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��ࡱ�>��	������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������y�	��0rbjbj��	; �{�{��,�������������***8b�. <*�e�j ��#$$$�$ &|�&@DeFeFeFeFeFeFe$�g�9jFje9�&�$�$�&�&je$$��e]*]*]*�&$$�]�]*�&De]*]*��8��:$�������@�������(`9�]�e0�et9j�)�j(�:�:�jP?@�&�&]*�&�&�&�&�&jeje]*�&�&�&�e�&�&�&�&��������������������������������������������������������������������j�&�&�&�&�&�&�&�&�&� �:	Foot-and-mouth disease virus transmission and vaccine efficacy in Punjab, Pakistan 
M. Roodgar1, A. M. Perez2,3, S. Grazioli6, G. Ferrari4, E. Khan5, E. Brocchi6, M. Abubakar7 and T.E. Carpenter3
1 Masters in Preventive Veterinary Medicine Program, School of Veterinary Medicine, University of California, Davis, CA, USA
2 CONICET, Facultad de Ciencias Veterinarias UNR, Argentina 3 Center for Animal Disease Modeling and Surveillance (CADMS), Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, Davis, CA, USA 4  Food and Agriculture Organization of the UN Via delle terme di Caracalla, 00153 Rome, Italy 5 NARC Premises Park Road, Chak Shahzad  P.O.Box 1476, Islamabad, Pakistan 6 Istituto Zooprofilattico Sperimentale della Lombardia e dell�Emilia Romagna (IZSLER), Brescia, Italy 7 National Veterinary Laboratory, Islamabad, Pakistan.
 
�
Correspondence:
Andres Perez, Center for Animal Disease Modeling and Surveillance (CADMS), Department of Medicine & Epidemiology, School of Veterinary Medicine, University of California, Davis, CA, United States. Tel.:+1 530 7521063; Fax +1 530 7521618; E-mail:  HYPERLINK "mailto:amperez@ucdavis.edu" amperez@ucdavis.edu




ABSTRACT 
Foot-and-mouth disease (FMD) is an acute disease due to the infection with a Picornavirus that causes vesicular lesions in cloven-hoofed animals HYPERLINK \l "_ENREF_1" \o "Li, 2011 #85"  HYPERLINK \l "_ENREF_1" \o "Forman, 2009 #83" . The objectives of this study were to estimate the adequate daily contact rate (k), the mean number of daily contacts by an individual adequate for the virus transmission, of FMD and the efficacy of FMD vaccines (VE) used in selected districts of the Punjab region of Pakistan. The study population included 1,825 cattle and buffaloes from 35 villages.  A modified Reed-Frost model was used to estimate k and VE for each village. The mean k was 0.12 per day (ranging from 0.01 to 0.22) and the mean VE was -4.35 (ranging from -48.7 to 0.56), suggesting that vaccination was not associated with reduced virus transmission. These findings may be explained, at least in part, by a delayed application of the vaccine, so it was too late to be protective, or that vaccine was improperly manufactured, stored, transported, or administered. Estimates of VE and k provided here will help evaluate the effectiveness of future prevention and control interventions in the region.
