Veterinary Microbiology, 28 ( 1991 ) 103-109 Elsevier Science Publishers B.V., Amsterdam
103
A mathematical model for Mycobacterium bovis excretion from tuberculous cattle S.D. Neill, J.J. O'Brien* and J. Hanna Bacteriology Department Veterinary Research Laboratories, Stormont, Be[fast, BT4 3SD, UK (Accepted 19 November 1990 )
ABSTRACT Neill, S.D., O'Brien, J.J. and Hanna, J., 1991. A mathematical model for M.vcobacterium bovis excrelion from tuberculous cattle. Vet. MicrobioL, 28: 103-109. An analysis was carried out of available information from a series of experiments on the excretion of M. boris from infected cattle. The analysis indicated that an inverse exponential relationship exists between "dose' of organisms given and the delay before excretion commences. This relationship was rcpresented mathematically. Available field data supported the relationship and indicated that in natural bovine tuberculosis excretion of M. boris begins around 87 days after infection occurs. It is also suggested that the data supports the concept of single nuclei infections in cattle.
INTRODUCTION
Most evidence suggests that the majority of cattle with tuberculosis are infected via the respiratory route (Francis, 1958; Wilesmith et al., 1982; Anon, 1984). It has been postulated that, in human pulmonary tuberculosis, mycobacteria contained in "droplet nuclei" are inhaled and pass to the alveoli where, after evaporation of the droplet, the mycobacteria are deposited on the alveolar lining and may give rise to pulmonary lesions (Ratcliffe and Palladino, 1953 ). Although the precise mechanisms involved are not fully understood, lung tubercules may serve as sources of infection. Mycobacteria shed from lesions into the respiratory tract, may subsequently be expelled mechanically to the external environment in aerosolised secretions. Until recently, it was generally accepted that only 1-2% of tuberculous cattle could be designated "open" cases capable of spreading tuberculosis (Gallagher, 1980; Anon, 1984). These were cattle found at abattoir inspection to have lesions both in their respiratory lymph nodes and lungs. Mcllroy et al. ( 1986 ) however, critically examined lungs and lymph nodes from tuberculin*Present address: Veterinary Division D u n d o n a l d House, Belfast BT4.
0378-1135/91/$03.50
© 1991 - - Elsevier Science Publishers B.V.
104
S.D. NEILL ET AL.
reacting cattle and demonstrated that the majority of animals with respiratory lymph node lesions also had lung lesions, and therefore were open cases. In addition they found that 19% of these cattle had Mycobacterium bovis in their respiratory secretions. Despite its obvious importance in the epidemiology of bovine tuberculosis, there is relatively little published information on M. boris excretion from tuberculous cattle. Rempt (1954) reported that 6% of 40 000 specimens from tuberculin-reacting animals in the Netherlands were positive for M. bovis; Krishnaswamy et al. ( 1974 ) isolated M. bovis from sputum of 15.6% of tuberculin-reacting cattle in a herd in India; De Kantor et al. ( 1989 ) reported M. bovis in nasal secretions from 9.3% of tuberculin-reacting cattle in a herd in Argentina and Neill et al. (1988a) in a second study isolated M. bovis from the anterior respiratory tracts of 20% of randomly taken tuberculous cattle at an abattoir in Northern Ireland. The suggestion that all tuberculous cattle should be regarded as excretors of M. bovis (McIlroy et al., 1986) is substantiated by the findings of more recent studies by Neill et al. ( 1988b; 1989 ). These studies have shown experimentally that excretion of M. bovis is a consistent feature of tuberculosis in cattle. In an attempt to understand and define when tuberculous cattle might first become infectious, an analysis was carried out of available experimental data on M. bovis excretion. This paper reports the findings of the analysis. MATERIALS AND METHODS
