-control west African (savanna), Mexican, and Guatemalan data to explore two hypotheses relating human infection to transmission intensity: microfilarial (mf) loads either saturate with increasing ATP or become (asymptotically) proportional to the ATP. The estimated proportion of L3 developing into adult worms ranged from 7% to 0.3% (low and high intensity areas, respectively). Relationships between mf prevalence and both mf and transmission intensity were nonlinear and statistically similar between west Africa (Simulium damnosum s.l.) and Meso America (S. ochraceum s.l.). This similarity extended to the relationship between mf intensity and ATP. The critical biting rates for onchocerciasis introduction and persistence (which depended on vector competence and host preference), were approximately 10-fold higher in settings where onchocerciasis is transmitted by S. ochraceum than in those where the vector is S. damnosum. A role for focal vector control in Mexico and Guatemala, in addition to nodulectomy and ivermectin, is suggested. establishment, could be encapsulating a variety of other regulatory processes affecting, among others, parasite survival, parasite fecundity, and host survival. The relationship between intensity of mf infection, blindness, and higher death rates among the blind has been described for west African savanna settings,12–14 but this would be chiefly observed in the older age groups and mainly limited to the blinding strain of the parasite. Although densitydependent regulation of mf production has been suggested,15 this phenomenon has not been substantiated by other researchers in either O. volvulus16 or O. ochengi.17 In other filarial species such as Wuchereria bancrofti in humans18 and Brugia pahangi in the cat model,19,20 there is no evidence of saturation of mf output at high parasite densities (a pattern that would indicate the operation of density-dependent checks on per capita fecundity). In contrast, there are strong indications in favor of the operation of exposure-dependent, and possibly immunologically mediated, constraints on infection rates.21–25 These mechanisms would act mainly against incoming parasites, not upon established worms.26–28 In consequence, we focus upon parasite establishment within humans, although our approach is more phenomenological than mechanistic, i.e., we do not intend to model, at this stage, the precise nature of the underlying processes by which such constraints operate. This paper explores the relationship between pre-control entomologic indices of transmission intensity (ABR and ATP) and human infection data (mf prevalence and intensity) from endemic communities where the simuliid vectors lack (west Africa) or possess (Meso America) well-developed cibarial armatures.29 Datasets are used from Cameroon, Burkina Faso, Côte d’Ivoire, Mexico, and Guatemala to explore functional relationships and estimate parameter values to be used in models of onchocerciasis population biology that incorporate regulatory processes in the definitive host. Such models already include vector-parasite density-dependent interactions that would translate into the observed ATP values.1,7

INTRODUCTION At the start of the 21st century onchocerciasis or “river blindness” still poses a threat to public health in many tropical regions of Africa and more focally in Latin America despite a concerted research effort and high expenditure on control programs. Although much research has been conducted on the biology and epidemiology of the host-parasite interaction, relatively little is known about the population dynamics of the parasite in terms of the key regulatory constraints on population growth. In an attempt to further understanding of such processes, a number of researchers have explored the properties of simple and complex mathematical models of the transmission dynamics of human onchocerciasis.1 Considerable progress has been made concerning the regulatory constraints operating within the vector,2–6 with some progress being recently made in investigating those acting within the human host.7,8 A previous mathematical model9 used an empirical relationship between the observed mean microfilarial (mf) load per milligram of skin per person in the community and the intensity of transmission in such a community, measured by the annual transmission potential (ATP). The ATP represents the total number of infective (L3) larvae potentially received by a person exposed to the diurnal bites of Simulium flies during a whole year.10,11 It is quantified as the product of the annual biting rate (ABR) and the mean number of L3 larvae indistinguishable from Onchocerca volvulus per biting fly. The relationship of Dietz,9 based on data for west African savanna villages located in Burkina Faso, Côte d’Ivoire, and Cameroon, suggested that the mean mf load of the village might increase with increasing ATP at two successively differing rates. A steeper initial slope would imply a higher initial fraction of L3 larvae reaching the adult stage within the human host when ATP values are small. A subsequent, lower slope would represent a smaller proportion of L3 larvae attaining maturity when ATP values are large. However, this empirical relationship between L3 input and mf output within the human host, hinging mainly on constraints to parasite

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Ń ˜ EZ AND OTHERS BASA

MATERIALS AND METHODS West African data sources. Parasitologic data. The parasitologic information from West African savanna settings, for which there is also accompanying entomologic detail regarding biting rates and transmission potentials, has already been presented.7 These investigators also show pre-ivermectin mf prevalence and intensity data from 25 villages in the Vina valley of northern Cameroon. In all these villages, the vectors are mainly the savanna members of the S. damnosum complex, i.e., S. damnosum s.s. and S. sirbanum. Infection prevalence and intensity data from Burkina Faso and Côte d’Ivoire30 and from Cameroon31 were adjusted for age and sex according to a standard population of the Onchocerciasis Control Program (OCP) in West Africa.32 Values from the Vina valley in northern Cameroon were standardized by age and sex from raw data33 using the direct method.34 Earlier data from Cameroon35 had also been age- and sex-adjusted by the direct method. Village mf load is reported as the arithmetic mean no. per person (ⱖ 5 years old) of mf/mg of skin in snips incubated for 24 hours (including negative individuals). When reported incubation period of biopsies was less than this, values were corrected according to standardized criteria36 that had been successfully applied previously.2 When mf burden was presented per skin snip (buttocks only),31 an average weight of 2.0 mg/snip was used.9 Because some investigators30 gave only geometric means (iliac snips), their values are those presented by Dietz,9 who calculated arithmetic averages from the original data set at OCP headquarters. The remaining data35 are arithmetic mean nos. of mf/mg of buttock biopsies. Entomologic data. The ABR and ATP values (the latter based on total number of L3, not just in the fly’s head) are as previously published,30,35,37 with the exception of the localities of Koumbán and Bédara in Cameroon, for which no