Key words: Foot-and-mouth disease, modeling, Pakistan, transmission






Introduction 
Foot-and-mouth disease (FMD) is one of the most important infectious diseases of livestock because of its rapid transmission between wide ranges of species and often leading to a decline in milk production in dairy cattle, as well as a decrease in weight gain in other species ADDIN EN.CITE <EndNote><Cite><Author>James</Author><Year>2002</Year><RecNum>96</RecNum><DisplayText>(James and Rushton, 2002)</DisplayText><record><rec-number>96</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">96</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>James, A. D.</author><author>Rushton, J.</author></authors></contributors><auth-address>Veterinary Epidemiology and Economics Research Unit (VEERU), University of Reading, Department of Agriculture, Earley Gate, P.O. Box 236, Reading, Berkshire RG6 6AT, United Kingdom.</auth-address><titles><title>The economics of foot and mouth disease</title><secondary-title>Rev Sci Tech</secondary-title></titles><periodical><full-title>Rev Sci Tech</full-title></periodical><pages>637-44</pages><volume>21</volume><number>3</number><edition>2003/01/14</edition><keywords><keyword>Animals</keyword><keyword>Costs and Cost Analysis</keyword><keyword>Emergencies/economics/veterinary</keyword><keyword>Foot-and-Mouth Disease/ economics/prevention &amp; control</keyword><keyword>Primary Prevention/economics</keyword><keyword>Vaccination/economics/ veterinary</keyword></keywords><dates><year>2002</year><pub-dates><date>Dec</date></pub-dates></dates><isbn>0253-1933 (Print)&#xD;0253-1933 (Linking)</isbn><accession-num>12523703</accession-num><urls></urls><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_8" \o "James, 2002 #96" James and Rushton, 2002) HYPERLINK \l "_ENREF_6" \o "James, 2002 #51" . The economic consequences of infection within a country may be severe, preventing the export of meat and milk into FMD-free regions of the world, eliminating a vital source of revenue for infected countries ADDIN EN.CITE <EndNote><Cite><Author>Carpenter</Author><Year>2011</Year><RecNum>80</RecNum><DisplayText>(Carpenter et al., 2011)</DisplayText><record><rec-number>80</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">80</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Carpenter, T. E.</author><author>O&apos;Brien, J. M.</author><author>Hagerman, A. D.</author><author>McCarl, B. A.</author></authors></contributors><auth-address>Department of Homeland Security funded Center of Excellence for Foreign Animal and Zoonotic Disease Defense, School of Veterinary Medicine, University of California, Davis, CA 95616, USA. tecarpenter@ucdavis.edu</auth-address><titles><title>Epidemic and economic impacts of delayed detection of foot-and-mouth disease: a case study of a simulated outbreak in California</title><secondary-title>J Vet Diagn Invest</secondary-title></titles><periodical><full-title>J Vet Diagn Invest</full-title></periodical><pages>26-33</pages><volume>23</volume><number>1</number><edition>2011/01/11</edition><keywords><keyword>Animals</keyword><keyword>California/epidemiology</keyword><keyword>Cattle</keyword><keyword>Cattle Diseases/ economics/ epidemiology</keyword><keyword>Computer Simulation</keyword><keyword>Disease Outbreaks/economics/ veterinary</keyword><keyword>Female</keyword><keyword>Foot-and-Mouth Disease/ economics/ epidemiology</keyword><keyword>Foot-and-Mouth Disease Virus/isolation &amp; purification</keyword><keyword>Models, Biological</keyword><keyword>Models, Economic</keyword><keyword>Stochastic Processes</keyword></keywords><dates><year>2011</year><pub-dates><date>Jan</date></pub-dates></dates><isbn>1943-4936 (Electronic)&#xD;1040-6387 (Linking)</isbn><accession-num>21217024</accession-num><urls></urls><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_3" \o "Carpenter, 2011 #80" Carpenter et al., 2011). 