Groups consisting of five 4-7 month old calves, were infected by intranasal instillation of field isolates of M. bovis. Specimens of nasal mucus were collected from each calf prior to inoculation and at weekly intervals thereafter. Details of the experimental procedures and culture methods employed have previously been reported (Neill et al., 1988b). The time period between inoculation and the initial detection of M. bovis in the nasal mucus was determined for each calf in these experiments. The length of the delay or lag period before excretion began was also determined for two other calves which were similarly infected by intranasal instillation with 104 M. bovis organisms in a subsequent experiment (Neill, unpublished data). Transmission of tuberculosis by contact between infected and non-infected cattle has been demonstrated experimentally and the procedures and cultural methods employed were published (Neill et al., 1989 ). The time between the introduction of the uninfected calf to the tuberculous cattle and the first detection of M. bovis in the nasal mucus from the former animal was noted. In addition the contact period before the initial detection of M. bovis in nasal mucus from another calf infected after introduction to tuberculous cattle in a second similar experiment was also determined (Neill, unpublished data). Using assumed values of 100, 10 and 1 respectively, for the number of or-
MATHEMATICALMODEL FOR M. BO~TSEXCRETION FROM TUBERCULOUSCATTLE
105
ganisms required to cause "natural" infection, regression equations to describe the relationship between the number of organisms in the inoculum and the lag period before excretion began were determined. The statistical and graphical computer packages Stat 80 and Grafit 1000 (Zyxomma) were employed. RESULTS
Table 1 shows, for twelve animals, the delay before excretion was detected following intranasal inoculation with M. bovis. Table 2 shows, for two animals, the periods of contact with infected cattle prior to the initial isolation ofM. bovis from nasal mucus of the two animals which subsequently became infected. Table 3 shows the proportions of variation explained by the regression TABLE 1 Delay before initial detection of Mycobacterium bovis in nasal mucus of experimental cattle infected intranasally Animal Number
lnoculum (cfu's)
Delay period (days)
1357 1356 1300 1299 1338 1841 1840 A462 A465 2149 2148 1245
1X 106 1X 106 1X 106 IX 106 1X 106 4 X 104 4 X l04 9.6X l03 9.6×103 9.6X 103 9.6X 103 9.6× 103
7 12 12 12 12 22 30 7 29 15 22 15
*cfu's: Colony forming units. TABLE 2 Delay before initial detection ofM. bovis in nasal mucus of cattle following contact with tuberculous cattle
Animal Number
lnoculum
Delay period (days)
A467 1862
U* U
92 82
*U = unknown.
106
S.D. NEILL ET AL.
TABLE 3 The proportion of variation explained by fitting regression equations when different hypothetical values for number of organisms involved in natural infection Number of organisms
Variation
100 10
67% 78% 84%
1
equations when hypothetical values of 100, 10 and 1 M, bovis organisms respectively were used for those animals infected naturally. The relationship between the inoculum size (log2 number of organisms in the inoculum) and the delay before excretion, was best represented by the equation y = - 0 . 2 2 8 x + 20.04. (The standard error of the slope is + 0.028. ) The proportion of variation explained by fitting the regression equation (R 2 ) was 84% and the F statistic was very highly significant ( P < 0.001 ). In this it was assumed that natural infection was caused by one organism. DISCUSSION
While evidence suggests that M. bovis infection usually occurs via the respiratory route, the precise pathogenesis remains unclear. Both the size of the inhaled droplet nucleii and the number of mycobacteria contained within them appear to be major factors in establishing tuberculosis (Wells et al., 1948 ). It is impossible to know the droplet size of the quantity of mycobacteria present at the initiation site (s) of infection. In the experimental infections from which the current data is drawn (Neill et al., 1988b; 1989; unpublished data) the inocula had been sonicated prior to use to disrupt any "clumped" mycobacterial cells and to produce an even distribution of organisms for delivery to the cattle. The numbers of mycobacteria delivered to each animal were estimated from reproducible viable count determinations. No such quantitative estimations could be ascertained for those animals infected naturally in the field or under experimentation by contact transmission. The number of mycobacteria involved in such infections must therefore be hypothetical. From the initial inspection of the data compiled (Tables 1 and 2) there appears to be an inverse relationship between the number of organisms delivered to each animal and the lag period before M. bovis excretion began. This lag or adaptive period is complex and will obviously reflect possible phenotypic changes in the organism and any host-organism interaction. An inverse exponential relationship between the quantity of organisms given and the lag period before excretion occurred, was confirmed by the analysis carried out. Despite the additional assumption that mycobacteria are also uniformly dis-