single ATP value was given.35 These investigators reported that in Koumbán the ATP at the Vina du Nord beach (4,400 L3/person-year) was nearly 2.5 times as high as that in the village itself (1,800). We have calculated a weighted mean ATP value with proportional contributions of 0.75 for the beach and 0.25 for the village (resulting in an average of 3,750 L3/person-year) to reflect their observation that frequent visits by the villagers to the riverside at the times of peak fly biting activity are likely to have increased the overall ATP of Koumbán to nearer the level estimated for the beach. In contrast, for Bédara, a weighted mean of 6,925 L3/person-year, with proportions of 0.25 for the beach (Mbéré River, ATP ⳱ 19,000) and 0.75 for the village (well at village, ATP ⳱ 2,900), would reflect the observation that although this community already had the highest transmission potential, visits by some individuals to the river might have further increased its overall ATP value.35 It is also possible that the infection patterns of those visiting the beach, and therefore exposed temporarily to very high numbers of parasites, would have been different from those of people with lower but more continuous exposure in the village itself. Unfortunately, the data in the report by Duke and others35 do not permit exploration of this issue. These investigators have postulated that economically viable villages could not have been located at sites with the extreme ATP values (of the blinding form of the parasite) observed in some river beaches of the savanna areas as in those of the Mbéré rapids. Meso American data sources. Parasitologic data. Table 1 shows data for Mexico and Guatemala, where the main vectors are members of the S. ochraceum complex. The data from Guatemala38 were adjusted for age and sex using the direct method. Original records were used to calculate mf prevalence and village mf load as described earlier in this report. Additional data from Guatemala,39,40 as well as data

TABLE 1 Dataset from Guatemala and Mexico used, together with a published West African dataset,7 for the estimation of parameter values k(M), ␦H0, ␦H⬁, cH0, and cH⬁* Locality

Country

ABR

ATP

Pobs (%)

Panimaquib El Jardín Jalapa Nueva América Hoja Blanca Patrocinio Los Ríos Cuauhtémoc Providencia Sta. Emilia Los Tarrales Golondrinas Guachipilín Pacajal Rosario Zacatonal Tarrales TZ Morelos Los Andes El Vesubio Sta. Isabel Panajabal

G G M M M G G M G G G M G G M

8,277 8,800 9,821 33,127 33,672 40,150 53,801 72,124 – 78,612 92,585 96,378 105,120 – 136,328

0 19 0 99 8 – – 0 – 736 350 171 – – 545

13.8 33.6 41.1 46.4 22.7 31.8 41.9 18.9 38.1 88.0 64.6 69.1 64.3 74.4 79.0

G M G G G G

166,782 179,951 301,065 336,867 550,559 –

568 432 331 2,077 2,202 –

76.3 66.0 74.0 86.8 90.2 91.4

Mobs (mean no. of mf/mg)

Mest (mean no. of mf/mg)

Lobs (mean no. of L3/fly)

References

– 2.9 5.0 – 1.4 – – – 9.0 64.3 18.2 – – 30.9 –

0.7 – – 7.2 – 3.1 5.7 1.1 – – – 22.5 17.7 – 38.0

0.0000 0.0022 0.0000 0.0030 0.0002 – – 0.0000 – 0.0094 0.0038 0.0018 – – 0.0040

38, 44 38, 44 41, 47 42, 46 41, 47 40 40 42, 46 38 39, 45 38, 44 42, 46 40 38 42, 46

37.5 – – 50.7 66.9 118.0

– 19.3 28.9 – – –

0.0034 0.0024 0.0011 0.0062 0.0040 –

39 48 39, 45 43, 38 38, 44 38

* The main vectors in Meso America are species of Simulium cochraceum s. l. ABR ⳱ annual biting rate; ATP ⳱ annual transmission potential; Mobs ⳱ observed age- and sex-adjusted microfilarial (mf) load; Mest ⳱ mf load estimated from Pobs (observed standardized mf prevalence) using equation 1 with parameter values for Meso American settings (see Materals and Methods); Lobs ⳱ observed number at equilibrium of infective (L3) larvae; G ⳱ Guatemala; M ⳱ Mexico; TZ ⳱ transmission zone.

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from Mexico,41,42 were also collated. Standardization of skin incubation times followed the criteria described for the west African data. Entomologic data. The ABR and ATP values for Guatemala are as previously40,43,44 or calculated from original datasets.39,45 Data from pre-control entomologic surveys in Mexico were also used.46–48 In both west Africa and Meso America, only villages at (pre-control) endemic equilibrium, with local as opposed to migrant populations, were included. The resilient and stable nature of non-intervened macroparasite populations is confirmed by the fact that in those villages common to the studies in Cameroon and Guatemala, mf prevalence and intensity remained remarkably constant, although parasitologic surveys had been conducted 10−15 years apart. Although removal of onchocercal nodules (harboring the adult worms) has been carried out in Mexico and Guatemala, it has been shown that, on its own, nodulectomy has limited impact upon overall parasite population abundance.1 Data analysis. Model fitting and parameter estimation. The models that follow were fitted to the data by Bayesian Markov Chain Monte-Carlo (MCMC) techniques49 using the Windows version of BUGS (Bayesian inference Using Gibbs Sampler).50 Vague (normal or gamma) priors were assumed. The numbers of people infected with mf were assumed to be binomially distributed, and after a square-root transformation, the mean number of mf/mg was assumed to be normally distributed. Various diagnostic MCMC statistics were calculated, including the convergence statistic of Gelman and Rubin.51 These showed that a “burn-in” of 30,000 samples was required for the analysis of the relationship between mf prevalence and mf intensity, but that a “burn-in” of 10,000 iterations was adequate to achieve convergence in the modeling of the relationship between mf load and the ATP. After burn-in, 40,000 further iterations were carried out in all cases for computation of mean parameter values and their 95% Bayesian credible intervals (BCI). In those cases where it was required to test whether a parameter was significantly greater than zero, Bayesian P values were derived, corresponding to the proportion of the parameter’s posterior distribution to the left of zero. Relationship between infection prevalence and intensity. The following expression (derived from the negative binomial distribution)52,53 was fitted to the relationship between the proportion of people infected with O. volvulus mf in a village, P, and the mean mf load, M, P= 1−

