Bayesian true prevalence estimation of brucellosis in sheep, goats, cattle and camels in southeast regions of Iran

Brucellosis is worldwide one of the most prevalent zoonotic diseases with serious public health hazard affecting domestic livestock and causing economic losses. Objective of this study is to estimate the true prevalence of brucellosis in livestock, specifically cattle, sheep, goats and camels, using a novel Bayesian latent class model, adjusting for the imperfect sensitivity and specificity of the applied tests, where the second test was restricted only to first test‐positive samples.


| INTRODUC TI ON
Brucellosis is worldwide one of the most prevalent zoonotic diseases with serious public health hazard affecting domestic livestock and causing economic losses.Currently, it is endemic in many developing countries and only some developed countries have achieved freedom from infection (Zhang et al., 2018).Among brucella species identified four of them are zoonotic (Brucella melitensis, Brucella abortus, Brucella suis and Brucella canis), targeting cattle, sheep, goats, swine and canids (Hull & Schumaker, 2018).Furthermore, camels are highly susceptible to brucellosis caused by B. melitensis and B. abortus (Gwida et al., 2012).
Brucella spp.are Gram-negative bacteria that belong to the family Brucellaceae, named after Sir David Bruce, who isolated B. melitensis (B.melitensis) in 1887 from British soldiers who died from fever in Malta (Golshani & Buozari, 2017).Until now, brucellosis remains endemic and a major public health problem in the Mediterranean region, Middle East, parts of Africa and Asia (Bagheri Nejad et al., 2020).Its high public health concern was neglected in many developing countries as Iran, where in most parts of the country the disease is endemic and especially in areas where human lives are in a close contact with livestock (Golshani & Buozari, 2017).In Iran, the livelihood of more than half of the rural population depends on farming and livestock rearing (Kamalzadeh et al., 2008).According to recent reports of the Statistical Centre of Iran, the livestock population of Iran currently consists of 46.7 million sheep, 16.7 million goats, 5.41 million cattle and 155 thousand camels.Less than 15% of the overall livestock population is raised in the southeast region of Iran (Statistical Centre of Iran).However, rural communities lack awareness regarding disease status in Iran, transmission routes, risk factors and its high public health concern, thus highlighting the need to place priority towards surveillance programmes to control the disease (Behzadifar et al., 2021).A first step towards that direction is to evaluate the current disease status of the population, that is important for the planning of public health services.
Brucella spp., as intracellular bacteria, invade, survive and replicate within host cells for a successful infection process (Oliveira, 2021).Brucellae reside mostly within macrophages, where they can suppress specific immune responses, thus establishing an environment suitable for proliferation and causing both acute and chronic infections.The host's immune response is triggered after activation of macrophages, mobilization of the cellular immunity and production of cytotoxic T cells, that induce lysis of the infected macrophages.T lymphocytes are associated with cell-mediated immunity and antibody production (Wyckoff III, 2002).The immune response against Brucella spp.involves production of immunoglobins IgM and IgG that mainly acute and chronic infections respectively.Specifically, IgG responses are rapid and are induced 1 or 2 weeks later than the IgM responses but will last for long periods of time (Godfroid et al., 2010).
Clinical signs of brucellosis involve abortion, infertility and reproductive failure resulting in severe impacts on foetal development (Dadar et al., 2021).The microorganism can be detected in the milk, urine and products of pregnancy, indicating that there is a high risk of transmission from infected animal to persons being employed in animal husbandry.Furthermore, consumption of unpasteurized dairy products is a significant risk factor for brucellosis.Clinical symptoms of human brucellosis are undulant fever, arthralgia and fatigue, while human-to-human transmission is extremely rare (Hull & Schumaker, 2018).
Serological testing for diagnosis of brucellosis is considered an ideal first-line test.Many serological tests have been developed over the last years and have been used to estimate the seroprevalence of brucellosis.It is reported that these methods do not have a perfect discriminatory ability and even though, both the sensitivity (Se) and the specificity (Sp) of these methods have been evaluated, the true disease prevalence adjusting for the imperfect Se and Sp has not been estimated (Godfroid et al., 2010).The objective of this study was to estimate the true prevalence of brucellosis in livestock, using a Bayesian modelling approach, based on RBPT, STAT and iELISA test results collected southeast of Iran (Figure 1).