MATHEMATICAL MODEL FOR M. B O V I S EXCRETION FROM TUBERCULOUS CATTLE
107
tributed in inocula received by naturally infected cattle, the linear equation representing the transformed data (Fig. 1 ) was highly significant ( P < 0.001 ). The proportions of variation shown in Table 3 indicate an improvement in the relationship as the hypothetical numbers of organisms involved in the natural infections approach unity. From this one might suggest that as few as one single organism may be sufficient to cause infection. This would concur with work cited by Francis ( 1947 ) in which Chausse ( 1913 ), from studies on sheep and cattle, suggested that probably only one organism would produce a lesion in lung tissue. Lurie et al. (1950) produced tuberculosis in rabbits when as few as three tubercle bacilli were inhaled and Ratcliffe and Palladino ( 1953 ) have shown that in the guinea pig, mouse and rat, inhalation of single organisms could produce tuberculosis. These latter authors postulated that in man tuberculosis could also develop from inhalation of a single bacillus. The concept of single nuclei infections in cattle would be supported by the findings of the study reported by McIlroy et al. (1986). These workers found only single lesions present in 63% of lungs from tuberculous cattle, despite critical laboratory examinations. The precise mycobacterial load involved in initiating bovine field infections is unknown and may be different in every instance. Thus, individual cattle may begin to excrete M. bovis at different times after infection is initiated. In the experiments ofNeill et al. (1988b; 1989), sampling of nasal mucus for culture examination was limited, approximately every seventh day. However, from the limited data available, it would appear that in natural tuberculosis, initial excretion ofM. bovis would possibly occur around 87 days (SD _+7.1 days) after infection takes place.
.~. 2 0 i
r) ~4
o~ ~
,,
~ ¢o
E 0
i 0
,
i
,
50
Delay
before
~r~
~
i 1 O0
(days)
excretion
Fig. I. Relationship between the number of organisms given to experimental ca[tie and the delay before excretionwas detected.
lO~
S.D. NEILL ETAL.
Abattoir studies of tuberculin-reacting cattle in Northern Ireland (Mcllroy el al., 1986; Neill et at., 1988) revealed animals from which M. bovis was isolated from nasal mucus at the time of slaughter, The periods between recovery of M. boris in respiratory tracts of these animals and the time at which the last negative tuberculin test was performed were reported. Usually this simply reflects the intratest period during which the infection could have occurred at any stage. However in the study by Neill et al. (1988), four of the five mucus-positive animals were reported to have been tested solely because they were in contact with tuberculous cattle on neighbouring farms. Therefore for these four animals, with test intervals of 68, 69, 56 and 87 days respectively, it appears that the time between the infection occurring and M. boris excretion beginning was at most 87 days. A new equation ( y = - 0 . 2 5 6 x+20.147) derived from the experimental data (Tables 1 and 2) and the four specific lag periods related to the field cases above, did not differ significantly from that representing the experimental data alone. The proportion of variation accounted for by fitting the exponential model was increased to 87%. It would therefore appear that in natural tuberculosis the projected experimental estimate of around 87 days for the delay between infection and excretion was realistic. ACKNOWLEDGEMENTS