FMD is endemic in Pakistan and its neighboring countries,  imposing a substantial  negative impact on their livestock industries ADDIN EN.CITE <EndNote><Cite><Author>Zahur</Author><Year>2006</Year><RecNum>87</RecNum><DisplayText>(Zahur et al., 2006)</DisplayText><record><rec-number>87</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">87</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Zahur, A. B.</author><author>Irshad, H.</author><author>Hussain, M.</author><author>Anjum, R.</author><author>Khan, M. Q.</author></authors></contributors><auth-address>Animal Health Laboratories, Animal Sciences Institute, National Agricultural Research Centre, Islamabad, Pakistan.</auth-address><titles><title>Transboundary animal diseases in pakistan</title><secondary-title>J Vet Med B Infect Dis Vet Public Health</secondary-title></titles><periodical><full-title>J Vet Med B Infect Dis Vet Public Health</full-title></periodical><pages>19-22</pages><volume>53 Suppl 1</volume><edition>2006/11/25</edition><dates><year>2006</year><pub-dates><date>Dec</date></pub-dates></dates><isbn>0931-1793 (Print)&#xD;0931-1793 (Linking)</isbn><accession-num>17123361</accession-num><urls></urls><electronic-resource-num>10.1111/j.1439-0450.2006.01015.x</electronic-resource-num><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_15" \o "Zahur, 2006 #87" Zahur et al., 2006). The most prevalent serotype of FMD virus (FMDV) in Pakistan is O followed by Asia1 and A, respectively. Serotype C has also been reported sporadically in 1954, 1963 and 1995 ADDIN EN.CITE  ADDIN EN.CITE.DATA ( HYPERLINK  \l "_ENREF_6" \o "Jamal, 2010 #52" Jamal et al., 2010;  HYPERLINK  \l "_ENREF_7" \o "Jamal, 2011 #86" Jamal et al., 2011) HYPERLINK \l "_ENREF_7" \o "Jamal, 2010 #52" .  Efforts to control FMD in Pakistan have been limited by the lack of resources available in the country and many features of the transmission and control of FMD in Pakistan are yet to be elucidated. Traditional practices, such as unregulated animal movement in and between nomadic and transhumant herds, limits the effectiveness of veterinary services. FMD vaccines are not used systematically in Pakistan and thus attributes such as the efficacy, potency, and strain composition of the vaccines are uncertain ADDIN EN.CITE <EndNote><Cite><Author>Jamal</Author><Year>2010</Year><RecNum>52</RecNum><DisplayText>(Jamal et al., 2010)</DisplayText><record><rec-number>52</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">52</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Jamal, S. M.</author><author>Ahmed, S.</author><author>Hussain, M.</author><author>Ali, Q.</author></authors></contributors><auth-address>National Veterinary Laboratory, Park Road, Islamabad, Pakistan. jamal115@yahoo.com</auth-address><titles><title>Status of foot-and-mouth disease in Pakistan</title><secondary-title>Arch Virol</secondary-title></titles><periodical><full-title>Arch Virol</full-title></periodical><pages>1487-91</pages><volume>155</volume><number>9</number><edition>2010/06/24</edition><keywords><keyword>Animals</keyword><keyword>Buffaloes</keyword><keyword>Cattle</keyword><keyword>Cattle Diseases/ virology</keyword><keyword>Disease Outbreaks</keyword><keyword>Foot-and-Mouth Disease/ epidemiology/virology</keyword><keyword>Foot-and-Mouth Disease Virus/classification/genetics/ isolation &amp; purification</keyword><keyword>Prevalence</keyword></keywords><dates><year>2010</year><pub-dates><date>Sep</date></pub-dates></dates><isbn>1432-8798 (Electronic)&#xD;0304-8608 (Linking)</isbn><accession-num>20571838</accession-num><urls></urls><electronic-resource-num>10.1007/s00705-010-0732-y</electronic-resource-num><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_6" \o "Jamal, 2010 #52" Jamal et al., 2010). Transmission rate of FMDV is unknown and most important; it is unclear whether vaccination has decreased the spread of FMD in Pakistan. Additional knowledge on the epidemiology of FMD in Pakistan is necessary to design and implement effective control programs for the disease in this country.
The adequate contact rate (k) is the mean number of contacts made in a single time period, sufficient to cause disease transmission if one individual is infectious and the other susceptible.  Vaccine efficacy (VE) is a measure that shows risk reduction of a disease incidence among vaccinated animals compared to non-vaccinated animals. The purpose of this study was to estimate k and VE using data collected in one of the most densely populated regions of Pakistan. Estimates of k value quantitatively provide a better understanding of the disease transmission dynamic in the FMD endemic situation and thus, are useful in control programs. Here, VE is defined in a broad sense as effectiveness of the vaccination program. Because the value of VE is influenced by a number of factors, including, for example, time when the vaccine was applied, strains used in the vaccine and their relation with circulating strains, conditions of maintainence and application, and quality of the vaccine, then the value of VE is a measure of the strength of the intervention and its success in preventing diseases spread. Estimates of VE value indicate how effective vaccination is as a prevention program; values of VEd"0 indicate that the program is not effective in controlling diseases spread, whereas values of VE>0 indicate that the program has been effective in controlling disease and the higher the value of VE, the more successful the intervention. Both  estimates of k and VE  are important   in understanding the mechanisms of disease transmission and improving the effectiveness of control efforts for FMD in Pakistan ADDIN EN.CITE <EndNote><Cite><Author>Greenwood</Author><Year>1915</Year><RecNum>145</RecNum><DisplayText>(Greenwood and Yule, 1915)</DisplayText><record><rec-number>145</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">145</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Greenwood, M.</author><author>Yule, G.U.</author></authors></contributors><titles><title>The statistics of anti-typhoid and anti-cholera inoculations, and the interpretation of such statistics in general</title><secondary-title>Proceedings of the Royal Society of Medicine</secondary-title></titles><periodical><full-title>Proceedings of the Royal Society of Medicine</full-title></periodical><pages>113</pages><volume>8</volume><number>Sect Epidemiol State Med</number><dates><year>1915</year></dates><urls></urls></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_4" \o "Greenwood, 1915 #145" Greenwood and Yule, 1915).