冉

1+

M k共M兲

冊

− k共M兲

( 1)

Equation 1 was initially fitted to west African and Meso American data separately. For both datasets, a general relationship between aggregation parameter k and mean M was used, k共M兲 = k0 Mk1 + k2

( 2)

which encapsulates the possibilities of k being constant; linear with M, or exhibiting a more complex (power) relationship. Once parameters were estimated, equation 1 allowed M to be obtained iteratively from known P in those cases where only mf prevalence had been reported (Table 1). Since there was no statistically significant difference between both sets of pa-

rameters estimated separately (BCI overlapped), equation 1 was refitted to the combined data (Figure 1A). Microfilarial load and entomologic indices. The relationship between the mean no. of mf/mg per person examined in the village and the potential number of L3 larvae received annually by a person living in such a village are shown in Figure 2A. Many steps of the parasite lifecycle are involved from the time when L3 larvae are inoculated through Simulium bites and the time when mf appear in the skin of the host: L3 larvae must attain maturity, male and female worms must meet and mate, and inseminated female worms must produce mf that

FIGURE 1. A, Microfilarial (Mf) prevalence (%) in west Africa (squares) and Meso America (triangles) plotted as a function of mf intensity (arithmetic mean no. of mf/mg). The solid line is equation 1 with k(M) ⳱ k0Mk1 for all data combined (see Materials and Methods), with parameter values k0 ⳱ 0.0549 and k1 ⳱ 0.4718. Data from Cameroon are from references 7, 31, and 35; data from Burkina (B.) Faso and Côte (C.) d’Ivoire are from reference 30; data from Mexico are from references 41 and 42; and data from Guatemala are from reference 38. Vertical bars are exact 95% confidence limits. Mexican data were not entered into the analyses but are included in the graph to show agreement with the predicted prevalence. B, Mf prevalence (%) versus ␭ (⳱ annual transmission potential [ATP]: no. of infective larvae [L3] potentially received by a person during a year) on a log-scale. The solid line assumes weaker constraints upon parasite establishment within the human host (␦H⬁ > 0). The dotted line corresponds to saturation of infection levels in the host population with increasing transmission intensity (␦H⬁ ⳱ 0). The fitted model is P* =

冋冉 1−

1+

M*共␭兲 k0共M*共␭兲兲k1

冊

− k0共M*共␭兲兲k1

册

with M* (␭) as in equation 6. Parameters k0 and k1 and the vertical bars are as in A.

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where ␦H is the fraction of L3 larvae attaining maturity within the human host (the probability that an infective larva develops into an adult parasite); m␤ is the annual biting rate (m ⳱ V/H, the vector to host ratio, and ␤ ⳱ h/g, the biting rate per fly on humans, with h equal to the proportion of human blood meals, and g the average interval between two consecutive blood-meals); L* is the equilibrium mean number of L3 per fly; m␤L* is the equilibrium, pre-control ATP value; ␴W and ␴M are the per capita mortality rates of adult worms and microfilariae, respectively; µH is the per capita death rate of the human host; s is the proportion of adult female worms in the population of mature parasites; ␾ is the mating probability, and F is the per capita fecundity rate of female worms scaled per mg of skin.1,7 Because there is insufficient evidence to date in support of the operation of density-dependent constraints upon worm fecundity and survival, we will assume that the main mechanism regulating parasite population abundance acts through limiting parasite establishment.54,55 Our conjecture is that the proportion of L3 larvae developing into adult worms, ␦H, is dependent on the intensity of exposure to L3 larvae as measured by the ATP. A functional relationship between ␦H and ATP from Dietz9 has consequently been modified as follows, ␦H共␭兲 =

FIGURE 2. A, Infection intensity (mean no. of microfilaria [mf]/ mg) as a function of annual transmission intensity (ATP) for west African (squares) and Meso American (triangles) communities (equation 5). The solid lines corresponds to incomplete regulation of parasite burdens (␦H⬁ > 0), with the thin line assuming ␦H0 ⳱ 16% and the thick line estimating ␦H0 ⳱ 7%. The dotted line assumes saturation (␦H⬁ ⳱ 0). Parameter values are as given in the Materials and Methods. Under the conjecture of limitation, village mf loads (all individuals ⱖ 5 years old) would saturate at 84 mf/mg; under the alternative hypothesis, mf loads would become asymptotically proportional to transmission intensity, with the fraction of infective (L3) larvae developing into adult parasites ␦H⬁ ⳱ 0.3-0.4% as ATP → ⬁. Date from localities in Cameroon are from references 35 and 37, and data from localities in Burkina (B.) Faso and Côte (C.) d’Ivoire are from reference 30. Data from localities in Mexico and Guatemala are as in Table 1. B, Estimated proportion of infective larvae attaining maturity within the human host as a function of transmission intensity according to model assumptions (equation 5). Lines are as in A.