The authors are extremely grateful to Mr. J. Rainey (Agricultural Biometrics, Department of Agriculture for N. Ireland) for his help and advice with this publication. REFERENCES Anon, 1984. Ann. Report on Research and Technical Work, Belfast. Her Majesty's Stationery Office. p. 244. Chausse. P., 1913. Des methodes a employer pour realiner la tuberculose experimentale par inhalation. Bull. Soc. Med. Vet., 31: 267-274. Francis, J., 1947. Bovine Tuberculosis. Staples Press, London, p, 87. Francis, J., 1958. Tuberculosis in animals an man. Cassell, London, p. 16. Gallagher, J., 1980. In: Lord Zukermann (Editor), Badgers, cattle and tuberculosis. The role of other animals in the epidemiology of TB of the Badger. Her Majesty's Stalionery Office, London, p. 86-94. Kantor, 1.N. de, Bioch, D. and Roswurm, J.D., 1978. Mycobacteria isolated from nasal secretions of tuberculin test reactor cattle. Am. J. Vet. Res., 39: 1233-1238. Krishnaswamy, S., Nagaraja, K.V., Keshavamurthy, B.S., Adinarayanaich, C.L. and Nanjiah, R.D., 1984. Isolation and identification of tubercule bacilli from "open cases" of bovine tuberculosis. Mysore. J. Agric. Sci., 8: 423-428. Lurie, M.B., Heppelston, A.G., Abramson, S. and Swartx, 1.B., 1950. Evaluation of method of quantitative airborne infection and its use in study ofpathogenesis of tuberculosis. Am. Rev. Tuberc., 61: 765-797. Mcllroy, S.G., Neill, S.D. and McCracken, R.M., 1986. Pulmonary lesions and Mycobacterium
MATHEMATICAL MODEL FOR M. BOFIS EXCRETION FROM TUBERCULOUS CATTLE
109
bovis excretion from the respiratory tract of tuberculin reacting cattle. Vet. Rec., 118: 718721. Neill, S.D., O'Brien, J.J. and McCracken, R.M., 1988a. Mycobacterium boris in the anterior respiratory tracts in the heads of tuberculin reacting cattle. Vet. Rec., 122:184-186. Neill, S.D., Hanna, J. and O'Brien, J.J., 1988b. Excretion of Mycobacterium bovis by experimentally infected cattle. Vet. Rec., 123: 340-343. Neill, S.D., Hanna, J. and O'Brien, J.J,, 1989. Transmission of tuberculosis from experimentally infected cattle to in-contact calves. Vet. Rec., 124: 269-271. Ratcliffe, H.L. and Palledino, V.S., 1953, Tuberculosis induced by droplet nuclei infection: initial homogenous response of small mammals (rats, mice, guinea pigs and hamsters) to human and bovine bacilli, and rate and pattern oftubercule development. J. Exper. Med.. 97: 61-67. Rempt, D., 1954. Veterinary work in the Netherlands. 1953. Netherlands Veterinary Service, p. 80. Wells, W.F., Ratcliffe, H.L. and Crumb, C., 1948. On the mechanism of droplet nuclei infection. Am. J. Hyg., 47:11-28. Wilesmith, J.W., Little, W.A., Thompson, H.V. and Swan, C., 1982. Bovine tuberculosis in domestic and wild mammals in an area of Dorset. J. Hyg., 89:195-210.
103
A mathematical model for Mycobacterium bovis excretion from tuberculous cattle S.D. Neill, J.J. O'Brien* and J. Hanna Bacteriology Department Veterinary Research Laboratories, Stormont, Be[fast, BT4 3SD, UK (Accepted 19 November 1990 )
ABSTRACT Neill, S.D., O'Brien, J.J. and Hanna, J., 1991. A mathematical model for M.vcobacterium bovis excrelion from tuberculous cattle. Vet. MicrobioL, 28: 103-109. An analysis was carried out of available information from a series of experiments on the excretion of M. boris from infected cattle. The analysis indicated that an inverse exponential relationship exists between "dose' of organisms given and the delay before excretion commences. This relationship was rcpresented mathematically. Available field data supported the relationship and indicated that in natural bovine tuberculosis excretion of M. boris begins around 87 days after infection occurs. It is also suggested that the data supports the concept of single nuclei infections in cattle.
INTRODUCTION
Most evidence suggests that the majority of cattle with tuberculosis are infected via the respiratory route (Francis, 1958; Wilesmith et al., 1982; Anon, 1984). It has been postulated that, in human pulmonary tuberculosis, mycobacteria contained in "droplet nuclei" are inhaled and pass to the alveoli where, after evaporation of the droplet, the mycobacteria are deposited on the alveolar lining and may give rise to pulmonary lesions (Ratcliffe and Palladino, 1953 ). Although the precise mechanisms involved are not fully understood, lung tubercules may serve as sources of infection. Mycobacteria shed from lesions into the respiratory tract, may subsequently be expelled mechanically to the external environment in aerosolised secretions. Until recently, it was generally accepted that only 1-2% of tuberculous cattle could be designated "open" cases capable of spreading tuberculosis (Gallagher, 1980; Anon, 1984). These were cattle found at abattoir inspection to have lesions both in their respiratory lymph nodes and lungs. Mcllroy et al. ( 1986 ) however, critically examined lungs and lymph nodes from tuberculin*Present address: Veterinary Division D u n d o n a l d House, Belfast BT4.