Materials and methods 
Data
Serological samples and epidemic and demographic data were collected from June through December 2008 from 32 districts in the Punjab province of Pakistan.  Because in 3 districts samples were collected from 2 villages, the total number of sampled villages was 35. A two stage sampling design was used, in which the first stage was to select the village and the second stage was to select the animals (cattle and buffalo) to be sampled. Within each selected village, 48 individual blood samples were collected, using a stratified design (16 samples from each category of  < 1, 1-2, and >2 years of age ) Sample size was 48 because 43 is the number of samples required to estimate prevalence in a population of infinite size, with a confidence interval of 95%, expected prevalence of 50%, and error boundaries of 15%, using a normal approximation to the binomial distribution; five extra samples (n=48) were collected to prevent problems with quality of samples collected, which may reduce the effective number of samples analyzed at the laboratory. For each selected village, animals were selected using systematic random sampling. Starting from one end of the main road of the village, the first household on the right side with cattle or buffalo was selected, with up to 5 individual samples collected from a household, meaning that on average, animals from at least 10 households were sampled in each village.  If necessary, sampling continued at the opposite end and side of the road until completed. Samples were tested for identification of antibodies against non-structural proteins (NSP). The NSP test was used because it discriminates between the presence of antibodies due to virus infection and vaccination with purified vaccines, and can be used as a proxy to denote FMD-status in vaccinated and non-vaccinated animals.
Serological tests
The serological assay used to detect anti-NSP antibodies is the previously validated 3ABC-trapping ELISA from IZSLER-Brescia, Italy ADDIN EN.CITE  ADDIN EN.CITE.DATA ( HYPERLINK  \l "_ENREF_1" \o "Brocchi, 2006 #356" Brocchi et al., 2006). Ready-to-use kits (presensitized ELISA immunoplates, TMB chromogen instead of OPD) were produced at IZSLER and provided to the Laboratory in Pakistan that performed testing of all samples. A subset of 500 sera was re-tested at IZSLER for an external evaluation to confirm the results. According to a previous validation study, the diagnostic performances of the IZSLER-Brescia kit were comparable to those of the NCP anaftosa-screening index method described in the Diagnostic Manual of the World Animal Health Organization. In particular, the specificity exceeded 99% and the sensitivity varied depending on the time-period after infection and on the previous vaccination status, achieving 100% for non-vaccinated cattle exposed to infection and 86,4% for the detection of carriers in vaccinated cattle  ADDIN EN.CITE  ADDIN EN.CITE.DATA ( HYPERLINK  \l "_ENREF_1" \o "Brocchi, 2006 #356" Brocchi et al., 2006). 
