Computer Simulation of Babesia bovis (Babes) and B. bigemina (Smith & Kilborne) Transmission by Boophilus Cattle Ticks (Acari: Ixodidae) D. G. HAILE, G. A. MOUNT, AND L. M. COOKSEY 1 Medical and Veterinary Entomology Research Laboratory, USDA-ARS, Gainesville, Florida 32604

KEY WORDS Arachnida, Boophilus spp., babesiosis, computer modeling

The cattle fever p&rasitesBabesia bovis (Babes) and Babesia bigemina (Smith & Kilborne) and their Boophilus tick vectors were eradicated from the United States during the first half of the 20th century. However, these cattle parasites are a continuing threat to the cattle industry in the United States because of the proximity of Babesia-infected cattle and ticks in Mexico (Teclaw et al. 1985) and the Caribbean. Although babesiosis is now considered an exotic disease of cattle in the United States, it is an important disease of cattle in tropical and subtropical regions of the world. It is estimated that one half billion cattle throughout the world are at risk of infection with the disease caused by one or more species of Babesia. B. bovis and B. bigemina occur in Africa, Australia, Asia, and Central and South America. Enzootic zones typically have stable populations of ticks with densities sufficient to ensure inoculation of all calves with Babesia before =9 mo of age. Colostral antibodies and age resistance protect exposed calves from developing severe reactions (Hall 1960, 1963; Mahoney 1972). Marginal zones are characterized by variations in vector tick population densities because of either marginal environments or intermittent tick control efforts. When tick densities are low, some cattle escape 1

1950-F Leslie Drive, Kerrville, Texas 78028.

infection until after 9 mo of age. New Babesia infections in cattle 9 mo of age are severe and death may occur. A real probability of epidemic babesiosis exists when high Boophilus tick densities are reduced to low levels for a year or more and then allowed to increase to earlier levels (Curnow 1973a,b). Successful management of babesiosis in cattle where Boophilus tick eradication is not feasible will depend on increased knowledge of the interactions between the Babesia parasites, their tick vectors, and cattle hosts. Computer modeling represents an important research tool for the development of new knowledge and strategies for the management of Babesia. Methods for development of simulation models that combine dynamics of tick vector population and disease transmission were demonstrated by Mount & Haile (1989) and Cooksey et al. (1990). Recently, Mount et al. (1991) developed a computer simulation model (BCTSIM) on the population dynamics of the tick vectors of Babesia, B. microplus and B. annulatus (Say). Previous modeling research on Babesia transmission includes a mathematical analysis of the transmission process for B. bovis parasites in Bos taurus cattle (Ross & Mahoney 1974). Smith (1983) extended this basic mathematical approach to include parameters related to growth and development of B. microplus.

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J. Med. Entomol. 29(2): 246-258 (1992) ABSTRACT A computer model was developed to simulate the processes involved in transmission of the cattle fever parasites Babesia bovis (Babes) and Babesia bigemina (Smith & Kilborne) between cattle and Boophilus ticks. The model of Babesia transmission was combined with a dynamic life history model for population dynamics of the tick vectors, Boophilus microplus (Canestrini) and B. annulatus (Say). Epidemiological parameters and relationships in the model include the reduction in fecundity of infected ticks, rate of transovarial transmission, effect of cattle type and inoculation rate on infectivity of cattle, variation of infected cattle recovery rate with age of infection, inoculation rate, and species of parasite. Some parameters in the model were fitted by iterative simulations to produce realistic rates of Babesia infection in larval ticks. Comparisons of simulated and reported epidemiological data from one location in Australia indicated a reasonable level of validity for the model. Theoretical tick density thresholds for maintenance of Babesia in cattle and for inoculation of s99.5% calves were determined by iterative simulations at 10 locations with B. microplus and six locations with B. annulatus. The model and transmission thresholds can serve as the basis for further simulation studies on strategies for control or eradication of babesiosis.

March 1992

HAILE ET AL.: COMPUTER SIMULATION OF

Our objective in this study was to extend BCTSIM to include simulation of Babesia transmission between and within Boophilus ticks and cattle. In this paper, we describe the development and validation of the Babesia portion of the model. We also present results of computer simulations to determine the relative sensitivity of model variables. Simulations were used to estimate tick density thresholds for maintenance of Babesia in cattle and for inoculation of ^99.5% calves by 9 mo of age. Simulation of strategies for control or eradication of Boophilus ticks and Babesia parasites will be the subject of a later article. Modeling Methods