共␦H0 + ␦H⬁cH␭兲共1 + cH ␭兲

( 5)

where ␭ (⳱ m␤L*) is the annual transmission potential; ␦H0 and ␦H⬁ are the fractions of parasites maturing when ATP → 0 or ATP → ⬁, respectively, and cH is a measure of the constraints acting upon parasite establishment as described later in this report. At endemic equilibrium, equations 3–5 allow the mean mf burden in the village to be expressed as a function of ATP, M*共␭兲 =

s ␾F ␦H共␭兲 ␭ 共␴W + ␮H兲共␴M + ␮H兲

( 6)

Equation 6 was fitted to the data in Figure 2A to test the following hypotheses: if cH ⳱ 0, parasite establishment is constant and the relationship between equilibrium mf load and ATP is linear; if cH > 0, the relationship may be more complex, with ␦H⬁⳱ 0 describing limitation of mf burden in the human host population as the intensity of transmission increases with maximum village mf load given by s␾ F␦H0

finally reach the dermis. Assuming that the population of infective stages is at equilibrium within the vector population, i.e., that the mean no. of L3 larvae per fly, L, remains approximately constant with time (in comparison to changes taking place in the population of longer-lived parasite stages such as adult worms and mf), it is possible to write two differential equations describing, respectively, the rate of change with respect to time of the mean no. of adult worms, W, and of dermal mf, M (ignoring explicit age-structure of host and parasite populations), dW共t兲 = ␦H m ␤ L* − 共␴W + ␮H兲W共t兲 dt

( 3)

dM共t兲 = 共s ␾ F兲W共t兲 − 共␴M + ␮H兲M共t兲 dt

( 4)

cH共␴W + ␮H兲共␴M + ␮H兲 The alternative hypothesis, ␦H0> 0, would imply that there is incomplete regulation of worm burden with increasing ATP. When ␦H⬁⳱ 0, cH would be a straightforward measure of the severity of limitation of parasite success within humans. In the alternative model (␦H0> 0), parameter cH is the reciprocal of the ATP value for which ␦H(ATP) ⳱ (␦H0+␦H⬁)/2, and thus is an inverse measure of the transmission intensity at which there occurs a reduction in the probability of parasite establishment within the human host. The former will be referred to as cH0, corresponding to the case when ␦H⬁ ⳱ 0. The latter will be represented by cH⬁ to indicate that it will apply when␦H⬁ > 0. Table 2 lists the parameter values used in estimating ␦H0, ␦H⬁, cH0, and cH⬁ using equation 6. The relationship between village mf load and annual biting

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TABLE 2 Values of human and vector host-related parameters* Parameter

Definition

µH µV ␾

Per capita mortality rate of human host Per capita mortality rate of vector host Mating probability

F s ␴W ␴M ␴L l/g

Per capita fecundity rate of female worms per mg of skin Proportion of female worms Per capita mortality rate of adult worms Per capita mortality rate of microfilariae Per capita mortality rate of infective larvae Biting frequency g ⳱ interval between two consecutive blood-meals (length of gonotrophic cycle) Proportion of infective larvae released per bite

aH

Average

0.02† 26 1† (as W* → 10) 0.6674† 0.5† 0.1† 0.8† 52 104† 0.8†

Minimum

Maximum

0.0167 0.025 12 52† Dioecious, polygamous worms

References

84 85, 86 87

0.5423

0.7926

0.0909 0.5 26 91

0.1111 1.0 104† 122

7 88 89 16 90 91

0.54

1.0

63, 65

* Values of rates and frequencies are expressed per year. Probabilities and proportions are dimensionless. † Denotes values used in models.

rate is shown in Figure 3B. The different lines represent model results for various degrees of vector anthropophagy (as measured by parameter h, the human blood index). Model details are given in the Appendix, with parameter values as in Table 2, the Results, and the corresponding figure legend. RESULTS Figure 1A presents observed and expected mf prevalence as a function of mf intensity for west African and Meso American villages combined. When the general model k(M) ⳱ k0Mk1 + k2 was fitted to the combined data, parameter values were k0 ⳱ 5.35 × 10−2 (95% BCI ⳱ 1.56 × 10−2, 11.65 × 10−2), k1⳱ 4.98 × 10−1 (3.31 × 10−1, 7.23 × 10−1), and k26.83 × 10−3 (−8.34 × 10−2, 7.86 × 10−2). From this it can be seen that parameter k2 was not significantly different from 0 (P ⳱ 0.36, degrees of freedom [df] ⳱ 48) and it was consequently dropped from subsequent analyses. When west African and Meso American data were considered separately, parameter values were k0 ⳱ 5.26 × 10−2 (95% BCI ⳱ 4.34 × 10−2, 6.30 × 10−2) and k1 ⳱ 4.81 × 10−1 (4.31 × 10−1, 5.31 × 10−1) for west Africa (n ⳱ 43) and k0 ⳱ 7.36 × 10−2 (95% BCI ⳱ 4.71 × 10−2, 10.73 × 10−2) and k1 ⳱ 4.19 × 10−1 (3.10 × 10−1, 5.35 × 10−1) for Guatemala (n ⳱ 8). For all data analyzed together, parameter values were k0 ⳱ 5.49 × 10−2 (95% BCI ⳱ 4.60 × 10−2, 6.45 × 10−2) and k1 ⳱ 4.72 × 10−1 (4.27 × 10−1, 5.18 × 10−1). Figure 1B shows, in log-scale, the relationship between the community prevalence of mf infection and ATP for the two conjectures of parasite establishment in the human host. Figure 2A shows the relationship between mean mf load in the village and ATP (n ⳱ 33). This relationship is clearly nonlinear, and estimates of cH were all significantly greater than zero. The thinner of the solid lines assumes that ␦H0⳱ 0.16,9 and estimates ␦H⬁⳱ 4.30 × 10−3 (95% BCI ⳱ 2.81 × 10−3, 5.88 × 10−3) and cH⬁ ⳱ 1.83 × 10−2 (1.41 × 10−2, 2.41 × 10−2). The thicker solid line estimates all three parameters: ␦H0 ⳱ 7.12 × 10−2 (95% BCI ⳱ 3.82 × 10−2, 14.91 × 10−2), ␦H⬁ ⳱ 2.99 × 10−3 (8.51 × 10−4, 5.02 × 10−3), and cH⬁ ⳱ 5.86 × 10−3 (1.75 × 10−3, 16.77 × 10−3). It can be seen that parameter ␦H⬁ is significantly greater than zero (P ⳱ 0.005, df ⳱ 30). The dotted line sets ␦H⬁ to 0 and associated parameter estimates are ␦H0 ⳱ 4.19 × 10−2 (95% BCI ⳱ 2.99 × 10−2, 5.85 × 10−2) and cH0 ⳱ 1.71 × 10−3 (9.61 × 10−4, 2.81 × 10−3). An important result is that in both geographic regions, compa-