0378-1135/91/$03.50
© 1991 - - Elsevier Science Publishers B.V.
104
S.D. NEILL ET AL.
reacting cattle and demonstrated that the majority of animals with respiratory lymph node lesions also had lung lesions, and therefore were open cases. In addition they found that 19% of these cattle had Mycobacterium bovis in their respiratory secretions. Despite its obvious importance in the epidemiology of bovine tuberculosis, there is relatively little published information on M. boris excretion from tuberculous cattle. Rempt (1954) reported that 6% of 40 000 specimens from tuberculin-reacting animals in the Netherlands were positive for M. bovis; Krishnaswamy et al. ( 1974 ) isolated M. bovis from sputum of 15.6% of tuberculin-reacting cattle in a herd in India; De Kantor et al. ( 1989 ) reported M. bovis in nasal secretions from 9.3% of tuberculin-reacting cattle in a herd in Argentina and Neill et al. (1988a) in a second study isolated M. bovis from the anterior respiratory tracts of 20% of randomly taken tuberculous cattle at an abattoir in Northern Ireland. The suggestion that all tuberculous cattle should be regarded as excretors of M. bovis (McIlroy et al., 1986) is substantiated by the findings of more recent studies by Neill et al. ( 1988b; 1989 ). These studies have shown experimentally that excretion of M. bovis is a consistent feature of tuberculosis in cattle. In an attempt to understand and define when tuberculous cattle might first become infectious, an analysis was carried out of available experimental data on M. bovis excretion. This paper reports the findings of the analysis. MATERIALS AND METHODS
Groups consisting of five 4-7 month old calves, were infected by intranasal instillation of field isolates of M. bovis. Specimens of nasal mucus were collected from each calf prior to inoculation and at weekly intervals thereafter. Details of the experimental procedures and culture methods employed have previously been reported (Neill et al., 1988b). The time period between inoculation and the initial detection of M. bovis in the nasal mucus was determined for each calf in these experiments. The length of the delay or lag period before excretion began was also determined for two other calves which were similarly infected by intranasal instillation with 104 M. bovis organisms in a subsequent experiment (Neill, unpublished data). Transmission of tuberculosis by contact between infected and non-infected cattle has been demonstrated experimentally and the procedures and cultural methods employed were published (Neill et al., 1989 ). The time between the introduction of the uninfected calf to the tuberculous cattle and the first detection of M. bovis in the nasal mucus from the former animal was noted. In addition the contact period before the initial detection of M. bovis in nasal mucus from another calf infected after introduction to tuberculous cattle in a second similar experiment was also determined (Neill, unpublished data). Using assumed values of 100, 10 and 1 respectively, for the number of or-
MATHEMATICALMODEL FOR M. BO~TSEXCRETION FROM TUBERCULOUSCATTLE
105
ganisms required to cause "natural" infection, regression equations to describe the relationship between the number of organisms in the inoculum and the lag period before excretion began were determined. The statistical and graphical computer packages Stat 80 and Grafit 1000 (Zyxomma) were employed. RESULTS
Table 1 shows, for twelve animals, the delay before excretion was detected following intranasal inoculation with M. bovis. Table 2 shows, for two animals, the periods of contact with infected cattle prior to the initial isolation ofM. bovis from nasal mucus of the two animals which subsequently became infected. Table 3 shows the proportions of variation explained by the regression TABLE 1 Delay before initial detection of Mycobacterium bovis in nasal mucus of experimental cattle infected intranasally Animal Number
lnoculum (cfu's)
Delay period (days)
1357 1356 1300 1299 1338 1841 1840 A462 A465 2149 2148 1245
1X 106 1X 106 1X 106 IX 106 1X 106 4 X 104 4 X l04 9.6X l03 9.6×103 9.6X 103 9.6X 103 9.6× 103
7 12 12 12 12 22 30 7 29 15 22 15
*cfu's: Colony forming units. TABLE 2 Delay before initial detection ofM. bovis in nasal mucus of cattle following contact with tuberculous cattle
Animal Number
lnoculum
Delay period (days)
A467 1862
U* U
92 82
*U = unknown.
106
S.D. NEILL ET AL.