Model
A modified Reed�Frost model was used to estimate the value of k and VE. A comprehensive description of the model formulation and assumptions is available elsewhere ADDIN EN.CITE <EndNote><Cite><Author>Carpenter</Author><Year>2001</Year><RecNum>79</RecNum><DisplayText>(Carpenter, 2001)</DisplayText><record><rec-number>79</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">79</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Carpenter, T. E.</author></authors></contributors><auth-address>Department of Medicine and Epidemiology, School of Veterinary Medicine, University of California, Davis 95616, USA.</auth-address><titles><title>Evaluation of effectiveness of a vaccination program against an infectious disease at the population level</title><secondary-title>Am J Vet Res</secondary-title></titles><periodical><full-title>Am J Vet Res</full-title></periodical><pages>202-5</pages><volume>62</volume><number>2</number><edition>2001/02/24</edition><keywords><keyword>Animals</keyword><keyword>Communicable Disease Control</keyword><keyword>Computer Simulation</keyword><keyword>Disease Susceptibility/veterinary</keyword><keyword>Immunization Programs/ standards</keyword><keyword>Models, Biological</keyword><keyword>Population</keyword><keyword>Risk Assessment</keyword><keyword>Treatment Outcome</keyword><keyword>Vaccination/standards/ veterinary</keyword></keywords><dates><year>2001</year><pub-dates><date>Feb</date></pub-dates></dates><isbn>0002-9645 (Print)&#xD;0002-9645 (Linking)</isbn><accession-num>11212028</accession-num><urls></urls><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_2" \o "Carpenter, 2001 #79" Carpenter, 2001). Briefly, the model consisted of four FMD-infection states: susceptible, latently infected, infectious, and immune, either via natural exposure or vaccination. 
The simple Reed-Frost model is:
Ct+1 = St*(1-qCt)
Where t is the time period (day), Ct+1 is the number of infectious cases in time period t+1, St is the number of susceptible individuals in the time period of t, and q = 1-p is the probability of an individual avoiding adequate contact, and p is the probability of a given individual having an adequate contact with another given individual, and 
k = p*(N-1) where k is the mean number of adequate contact made in a single time period. An adequate contact is a contact, which if made between a susceptible and infectious individual would result in the infection of the susceptible individual. N is the population size. 
To account for extended latent and infectious durations, and the vaccine efficacy, the Reed-Frost equation was modified as,
Ct+1 = St*(1-qCIt)                                                                                                              (1) 
CI is the cumulative infectious,
Moreover, in order to reflect the vaccination protection, the model was modified even more in a way that the original equation for new susceptible individuals, St = St-1 + Ct , becomes
St = St-1(1-v.r.*VE) + Ct                                                                                                                 (2)
where
v.r. = vaccination rate.
The final model used to estimate the k and VE values is the combination of equations (1) and (2) above:
Ct+1 = [St-1(1-v.r.*VE) + Ct ] *(1-qCIt)  

 The inputs for k and VE calculation in each district are the total population in each district, the number of vaccinated animals, the number of NSP-positive vaccinated animals, and the number of NSP-positive non-vaccinated animals in each district. 
The value for k, which best fit the model equation �c� above to the village-level prevalence and vaccination data, was found using Microsoft Excel Solver (Microsoft Corp., Redmond, WA). Solver uses the generalized reduced gradient nonlinear optimization code ADDIN EN.CITE <EndNote><Cite><Author>Lasdon</Author><Year>1978</Year><RecNum>130</RecNum><DisplayText>(Lasdon et al., 1978)</DisplayText><record><rec-number>130</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">130</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Lasdon, L.S.</author><author>Waren, A.D.</author><author>Jain, A.</author><author>Ratner, M.</author></authors></contributors><titles><title>Design and testing of a generalized reduced gradient code for nonlinear programming</title><secondary-title>ACM Transactions on Mathematical Software (TOMS)</secondary-title></titles><periodical><full-title>ACM Transactions on Mathematical Software (TOMS)</full-title></periodical><pages>34-50</pages><volume>4</volume><number>1</number><dates><year>1978</year></dates><isbn>0098-3500</isbn><urls></urls></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_10" \o "Lasdon, 1978 #130" Lasdon et al., 1978) to find an optimal solution for a model by changing variable cells of a spreadsheet, in this case k and VE. Solver randomly applies different k and VE values into the modified Reed-Frost model to find the most probable values fitting current population data. Population data from each village includes the total population size, the number of vaccinated, NSP-positive vaccinated and NSP-positive nonvaccinated animals.  