FIGURE 3. A, Intensity of microfilarial (mf) infection in the village as a function of the annual transmission potential (ATP) on a logscale. The solid line is for ␦H⬁ > 0; the dotted line is for ␦H⬁ ⳱ 0. For a given ATP value, mf loads are very similar between west Africa (squares) and Meso America (triangles). B, Intensity of mf infection in the village versus the annual biting rate (ABR = m␤) on humans on a log-scale. In contrast to A, west African and Meso American communities fall into two distinct groups, with the former exhibiting lower values of ABR for a given mf density. The lines are model results (M*(m␤)) with ␦H⬁ > 0 and varying parameter h, the fraction of blood meals taken on humans (see Appendix); ␦v0 ⳱ 0.0166 mf-1, cV ⳱ 0.0205 mf-1, and ␣V ⳱ 0.5968 mf-1 for savannah species of Simulium damnosum; and ␦v0 ⳱ 0.0016 mf-1, cV ⳱ 0.1320 mf-1, and ␣V ⳱ 0.4327 mf-1 for S. ochraceum. The remaining parameters are as in Table 2 and the Materials and Methods.

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rable parasite loads develop in humans as a result of similar ATP values. For Figure 2B, the probability of L3 larvae developing into adult parasites within the human host as a function of transmission intensity has been calculated using equation 5. The three lines correspond to the models described for Figure 2A. The values of ATP at which the initially higher parasite establishment success rate would decrease are given by the reciprocal of cH⬁, ranging from 55 to 170 in this paper (equal to 28 in the report by Dietz9). These results indicate that our best model when all data are included (n ⳱ 33) is the one in which all three parameters are significantly different from zero (i.e., the model describing asymptotic proportionality between infection and transmission intensity). However, for two of the villages (Koumbán and Bédara), we had to make some assumptions regarding their ATP value. To test the sensitivity of our results to the magnitudes of these two villages in Cameroon, we refitted the model after their removal (n ⳱ 31). This time, parameter ␦H⬁ was not significantly different from zero (P ⳱ 0.15, df ⳱ 28) when all three parameters were estimated: ␦H0 ⳱ 8.44 × 10−2 (95% BCI ⳱ 2.72 × 10−2, 22.24 × 10−2); ␦H⬁ ⳱ 4.35 × 10−4 (−6.94 × 10−2, 8.85 × 10−3), and cH⬁ ⳱ 9.89 × 10−3 (0.12 × 10−3, 36.89 × 10−3). In the absence of Koumbán and Bédara, the best (most parsimonious) model was therefore the one describing a saturating relationship between mf load and ATP, with ␦H0 ⳱ 4.25 × 10−2 (95% BCI ⳱ 2.99 × 10−2, 5.99 × 10−2) and cH0 ⳱ 1.74 × 10−3 (9.64 × 10−4, 2.92 × 10−3). Figure 3 shows, with log-scaled x-axis, that while similar values of ATP result in similar mf outputs in both west Africa and Meso America (Figure 3A), the biting rates necessary to deliver a given yearly number of L3 larvae per person are very different in these two regions (Figure 3B). Simulium ochraceum s.l. exhibits ABR values that are in general one order of magnitude higher than those of S. damnosum s.l. Figure 3B also shows model outputs for ␦H⬁ > 0 (our best model, see Discussion) varying h, the human blood index. The points at which the lines meet the x-axis indicate the critical biting rates for each value of h, i.e., the values of ABR above which the basic reproductive number of the parasite, R0, would be greater than 1. R0, is a measure of the reproductive success of the parasite between one generation and the next for a given host population in a given environment assuming no constraints on parasite population growth. For macroparasites such as O. volvulus, R0 is defined as the average number of female offspring, themselves reaching maturity, produced by an adult female parasite during her reproductive life span in absence of density-dependent regulation.7 This is the threshold for introduction and endemic persistence of the infection in host populations. The minimum biting rates for endemic onchocerciasis in localities where the main vector species possesses a well-developed cibarial armature (S. ochraceum s.l.) are roughly 10 times as high as those required in localities where the simuliid vectors have unarmed cibaria (S. damnosum s.l.). For the former, and depending on the value of the human blood index, threshold ABRs are roughly 6,000 for h ⳱ 0.99; 8,000 (h ⳱ 0.75); 12,000 (0.5) and 24,000 (0.25). For the latter, minimum ABRs are 580 for h ⳱ 0.99, 860 (h ⳱ 0.67), 2,000 (0.3), and 6,000 (0.1). Critical ABRs are 260 for h ⳱ 0.99, 380 (h ⳱ 0.67), 850 (0.3), and 2,550 (0.1) when ␦H0 is assumed to be equal to 0.16 in west African settings.