TABLE 3 The proportion of variation explained by fitting regression equations when different hypothetical values for number of organisms involved in natural infection Number of organisms
Variation
100 10
67% 78% 84%
1
equations when hypothetical values of 100, 10 and 1 M, bovis organisms respectively were used for those animals infected naturally. The relationship between the inoculum size (log2 number of organisms in the inoculum) and the delay before excretion, was best represented by the equation y = - 0 . 2 2 8 x + 20.04. (The standard error of the slope is + 0.028. ) The proportion of variation explained by fitting the regression equation (R 2 ) was 84% and the F statistic was very highly significant ( P < 0.001 ). In this it was assumed that natural infection was caused by one organism. DISCUSSION
While evidence suggests that M. bovis infection usually occurs via the respiratory route, the precise pathogenesis remains unclear. Both the size of the inhaled droplet nucleii and the number of mycobacteria contained within them appear to be major factors in establishing tuberculosis (Wells et al., 1948 ). It is impossible to know the droplet size of the quantity of mycobacteria present at the initiation site (s) of infection. In the experimental infections from which the current data is drawn (Neill et al., 1988b; 1989; unpublished data) the inocula had been sonicated prior to use to disrupt any "clumped" mycobacterial cells and to produce an even distribution of organisms for delivery to the cattle. The numbers of mycobacteria delivered to each animal were estimated from reproducible viable count determinations. No such quantitative estimations could be ascertained for those animals infected naturally in the field or under experimentation by contact transmission. The number of mycobacteria involved in such infections must therefore be hypothetical. From the initial inspection of the data compiled (Tables 1 and 2) there appears to be an inverse relationship between the number of organisms delivered to each animal and the lag period before M. bovis excretion began. This lag or adaptive period is complex and will obviously reflect possible phenotypic changes in the organism and any host-organism interaction. An inverse exponential relationship between the quantity of organisms given and the lag period before excretion occurred, was confirmed by the analysis carried out. Despite the additional assumption that mycobacteria are also uniformly dis-
MATHEMATICAL MODEL FOR M. B O V I S EXCRETION FROM TUBERCULOUS CATTLE
107
tributed in inocula received by naturally infected cattle, the linear equation representing the transformed data (Fig. 1 ) was highly significant ( P < 0.001 ). The proportions of variation shown in Table 3 indicate an improvement in the relationship as the hypothetical numbers of organisms involved in the natural infections approach unity. From this one might suggest that as few as one single organism may be sufficient to cause infection. This would concur with work cited by Francis ( 1947 ) in which Chausse ( 1913 ), from studies on sheep and cattle, suggested that probably only one organism would produce a lesion in lung tissue. Lurie et al. (1950) produced tuberculosis in rabbits when as few as three tubercle bacilli were inhaled and Ratcliffe and Palladino ( 1953 ) have shown that in the guinea pig, mouse and rat, inhalation of single organisms could produce tuberculosis. These latter authors postulated that in man tuberculosis could also develop from inhalation of a single bacillus. The concept of single nuclei infections in cattle would be supported by the findings of the study reported by McIlroy et al. (1986). These workers found only single lesions present in 63% of lungs from tuberculous cattle, despite critical laboratory examinations. The precise mycobacterial load involved in initiating bovine field infections is unknown and may be different in every instance. Thus, individual cattle may begin to excrete M. bovis at different times after infection is initiated. In the experiments ofNeill et al. (1988b; 1989), sampling of nasal mucus for culture examination was limited, approximately every seventh day. However, from the limited data available, it would appear that in natural tuberculosis, initial excretion ofM. bovis would possibly occur around 87 days (SD _+7.1 days) after infection takes place.
.~. 2 0 i
r) ~4
o~ ~
,,
~ ¢o
E 0
i 0
,
i
,
50
Delay
before
~r~
~
i 1 O0
(days)
excretion
Fig. I. Relationship between the number of organisms given to experimental ca[tie and the delay before excretionwas detected.
lO~
S.D. NEILL ETAL.