| Study areas, population and sampling design
A cross sectional study was carried out in three major tropical provinces of southeast Iran including Kerman (located at latitude 30.29 and longitude 57.06), Sistan-Baluchestan (located at latitude 29.85 and longitude 60.02) and Hormozgan (located at latitude 27.75 and longitude 56.50).
A total of 3.5 million sheep (7.5% of total sheep population in Iran), 5.6 million goats (38.9% of total goat population in Iran), 500 thousand cattle (9.25% of total cattle population in Iran) and 85,000 camels (54.83% of total camel population in Iran) are located in the three southeastern provinces of the study area.A total of 157, 205, 210 and 31, sheep, goat, cattle and camels serum samples were taken respectively.Animal and herd level data during sampling were collected in a questionnaire.These three provinces are the highest rearing areas of camels and goats in Iran and most people in these provinces keep a small number of household animals.The study was conducted between July 2020 and June 2021.

| Sample collection, processing and preservation
Blood samples of 5-7 mL volume were collected for serological diagnosis of Brucella-specific antibodies in plain sterile vacutainer tube without anticoagulant from each case.Overall, 603 blood samples from all four species were collected from 16 herds.Specifically, 157 sheep samples from four dual purpose flocks with an average herd size of 250 sheep including more than 70% ewes, 205 goat samples from five multipurpose herds with an average herd size of 350 goats including more than 75% female, 210 cattle samples from four semiindustrial dairy herds with an average herd size of 250 cows and 31 camel samples from three multipurpose herds with an average herd size of 70 camels including more than 85% female.
All blood samples were allowed to clot at room temperature and kept in the refrigerator overnight.Later, sera were separated by centrifuging at 3000 g for 10 min, finally transferred into a sterilized 1.5 mL Eppendorf tube and stored at −20°C until used.

Impacts
• Brucellosis is worldwide one of the most prevalent zoonotic diseases with serious public health hazard affecting domestic livestock and causing economic losses.
• We have constructed a Bayesian latent class model to estimate the true prevalence of disease, assuming the absence of a gold standard.
• The model posits that a second test is only performed if the first test result is positive.

| Serological tests and screening scheme
All samples were initially screened to determine presence of antibodies against Brucella spp. with RBPT.Positive RBPT samples from sheep were furtherly tested by iELISA, while STAT was performed on positive RBPT samples from goats, cattle and camels in the microbiology department lab at the faculty of veterinary medicine, Shahid Bahonar University of Kerman, Iran.

| Rose Bengal agglutination test (RBPT)
RBPT was conducted according to manual of diagnostic tests and vaccines for terrestrial animals, described by OIE (2021).The method qualitatively detects both IgM and IgG (Godfroid et al., 2010).A total of 25-30 μL of each serum sample and an equal volume of antigen were placed in a haemagglutination plate near each other.The serum and antigen were mixed thoroughly using a clean glass rod and the mixture agitated gently for 4 min at room temperature (22°C ± 4°C).
After that, agglutination was immediately read.Any visible antigenantibody reactions (agglutination) were considered to be positive.
A control sample was tested in parallel to verify the sensitivity of test conditions.Positive reactions were investigated using abovementioned confirmatory tests.

| Standard tube agglutination test (STAT)
STAT was performed on doubling dilution of serum from 1:20 to 1:320, as described by OIE (2021).The test tubes were incubated F I G U R E 1 Map of Iran showing the study areas (Southeastern provinces) and symbols representing location of the surveyed farms; green-sheep, brown-goats, blue-camels and grey-cattle.at 37°C ± 2°C for 24 h.Titres higher than 1:160 were determined for positive reactions.STAT detects agglutinin antibodies, of both types but, mainly of the IgM isotype directed against Brucella spp (Godfroid et al., 2010).