DISCUSSION The relationship between the prevalence and intensity of infection with O. volvulus mf appeared to be similar for endemic areas situated both in northern Cameroon and Guatemala (although the latter was a small dataset). This is an important finding since it has generally been thought that patterns of infection in Africa are very different from, and much more severe than, those in Latin America. The prevalence-intensity relationship was somewhat different for localities in Burkina Faso and Côte d’Ivoire, as can be observed in Figure 1A, where the values are consistently situated below the fitted line. Since the data were standardized before proceeding with the analyses, this may reflect true regional differences in parasite distribution among host populations, as has been revealed in human lymphatic filariasis (compare the mf prevalence-intensity relationships for W. bancrofti in Papua New Guinea56 with those for east Africa28). As expected, both the infection prevalence−infection intensity (mf prevalence versus mean no. of mf/mg, Figure 1A) and the infection prevalence−transmission intensity (mf prevalence versus ATP, Figure 1B) relationships are strongly nonlinear. A consequence of this, for the evaluation of control programs in hyperendemic areas, is that mf loads and ATP values would have to be decreased very substantially before noticeable changes in mf prevalence can be expected.57 An additional important result is that we are now able to link transmission intensity with onchocerciasis endemicity across a wide-range of epidemiologic settings in both west Africa and Latin America: a prevalence of mf infection ⱖ 60% (indicative of hyperendemicity) is associated with ATP values ⱖ 100 (L3 in all body regions of the fly) and a village mf load (arithmetic mean) of approximately 20 mf/mg in those individuals ⱖ 5 years old. This confirms the entomologic and parasitologic thresholds obtained for west African savanna populations of O. volvulus and extends them to neotropical foci. The relationship between ATP and the resulting mf load is also very similar between west African savanna localities and those in Meso America (Figures 2A and 3A). The resemblance in infection patterns reported here may lend some epidemiologic support to the finding that parasite isolates from Guatemala are genetically closely related to those of the west African savanna.58 Particularly under the hypothesis of saturation of mf burdens in the human host population with increasing transmission intensity, the relationship between these two variables is again strongly nonlinear. However, under the hypothesis of weaker regulatory constraints to parasite establishment, the relationship becomes asymptotically linear, with a constant (non-zero) probability, equal to ␦H⬁, that an infective larva becomes an adult parasite. This probability, which therefore becomes asymptotically independent of ATP, is equal to 0.003. Under the limitation hypothesis, village mf loads (for those individuals ⱖ 5 years old) would reach a plateau at approximately 84 mf/mg (as ␦H⬁ approaches zero). However, in addition to Bédara, with 119 mf/mg,35 we know of the existence of villages with 108 mf/mg (Babidan) and 122 mf/mg (Koubao), also in proximity to the Mbéré rapids.7 In Guatemala, the village of Panajabal has an infection intensity of 118 mf/mg (Table 1), and in the Orinoco region of southern Venezuela, the village of Obokoa-theri has an estimated mean intensity of 114 mf/mg. Unfortunately, we do not have accom-


panying entomologic data for these locations. Even for the localities with entomologic data, some assumptions had to be made to calculate an average ATP value for two of the Cameroonian villages included in the analysis (Koumbán and Bédara). However, these assumptions were not arbitrary, but followed the field observations of the investigators who collected these data.35 In support of these data, a pre-control relationship between ATP and mf load very similar to that for Koumbán has been recorded in the locality of Coyowë-their in southern Venezuela, with 3,900 L3/person-year and a village mf load of 64 mf/mg.59 The question then arises as to which of the two hypothesis under scrutiny here provides a better fit of the available data. When Koumbán and Bédara are included, the parameter ␦H⬁ is significantly greater than zero (P ⳱ 0.005). However, a re-analysis not considering these two data points indicated that this parameter became non-statistically different from zero (P ⳱ 0.15), with limitation between infection and transmission intensity becoming the most parsimonious model. Behavioral (rather than purely biologic) reasons may favor this hypothesis: the scarcity of villages at the upper end of the ATP spectrum may well reflect the fact that those intense transmission regimes threaten the viability of such communities, particularly in the case of the blinding strain of O. volvulus.35,37 Another important consideration when analyzing the relationship between transmission and infection intensity in human onchocerciasis is that the advent of molecular probes for specific parasite identification60 has confirmed what had long been suspected on morphobiometric grounds: that not all L3 found in samples of S. damnosum s.l. are of human origin. Other species of the genus Onchocerca, such as O. ramachandrini, O. dukei, and O. ochengi, are also present in blackflies in northern Cameroon.61,62 Of particular concern is O. ochengi, the closest phylogenetic relative of O. volvulus and thus the most similar in the infective stage and in sharing the same vectors. The ATP values used here refer to O. volvulus only (as judged by morphologic criteria63 and subsequently confirmed by DNA analysis64). However, those reported for other Cameroonian localities35 are ‘crude’ ATPs and may well overestimate true values. Our greatest uncertainty concerns the probability of parasite establishment within the human host, a parameter not measured by direct observation but, instead, estimated through mathematical and statistical modeling. As a first approximation, we used the value of 16% for ␦H0.9 This value could be further dissected into its components: 0.8, the proportion of L3 larvae released per bite,65 and 0.2, the fraction of L3 that survive and mature into adult worms16 (without considering the risk involved in the passage of larvae into the wound and human tissues). While some investigators assume that 25% of the L3 are lost on the skin,16 others conjecture that this loss amounts to 60%.66 The latter take 0.11 as the fraction of L3 reaching adulthood once into human tissues. Accordingly, their estimates of successful parasite establishment would amount to 12% and 4%, respectively. The percentage of L3 larvae emerging from the fly has been estimated to be 54% instead of 80% if the blood meal is interrupted, 63 and in experimental onchocerciasis in naive chimpanzees, 14% of O. volvulus L3 larvae attained maturity.67 This would give an estimate of 8% for ␦H0 In addition to the previously mentioned 16%, the estimates presented