Abattoir studies of tuberculin-reacting cattle in Northern Ireland (Mcllroy el al., 1986; Neill et at., 1988) revealed animals from which M. bovis was isolated from nasal mucus at the time of slaughter, The periods between recovery of M. boris in respiratory tracts of these animals and the time at which the last negative tuberculin test was performed were reported. Usually this simply reflects the intratest period during which the infection could have occurred at any stage. However in the study by Neill et al. (1988), four of the five mucus-positive animals were reported to have been tested solely because they were in contact with tuberculous cattle on neighbouring farms. Therefore for these four animals, with test intervals of 68, 69, 56 and 87 days respectively, it appears that the time between the infection occurring and M. boris excretion beginning was at most 87 days. A new equation ( y = - 0 . 2 5 6 x+20.147) derived from the experimental data (Tables 1 and 2) and the four specific lag periods related to the field cases above, did not differ significantly from that representing the experimental data alone. The proportion of variation accounted for by fitting the exponential model was increased to 87%. It would therefore appear that in natural tuberculosis the projected experimental estimate of around 87 days for the delay between infection and excretion was realistic. ACKNOWLEDGEMENTS
The authors are extremely grateful to Mr. J. Rainey (Agricultural Biometrics, Department of Agriculture for N. Ireland) for his help and advice with this publication. REFERENCES Anon, 1984. Ann. Report on Research and Technical Work, Belfast. Her Majesty's Stationery Office. p. 244. Chausse. P., 1913. Des methodes a employer pour realiner la tuberculose experimentale par inhalation. Bull. Soc. Med. Vet., 31: 267-274. Francis, J., 1947. Bovine Tuberculosis. Staples Press, London, p, 87. Francis, J., 1958. Tuberculosis in animals an man. Cassell, London, p. 16. Gallagher, J., 1980. In: Lord Zukermann (Editor), Badgers, cattle and tuberculosis. The role of other animals in the epidemiology of TB of the Badger. Her Majesty's Stalionery Office, London, p. 86-94. Kantor, 1.N. de, Bioch, D. and Roswurm, J.D., 1978. Mycobacteria isolated from nasal secretions of tuberculin test reactor cattle. Am. J. Vet. Res., 39: 1233-1238. Krishnaswamy, S., Nagaraja, K.V., Keshavamurthy, B.S., Adinarayanaich, C.L. and Nanjiah, R.D., 1984. Isolation and identification of tubercule bacilli from "open cases" of bovine tuberculosis. Mysore. J. Agric. Sci., 8: 423-428. Lurie, M.B., Heppelston, A.G., Abramson, S. and Swartx, 1.B., 1950. Evaluation of method of quantitative airborne infection and its use in study ofpathogenesis of tuberculosis. Am. Rev. Tuberc., 61: 765-797. Mcllroy, S.G., Neill, S.D. and McCracken, R.M., 1986. Pulmonary lesions and Mycobacterium
MATHEMATICAL MODEL FOR M. BOFIS EXCRETION FROM TUBERCULOUS CATTLE
109
bovis excretion from the respiratory tract of tuberculin reacting cattle. Vet. Rec., 118: 718721. Neill, S.D., O'Brien, J.J. and McCracken, R.M., 1988a. Mycobacterium boris in the anterior respiratory tracts in the heads of tuberculin reacting cattle. Vet. Rec., 122:184-186. Neill, S.D., Hanna, J. and O'Brien, J.J., 1988b. Excretion of Mycobacterium bovis by experimentally infected cattle. Vet. Rec., 123: 340-343. Neill, S.D., Hanna, J. and O'Brien, J.J,, 1989. Transmission of tuberculosis from experimentally infected cattle to in-contact calves. Vet. Rec., 124: 269-271. Ratcliffe, H.L. and Palledino, V.S., 1953, Tuberculosis induced by droplet nuclei infection: initial homogenous response of small mammals (rats, mice, guinea pigs and hamsters) to human and bovine bacilli, and rate and pattern oftubercule development. J. Exper. Med.. 97: 61-67. Rempt, D., 1954. Veterinary work in the Netherlands. 1953. Netherlands Veterinary Service, p. 80. Wells, W.F., Ratcliffe, H.L. and Crumb, C., 1948. On the mechanism of droplet nuclei infection. Am. J. Hyg., 47:11-28. Wilesmith, J.W., Little, W.A., Thompson, H.V. and Swan, C., 1982. Bovine tuberculosis in domestic and wild mammals in an area of Dorset. J. Hyg., 89:195-210.