Latent and infectious periods (LP and IP) were assumed to be 3 and 7 days, respectively ADDIN EN.CITE <EndNote><Cite><Author>Mardones</Author><Year>2010</Year><RecNum>59</RecNum><DisplayText>(Mardones et al., 2010)</DisplayText><record><rec-number>59</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">59</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Mardones, F.</author><author>Perez, A.</author><author>Sanchez, J.</author><author>Alkhamis, M.</author><author>Carpenter, T.</author></authors></contributors><auth-address>Center for Animal Disease Modeling and Surveillance (CADMS), School of Veterinary Medicine, University of California, Davis, CA 95616, USA. formardones@ucdavis.edu</auth-address><titles><title>Parameterization of the duration of infection stages of serotype O foot-and-mouth disease virus: an analytical review and meta-analysis with application to simulation models</title><secondary-title>Vet Res</secondary-title></titles><periodical><full-title>Vet Res</full-title></periodical><pages>45</pages><volume>41</volume><number>4</number><edition>2010/03/09</edition><keywords><keyword>Animals</keyword><keyword>Computer Simulation</keyword><keyword>Foot-and-Mouth Disease/ virology</keyword><keyword>Foot-and-Mouth Disease Virus/ classification</keyword><keyword>Models, Biological</keyword><keyword>Serotyping</keyword></keywords><dates><year>2010</year><pub-dates><date>Jul-Aug</date></pub-dates></dates><isbn>0928-4249 (Print)&#xD;0928-4249 (Linking)</isbn><accession-num>20205988</accession-num><urls></urls><custom2>2850150</custom2><electronic-resource-num>10.1051/vetres/2010017</electronic-resource-num><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_12" \o "Mardones, 2010 #59" Mardones et al., 2010). 
The strength of the association between vaccination status and NSP-prevalence was quantified by computing the prevalence ratio (PR) of FMD infection between vaccinated and unvaccinated groups on each village using Stata v. IC 10.1 (Stata Corp., College Station, TX); VE was subsequently calculated as,
 VE= (1-PR)*100%  ADDIN EN.CITE <EndNote><Cite><Author>Greenwood</Author><Year>1915</Year><RecNum>145</RecNum><DisplayText>(Greenwood and Yule, 1915)</DisplayText><record><rec-number>145</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">145</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Greenwood, M.</author><author>Yule, G.U.</author></authors></contributors><titles><title>The statistics of anti-typhoid and anti-cholera inoculations, and the interpretation of such statistics in general</title><secondary-title>Proceedings of the Royal Society of Medicine</secondary-title></titles><periodical><full-title>Proceedings of the Royal Society of Medicine</full-title></periodical><pages>113</pages><volume>8</volume><number>Sect Epidemiol State Med</number><dates><year>1915</year></dates><urls></urls></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_4" \o "Greenwood, 1915 #145" Greenwood and Yule, 1915) HYPERLINK \l "_ENREF_11" \o "Carpenter, 2001 #79" .
Sensitivity analysis
Because the true values of IP and LP are variable and uncertain, sensitivity analysis was used to quantify the influence parameter estimates had on the estimates of VE and k. The values of VE and k were recalculated using, alternatively, values of IP=4, 5, and 6 days, and LP=3, 4 and 5 days, respectively  ADDIN EN.CITE  ADDIN EN.CITE.DATA ( HYPERLINK  \l "_ENREF_9" \o "Kitching, 1992 #147" Kitching, 1992;  HYPERLINK  \l "_ENREF_5" \o "Haydon, 1997 #148" Haydon et al., 1997;  HYPERLINK  \l "_ENREF_12" \o "Mardones, 2010 #59" Mardones et al., 2010).
Results
Population size in the 32 districts ranged from 900 to 7650 animals. Table 1 shows the animal population size and the proportion of NSP-positive animals in each district. For example, 25% of the animals in Hafizabad and Pakpattan were NSP-positive (Table 1). Estimated k values and the statistical distributions that best fit these values varied depending on the assumed LP and IP. The estimated mean k was 0.23 adequate contacts per day assuming LP and IP, 3 and 7 days respectively (Table 2). The Weibull distribution provided the best fit (P > 0.49) for the estimated distribution of k (Figure 1). We also evaluated the changes in distribution of adequate contact rate (k) by changing the LP and IP simultaneously. Table 3 and Figures 2 (a, b, c) indicate these changes in k distribution. The Rayleigh distribution best fit adequate contact rate (k) values while assuming LP=3, 4, 5 and IP=4, 5, 6; however there was no significant change in distribution parameters while changing LP.