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here range from 4% (3−6%) for the case of limitation to 7% (4−15%) for the case of asymptotic proportionality, which are consistent with the values mentioned earlier. This contrasts with 0.3% (between 0.1% and 0.5%) for ␦H⬁ at very high ATP values. This agrees with the value of 0.0031 for the proportion of L3 attaining maturity within humans according to the simulation model ONCHOSIM.68 ONCHOSIM does not include major regulatory constraints operating within the human host, and it has been parameterized for the upper end of hyperendemic transmission in the west African savannah, with worm burdens being proportional to transmission intensity (similar to our situation of ␦H⬁ > 0). This estimate is, however, 10 times as large as the value of 0.043% estimated previously for the same parameter and geographic region.9 Looking again at O. ochengi in the cattle host as the possibly closest analog to the human parasite,69 the proportion of infective larvae developing to mature worms decreased from 16% (a mean of 4.4 adults of an average of 27 L3) to 0.5% (16−18 worms of ∼3,000 L3) in experimental infections conducted in Cameroon (Renz A, unpublished data). Our results, therefore, indicate that per capita parasite establishment would decrease with increasing transmission intensity (a measure of cumulative exposure) (Figure 2B). Results from recent filarial modeling work support this important finding. A decrease in the probability of forest O. volvulus L3 larvae attaining adulthood, from 0.09% (for an ATP of ∼400) to 0.02% (for an ATP of ∼4,000), has been estimated (Duerr HP, unpublished data). A monotonically decreasing theoretical probability of L3 establishing in the lymphatics has also been estimated for W. bancrofti, with 0.1%, 0.07%, and 0.02% corresponding to ATP values of, respectively, 10, 100, and ∼300 L3/person-year, respectively, in east African villages.28 When results were analyzed by ABR instead of by ATP, an interesting pattern emerged, since the critical biting rates for endemic onchocerciasis persistence were very different between west Africa and Meso America. In west Africa, endemic villages existed with recorded ABR values of 1,000 (three bites per person per day at Tcholliré, Cameroon), whereas there seemed to be none with less than 8,000 bites/ person-year (approximately 22 bites/person-day) in Mexico and Guatemala. We propose that this approximately 10-fold difference is due, in part, to the fact that the vector competence of ‘armed’ S. ochraceum s.l. is, on average, 10 times lower than that of ‘unarmed’ S. damnosum s.l., as suggested by both natural and experimental infection data. The mean no. of L3 larvae per biting S. ochraceum fly (in the wild) is 0.004 (SD ⳱ 0.002, n ⳱ 12; Table 1), whereas these values were 0.047 (SD ⳱ 0.034, n ⳱ 17, for S. damnosum).7 In fly-feeding experiments, the parasite yield (the proportion of ingested mf developing to L3 larvae measured in groups of flies engorged on mf carriers) ranged from 0% to 2.4% (n ⳱ 27) in S. ochraceum s.l., in contrast to 0–36% (n ⳱ 54) in S. damnosum s.l.3 The minimum vector biting density has been proposed to be an inverse measure of the stability of the host-parasite system; the higher the threshold vector density, the more feasible it is to achieve eradication of the infection using antivectorial measures.70 It has also been suggested that the apparent disappearance of Anopheles-transmitted lymphatic filariasis in some foci may be more due to insecticidal

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reductions in human-mosquito contacts (driving an already low R0 below 1) than to chemotherapy-based perturbations of endemic equilibria below a critical parasite density.71 The argument here is that the possession of a cibarial armature by the dipteran host (present in some simuliid and anopheline vectors of filarial parasites) would operate by reducing ␦V (the probability of successful mf establishment within the vector), producing an increase in the minimum biting rate required for the endemic establishment of the infection. We are not proposing, however, that the presence or absence of a toothed cibarium is the only determinant of vector competence. Classifying onchocerciasis vectors as ‘armed’ or ‘unarmed’ has been a convenient way to include analytical expressions for vector-related parameters into a family of mathematical models that explicitly incorporate the vector component.1 An example of an ‘unarmed’ vector with low vector competence (due to asynchronic larval development), is S. metallicum s.l. in northern Venezuela.5 Other factors such as fly size, vector’s immune response, and gut factors that limit parasite passage, among others, may also contribute to overall vector competence.3 It is also conceivable that vector-related factors are not completely independent from each other. A species with a well-developed armature (which seems to have evolved for reasons other than selection pressures imposed by filarial parasites),72 damages an important proportion of ingested mf. Such a species is, therefore, less likely to be affected by parasite-induced mortality4 or decreased fecundity,73 two components of lifetime fitness. Consequently, this species may have been subjected to lesser evolutionary pressures to evolve effective immune or apoptotic mechanisms against filarial larvae of the kind described for S. damnosum74 (an ‘unarmed’ simuliid). In turn, the parasite may manipulate ‘armed’ vectors as to increase, for instance, their ability to concentrate mf upon feeding, or their host contact rates enhancing an otherwise low chance of transmission. Therefore, the presence of one trait, in this case of a toothed cibarium, may actually represent a number of not necessarily unrelated factors that finally determine vector competence, vectorial capacity, and transmission intensity. The aim of this paper is not, however, to discuss the entomologic determinants of ATP, but to show that similar net transmission levels result in comparable mf loads in the human host (Figures 1B, 2A, and 3A, and equation 6). The relationship between community levels of infection and ATP is still very similar between vectors with or without a well-developed cibarial armature; the difference lies in the critical vector densities. The critical biting rate obviously depends also on host preference by the vector species. Our estimates of critical S. damnosum s.l. annual biting rates, ranging from 260 to 850 for human blood indices between 0.99 and 0.3, compare favorably with 288 (h ⳱ 0.99) and 720 (h ⳱ 0.5)9, using ␦H0 ⳱ 0.16 in both cases. Similarly, estimates for S. ochraceum s.l. varying between 6,000 (h ⳱ 0.99) and 8,000 (h ⳱ 0.75) compare well with the value, obtained for Guatemala, of 7,665 using a catalytic model for the prevalence of infection in humans, but ignoring possible variations in vector anthropophagy.75 Given the difficulties in collecting recently engorged resting blackflies for blood meal identification, estimates of parameter h rely on scarce data and indirect approaches, which are unlikely to provide unbiased estimates of host preference. Only one in three S. damnosum flies was found to have fed on