| Indirect enzyme-linked immunosorbent assay (iELISA)
iELISA was performed according to Vanzini et al. (1998).Briefly, final dilution of 1:50 of serum samples, positive and negative controls were added to the wells in duplicate and the plates incubated for 1 h at 22°C ± 4°C.After buffer washings, an appropriate dilution of horseradish peroxidase-conjugated monoclonal IgG was added to all the wells followed by 1 h of incubation at 22°C ± 4°C.Subsequently, after another five washings, chromogen substrate was added and after 15 min incubation at room temperature, a tetramethylbenzidine (TMB) stop solution was added.Colour development was assessed using an ELISA reader (Anthos 2020, Austria).The results (OD492-OD620) were expressed as antibody units in comparison with a reference serum.The cut off point for positive results was determined at 20 U/mL.iELISA is considered to detect mainly IgG or IgG sub-classes (Godfroid et al., 2010).

| Bayesian latent class analysis
Bayesian latent class models (BLCMs) are increasingly becoming popular for true prevalence estimation and diagnostic test evaluation (Cheung et al., 2021).BLCMs assume the absence of a gold standard, that is, a diagnostic method with perfect (100%) Se and Sp and treat the infection status as latent (i.e.hidden/unknown).Over the last years, both user-friendly software for BLCM implementation and guidelines for reporting of the design, conduct for studies on diagnostic accuracy and true prevalence estimation have been developed-STARD-BLCM guidelines (Kostoulas et al., 2017).The STARD-BLCM guidelines were followed in this analysis (Kostoulas et al., 2017).

| Definition of infection status
For any BLCM approach, definition of infection status is a crucial step since the infection status is considered unknown.BLCMs create their own probabilistic definition of infection that depends on the tests performed.In this setting, all tests detect humoral immune response, either IgG or IgM, after natural infection of the host; RBPT detects both IgG and IgM, STAT detects mainly IgM, and iELISA detects IgG.Hence, as defined in Pfukenyi et al. (2020), here 'infection' means that a Brucella spp. is present intracellularly and persistent within an animal long enough to produce a detectable humoral immune response at any time during their life.

| Model specification
As mentioned in the description of the screening scheme, a second test is performed only when the sample is RBPT-positive, that is the first performed test.Bayesian approaches allow to estimate the posterior distribution that are proportional to the prior information and the likelihood function.The likelihood function is computed through a statistical model for the observed data (Table 1).
The structure of the model is the same for all species and follows the multinomial distribution, that captures the probability of observing each test combination in each herd for each of the species, as a function of the herd's true disease prevalence and the tests' Ses and Sps.The same model, but with different prior specification was applied separately in each of the four species.However, the model was constructed to estimate the sampled group true disease prevalences, that is the main objective of this work.
According to Table 1, only three test result combinations can be observed in each herd, and Equation (1) describes the probability of observing each one of them: (1) i: herd number, T + : positive test result, T − : negative test result, pi i : i-herd true prevalence of disease, Se: Sensitivity and Sp: Specificity.
Here, pi i denotes each herd's true prevalence and can be modelled hierarchically to estimate the overall true prevalence of disease (sampled group prevalence), by adding two extra parameters (called hyperparameters); -expresses the average population prevalence and -describes the variance of the prevalence (Equation 2) (Hanson et al., 2003).

| Prior distribution
In a BLCM approach, prior distributions have to be specified for all parameters of interest.In this setting, each herd for each of the species offers two degrees of freedom, while the parameters of interest, for each species are six; two parameters associated with the sampled group prevalence (μ, γ) and four with the test characteristics of the two applied diagnostic methods (Se 1 , Se 2 , Sp 1 and Sp 2 ), assuming that the test characteristics remain constant between herds of the same species.Generally, it is necessary that the degrees of freedom offered from the data have to be equal or higher than the number of parameters interest to have an identifiable model.However, this condition is described as necessary but not sufficient for model identifiability (Meletis et al., 2022).Hence, informative prior information for the characteristics of the applied tests were introduced in the analysis.Specifically, the posterior estimates for the Se and Sp of RBPT, STAT and iELISA published in Rahman et al. (2013) were used as prior information for this study.Priors were specified with the beta distribution and the distributions were estimated with the PriorGen R-package (Kostoulas, 2018).Here, the same prior distributions for the tests' characteristics were used for all species.Table 2 summarizes the prior estimates and associated beta distributions for this analysis.Uninformative prior distributions were used for the prevalences, that are the main objective of this study.Specifically, uninformative priors for μ and γ, were specified with the beta and the gamma distribution respectively (see Table 2).