Results of the sensitivity analysis indicated that changing the LP and IP did not affect the values of VE which suggests that the model was robust to this parameterization (Figure 3). The obtained values of VE were the same for all three IPs and all three LPs, which indicates that VE is not sensitive to IP and LP. Moreover, in all conditions the risk of FMD infection was an average of 1.47 times higher in vaccinated animals compared with non-vaccinated animals (95% CI=1.30,1.66).
Discussion
The results of this study indicate that the average intra-district adequate contact rate (k) for FMD in Pakistan is 0.12 per day.  Moreover, the results show that the estimates of VE are negative in some of the districts. There are many alternative explanations for the negative values of VE obtained here. VE is influenced by a number of parameters, including the formulation of the vaccine; protection conferred by the vaccine strain to circulating strains in the field; techniques used to conserve, maintain, transport and apply the vaccine; the way the vaccine is administered, and time between disease introduction and application of the vaccine in the population. Vaccines may have been used selectively after the clinical detection of the disease and therefore done little or nothing to decrease spread of the virus. Another explanation is improper vaccine inactivation may have resulted on disease transmission associated with the vaccine. Alternatively, the vaccine strain used in the vaccinate may have not offer protection against circulating strains or that the vaccine was not kept under the environmental conditions required to maintain its efficacy. A study by Woolhouse  et al. (1996) in dairy cattle herds in Saudi Arabia concluded that FMD prevention may have not been practical using the vaccines available at that time due to a surprisingly short critical inter-vaccination interval HYPERLINK \l "_ENREF_7" \o "Woolhouse, 1996 #72" . Even though the cattle herds being studied were revaccinated every 4-6 months, the vaccine could not prevent FMD outbreaks ADDIN EN.CITE <EndNote><Cite><Author>Woolhouse</Author><Year>1996</Year><RecNum>72</RecNum><DisplayText>(Woolhouse et al., 1996)</DisplayText><record><rec-number>72</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">72</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Woolhouse, M. E.</author><author>Haydon, D. T.</author><author>Pearson, A.</author><author>Kitching, R. P.</author></authors></contributors><auth-address>Department of Zoology, University of Oxford, UK.</auth-address><titles><title>Failure of vaccination to prevent outbreaks of foot-and-mouth disease</title><secondary-title>Epidemiol Infect</secondary-title></titles><periodical><full-title>Epidemiol Infect</full-title></periodical><pages>363-71</pages><volume>116</volume><number>3</number><edition>1996/06/01</edition><keywords><keyword>Animals</keyword><keyword>Antibodies, Viral/ immunology</keyword><keyword>Cattle</keyword><keyword>Disease Outbreaks/prevention &amp; control/ veterinary</keyword><keyword>Foot-and-Mouth Disease/epidemiology/immunology/ prevention &amp; control</keyword><keyword>Half-Life</keyword><keyword>Models, Biological</keyword><keyword>Saudi Arabia/epidemiology</keyword><keyword>Vaccination</keyword><keyword>Viral Vaccines/ immunology</keyword></keywords><dates><year>1996</year><pub-dates><date>Jun</date></pub-dates></dates><isbn>0950-2688 (Print)&#xD;0950-2688 (Linking)</isbn><accession-num>8666082</accession-num><urls></urls><custom2>2271420</custom2><remote-database-provider>NLM</remote-database-provider><language>eng</language></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_14" \o "Woolhouse, 1996 #72" Woolhouse et al., 1996). 
Noteworthy, it is likely that vaccines were produced by more than one manufacturer and that therefore, conclusions may not be extended to every single vaccine type used in Pakistan in recent years, but as a general indication of the field situation in the country. In any case, the results here suggest that the role of FMD vaccination campaigns in Pakistan should be revisited and the methodology presented here may help to formulate analytical mechanisms to evaluate the impact of such campaigns and other field interventions in the prevention and control of disease spread. 