humans (h ⳱ 0.33) in northern Cameroon.76 Similarly, h was calculated to vary between 0.2 and 0.4 from the proportion of flies harboring infective larvae of human (O. volvulus) as opposed to non-human origin (fly populations at localities such as Touboro and Bonandiga would be located at the upper end of the anthropophagy spectrum).63,77 More recently, and using species-specific DNA probes instead of morphologic characters, maps have been generated of the percentage distribution of O. volvulus (versus. non-volvulus) found in simuliid population samples throughout the OCP area. These maps indicate an increasing proportion of human-derived L3 larvae from northwestern towards southeastern locations within the OCP.78 Our results suggest that of 13 Cameroonian localities, nine were best mirrored by model outputs in which h varied between 0.1 and 0.67, while the remaining four were compatible with values of h between 0.67 and 0.99 (the latter included Touboro and Bonandiga). The villages in Burkina Faso and Côte d’Ivoire all lay between h ⳱ 0.3 and 0.99. In Guatemala, and again based on identification of infective larvae, the human blood index of S. ochraceum s.l. has been assumed to be close to 1.0.79,80 Using the same criteria, it is possible to obtain an estimate of h ⳱ 0.75 for S. ochraceum s.l. populations in some Mexican endemic areas.81 Our results suggest that in some localities, the proportion of blood-meals taken on humans by this vector may be under 0.75 (Figure 3B). This possible variation in human blood index suggests that, contrary to the assumption of constant host preference, embedded in the biting rate term of most vector-borne disease models, parameter h is likely to vary spatially (and probably also temporally) with variation in factors such as total vector abundance and the ratio of human to non-human hosts.82 If this is the case, the basic reproductive ratio of the infection may increase nonlinearly with vector density (in contrast to equation A.2 of the Appendix), with important theoretical and practical implications.83 In conclusion, our work indicates remarkable similarities between the patterns of transmission intensity, infection prevalence, and infection intensity between west African savannah and Meso American localities. We plan to extend this investigation into the recorded patterns of eye disease for both regions. The per larva probability of successful parasite establishment within the human host was estimated to decrease with increasing transmission intensity, a finding substantiated by both experimental and theoretical approaches using animal and mathematical models of filarial parasites. However, this essentially phenomenologic (and deterministic) approach needs to be increasingly replaced by frameworks modeling mechanistically (and stochastically) the interaction between transmission and exposure intensity, experience of infection, and immunologic responses. The higher threshold vector biting rates for onchocerciasis endemicity obtained for S. ochraceum s.l. suggest a role for focal vector control40 in addition to removal of adult worms and ivermectin in Mexico and Guatemala.1 Acknowledgments: We thank Eddie Cupp, Neil Ferguson, Christophe Fraser, and two anonymous referees for helpful comments on the manuscript. María-Gloria Basáñez thanks the Wellcome Trust for grant support of the work conducted during this research between 1996 and 2000. Authors’ addresses: María-Gloria Basáñez, Department of Infectious Disease Epidemiology, Imperial College School of Medicine, St.


Mary’s Campus, Norfolk Place, London W2 1PG, United Kingdom, Telephone: 44-20-7594-3295, Fax: 44-20-7402-2150, E-mail: [email protected]. Dr. Richard C. Collins. P.O. Box 715, Sonoita, AZ 85637, Telephone: 520-455-4615, Fax: 520-455-4616. Charles H. Porter, Division of Parasitic Diseases, National Center of Infectious Diseases, Centers for Disease Control and Prevention, Atlanta, GA 30333, Telephone: 770-488-4108, Fax: 770-488-4838. Mark P. Little, Department of Epidemiology and Public Health, Imperial College School of Medicine, St. Mary’s Campus, Norfolk Place, London W2 1PG, United Kingdom, Telephone: 44-20-7594-3312, Fax: 44-20-74022150. David Brandling-Bennett, Pan American Health Organization, 525 23rd Street NW, Washington, DC 20037, Telephone: 202-9743178, Fax: 202-974-3608.

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APPENDIX The values of M* as a function of the basic reproductive ratio, R0, are given by the real and positive roots of the following fourth degree polynomial assuming ␦H⬁ > 0,

冋册冉冊冋冉冋冉冊冉 ␣vcv ␷

+

+

2

M*4 +

␣vcv ␷

␩⬁R0 + 2

␣v + cv ␷

冊册

M*3

␣v ␣v ␣v ␩⬁R0 + + cv ␩⬁R0 + cv − 共R0 − 4兲 ␷ ␷ ␷

冋冉

␩⬁R0 1 − R0

− 共R0 − 1兲 ⳱ 0

␦H⬁ ␦H0

冊冉冊 −

␣v + cv ␷

冊册

M*2

册

( A.1)

共R0 − 2兲 M*

with ␷=

冉

␴L + ␮v +

冊

共␴W + ␮H兲共␴M + ␮H兲cH⬁ aH , ␩⬁ = , g s ␾ F␦H0

and R0 a linear relationship of ABR as follows,7 R0 =

s␾ F m␤h␦H0␦V0 共␴W + ␮H兲共␴M + ␮H兲␷ g

( A.2)

where ␣V is excess vector mortality due to microfilarial (mf) intake (as a linear term), cV the severity of density-dependent limitation within the fly, ␴L is larval mortality,␮v is the mortality rate of uninfected flies, aH is the proportion of infective (L3) larvae released per bite, g is the mean duration of the interval between two consecutive blood meals (taken here as the mean duration of the gonotrophic cycle), h is the proportion of blood meals of human origin (the human blood index), and ␦V0 the proportion of mf developing within the fly as M → 0. The remaining parameters have been described in the Materials and Methods. The h values for Simulium damnosum s.l. were 0.99;9 0.67;78 and 0.1−0.3.63 The h values for S. ochraceum s.l. were 0.99;79 0.75;81 and 0.25−0.5 to cover most of the remaining villages.