| Software and model diagnostics
The model was run in the R programming language, using the runjags R-package (Denwood, 2016;R Core Team, 2021).The model was run for 30,000 iterations of three chains, with a burn-in phase of 4000 iterations.All checks, as described in Toft et al. (2007), suggested that convergence had occurred and autocorrelations had dropped off.

| RE SULTS
Posterior medians and 95% probability intervals (PIs) for all parameters of interest for each species are summarized in Table 3.The μ and γ parameters provide information about the overall animal-level true prevalence, while it is also possible to estimate the true prevalence of disease for all herds included in the study (Table 4).
Overall, the Ses and is of all tests are very high, and similar between species.Specifically, in sheep, iELISA was found to be more sensitive, but less specific compared to RBPT; Ses of RBPT and iEL-ISA, respectively, 0.83 (95% PI 0.65; 0.98) and 0.92 (0.86; 0.96) and Sps of RBPT and iELISA is 0.98 (0.97; 0.99) and 0.9 (0.84; 0.96).On the other hand, in goats, cattle and camels, the Sps of the applied tests (RBPT and STAT) were similar, a 98% posterior median and a 95% PI between 97% and 99%.STAT was more sensitive in goats and cattle and less sensitive compared to RBPT in camels.However, the 95% PI for the Se of STAT in camels is very wide, that highlights a high amount of uncertainty around that parameter value.
Regarding true prevalence estimation, the μ parameter describes the average sampled group prevalence and γ expresses the heterogeneity (between-group variance) of the prevalence.Hence, posterior median (95% PI) for the average true prevalence for sheep, goats, cattle and camels is 18% (4%-43%), 19% (7%-37%), 16% (5%-34%) and 18% (1%-48%) respectively.Brucellosis seems more prevalent in goats, sheep and camels than in cattle.The last column of Table 3 gives the estimates of the between-herd heterogeneity of true prevalence, where sheep and camels have the lowest posterior median compared to goats and cattle.Table 4 provides the posterior estimates (median-95% PIs) for the true prevalence for all the herds of the study.Most of the herds have posterior medians between 12% and 19%, while 3/16 herds have true prevalence median estimate below 5%.(Esmaeili, 2014).

| DISCUSS ION
From 2003, control    programme was based on the mass vaccination of lambs and kids at the age of 4-7 months, using full doses (1-3 × 10 9 colony-forming units [CFU]) of Rev.1 vaccine, and based on the immunization of the adult female animals with the reduced doses of the vaccine TA B L E 3 Posterior estimates (median-95% probability intervals [PIs]) for the sensitivity (Se) and specificity (Sp) of RBPT, STAT, iELISA and true prevalence for sheep, goats, cattle and camel (μ-mean population prevalence, γ-heterogeneity/variance of prevalence).
Cross-classified results of RBPT, STAT and iELISA.
TA B L E 1 a Positive.b Negative.c Indirect ELISA.d Standard tube agglutination test.e Rose Bengal plate agglutination test.f Not performed.
Median and 2.5thpercentile values and corresponding beta distributions for the sensitivity and specificity priors of the applied tests and the prevalence.
a Sensitivity.b Specificity.c Average population prevalence.d Variance of the prevalence.e Mean (Variance). of brucellosis for sheep, goats, cattle and camels from samples collected in southeast regions of Iran.The objective of this study was to estimate the true prevalence of brucellosis, adjusting for the Ses and and-slaughter campaign was conducted in adult sheep and goats using RBPT, SAT and 2ME tests Posterior estimates (median-95% PIs) for the true prevalence, herd size for all the herds of the study.
*Probability interval.TA B L E 4