In order to better evaluate FMD vaccination and control programs in Pakistan, future studies can be focused on spatiotemporal evolution patterns of FMDV during the disease outbreak. Moreover, the spatiotemporal assessment of FMD epidemics will help to investigate the local spread of FMD in Pakistan as well ADDIN EN.CITE <EndNote><Cite><Author>Mart�nez-L�pez</Author><Year>2010</Year><RecNum>149</RecNum><DisplayText>(Mart�nez-L�pez et al., 2010)</DisplayText><record><rec-number>149</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">149</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Mart�nez-L�pez, B.</author><author>Perez, AM</author><author>S�nchez-Vizca�no, JM</author></authors></contributors><titles><title>A simulation model for the potential spread of foot-and-mouth disease in the Castile and Leon region of Spain</title><secondary-title>Preventive veterinary medicine</secondary-title></titles><periodical><full-title>Preventive veterinary medicine</full-title></periodical><pages>19-29</pages><volume>96</volume><number>1-2</number><dates><year>2010</year></dates><isbn>0167-5877</isbn><urls></urls></record></Cite><Cite><Author>Mart�nez-L�pez</Author><Year>2010</Year><RecNum>149</RecNum><record><rec-number>149</rec-number><foreign-keys><key app="EN" db-id="revz2s0z5txss4evz01pwvae5sdexvfvd2x2">149</key></foreign-keys><ref-type name="Journal Article">17</ref-type><contributors><authors><author>Mart�nez-L�pez, B.</author><author>Perez, AM</author><author>S�nchez-Vizca�no, JM</author></authors></contributors><titles><title>A simulation model for the potential spread of foot-and-mouth disease in the Castile and Leon region of Spain</title><secondary-title>Preventive veterinary medicine</secondary-title></titles><periodical><full-title>Preventive veterinary medicine</full-title></periodical><pages>19-29</pages><volume>96</volume><number>1-2</number><dates><year>2010</year></dates><isbn>0167-5877</isbn><urls></urls></record></Cite></EndNote>( HYPERLINK  \l "_ENREF_13" \o "Mart�nez-L�pez, 2010 #149" Mart�nez-L�pez et al., 2010) HYPERLINK  \l "_ENREF_15" \o "Mart�nez-L�pez, 2010 #149" . 
Conclusion
The results of this study provide a better understanding of FMD epidemiology in the Punjab Province of Pakistan, including estimates of intra-district adequate contact rates (k) and the success of vaccination programs, as indicated by the value of vaccine efficacy (VE) in the study population. Results indicate that the vaccination campaign did not reduce disease incidence, which is suggested by the negative mean value of VE and by the higher relative risk of infection in vaccinated compared to unvaccinated animals. Estimates of the values of k and VE are useful in evaluating the efficacy of interventions and implementation of biosecurity programs in the study region ADDIN EN.CITE  ADDIN EN.CITE.DATA ( HYPERLINK  \l "_ENREF_2" \o "Carpenter, 2001 #79" Carpenter, 2001;  HYPERLINK  \l "_ENREF_11" \o "Li, 2011 #89" Li and Liu, 2011). This is the first estimate of k and VE for FMD in Pakistan published in the peer reviewed literature HYPERLINK \l "_ENREF_8" \o "Wongsathapornchai, 2008 #71" .

Conflict of interest statement
The authors declare that they have no conflict of interest. 
Acknowledgements
This work has been funded in part by grants from the United States Department of Agriculture Agricultural Research Service (USDA/ARS) and from the United Nations Food and Agriculture Organization (FAO).

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Fig. 1. Weibull distribution (2.42, 0.15) of FMD adequate daily contact rate (k), assuming 3-day latent period and 7-day infectious period days in Punjab, Pakistan.
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Fig. 3.  Normal Distribution of FMD Vaccine Efficacy (VE) in Punjab, Pakistan, assuming LP=3, 4, 5 and IP= 4, 5, 6 days.

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