TRANSMISSION

247

A simplified structure for dynamics of a cattle herd was used to separate numbers of susceptible and infected animals. Susceptible animals are separated into calves with weekly age classes 1-38 wk old and an accumulator for cattle 2:39 wk old. Weekly age classes for calves were used to account for inoculation before 39 wk of age. New calves are added to the cattle population at a weekly rate to represent various levels of calving in a herd. The cattle population remains at a constant level by removing cattle from all stages (susceptible and infected) at a weekly rate equal to the weekly calving rate. This procedure is somewhat artificial because removal of animals, calving, and herd replacement are normally seasonal. However, the constant removal and replacement method provides a stable cattle density for convenient and precise simulations of equilibrium tick populations. Moreover, we considered this method of modeling cattle dynamics to be adequate for this study. A more realistic procedure for calving and animal removal and replacement can be added to the model for future simulations. Infected animals are separated into weekly cohorts of infections after a primary infection from an infected tick. This procedure allows for variation of infectivity to ticks and recovery from infection with the age of infection. The inoculation rate or the proportion of cattle receiving an infection during each time step is determined from the number of infective ticks (discussed below). Cohorts of cattle that receive primary infections are prepatent for 2 wk and then become highly parasitemic for 1 wk (Callow & Hoyte 1961, Mahoney 1969). A death rate from the Babesia infection is included during the initial week of parasitemia. However, death rates can vary with species of parasite and type of cattle. For this study, the death rate was set to zero to provide constant densities of cattle during long simulation runs. A zero death rate is analogous to immediate replacement of dead cattle with previously inoculated cattle. The infectivity level of infected cattle is defined as the proportion of susceptible female ticks that become infected while feeding on a cohort of infected animals. The infectivity level for cattle infected with B. bovis during the initial week of high parasitemia was modeled at 0.9 for Bos taurus cattle, based on data from Mahoney (1969) and Mahoney & Ross (1972). Infectivity levels of 0.75 and 0.6 were used for Bos taurus x Bos indicus and Bos indicus cattle, respectively, based on data from Johnston (1967, 1978). Infectivity level for cattle infected with B. bigemina during the initial week of parasitemia was set at 0.6 for all types of cattle, based on data from Johnston (1967). After the initial week of parasitemia, cohorts of infected animals (carriers) have variable periods of parasitemia, depending on the species of

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Our approach to the development of a simulation model for Babesia transmission was similar to that used for Rocky Mountain spotted fever by Cooksey et al. (1990). The Babesia transmission model was constructed with discrete age classes for ticks and cattle. Weekly age classes and time steps were used for compatibility and integration with BCTSIM (Mount et al. 1991). Most model parameters represented values from the literature. However, some parameters were developed from the model itself by comparison of simulated epidemiological data with results reported in the literature. The structure of the Babesia model (Fig. 1) was designed to represent the movement of the parasite between and within ticks and cattle. The model incorporates the interactions between infective and susceptible individuals in the tick and cattle populations. Three general assumptions were required in construction of the model: (1) that every cow of one type is equally susceptible to Boophilus tick infestation, (2) that all cattle of the same type are equally susceptible to Babesia infection, and (3) that infected ticks survive equally long as noninfected ticks. Although these assumptions are not totally realistic, they are consistent with our objective of modeling mean tick populations and levels of disease transmission. Infection in Cattle. The ability of cattle to transmit Babesia to engorging ticks is dependent on parasitemia. Cattle are immune to clinical disease following recovery from a primary infection. However, a variable number of relapses with detectable parasitemia occur. B. bigemina is more rapidly controlled by the immune system than B. boms. Acquired immunity begins to eliminate B. bigemina ~6 mo after an infection, compared with >2 yr for B. bovis (Mahoney 1962, Mahoney & Ross 1972). The almost continuous parasitemia in cattle between 6 mo and 2 yr of age in enzootic areas is likely attributable to superinfection (reinfection with the same species of parasite) by ticks infected with different Babesia strains rather than relapse parasitemia (Mahoney 1962).

Babesia

248

Vol. 29, no. 2

JOURNAL OF MEDICAL ENTOMOLOGY

SUSCEPTIBLE TICKS Weekly Aga Classes for Ticks

INFECTED TICKS

MOOS

fHEM-LMNQLMVAE

ADULT 9 Q

ENQOftQED ADULT 9 9

Removals and

non-Babesle

Weekly Age Classes for Calves

d$ath$

Constant removal rats for all cattle stages '

New Calves

INFECTED CATTLE

3 }

InfectMty levels varied byBabeala species, Inoculation rate and cattle type

~

Initial Parasltemta HlghlnfectMty~^

Recovery rate variable with Inoculation rate. Babes/a species and age of Infection

* Partially Infective, Recovering

RECOVERED, IMMUNE AND NONINFECTIVE U m Maximum Age of Infection 283 weeks for Bsbesla bovts it weeks lor Babeala blgemlna

Fig. 1. Model representation of the transmission of B. bovis and B. bigemina between populations of Boophilus ticks and cattle.

Babesia and amount of superinfection (Johnston 1967, Mahoney 1969, Mahoney et al. 1973). This variable parasitemia is represented in the model by variation of infectivity level with inoculation rate (Fig. 2) as an indicator of the level of superinfection. The relationships on cattle infectivity shown in Fig. 2 are calculated from mean reported maximum and minimum levels of infectivity (Johnston 1967, Mahoney 1969, Mahoney

et al. 1973). Infectivity level in cattle infected with B. bovis also is varied with type of cattle. Recovery of cattle is modeled as complete elimination of parasites and transfer to an immune, noninfective state. Recovery rate is dependent on age of infection and inoculation rate. The basic recovery rate (R) for low inoculation rates (5 yr until tick density and Babesia infection rates in ticks and cattle reached an equilibrium level. At the end of each simulation run, a summary display was printed that included average parameters for the final year to compare with other simulation results. Selected results are presented in Table 2 for B. bovis transmission and in Table 3 for B. bigemina transmission. Table 2 shows that inoculation rates for B. bovis transmitted by both species of ticks are sensitive to deviations in all variables. The maximum-minimum ratios for inoculation rates indicate that transmission by B. microplus is most sensitive to the biotic variables (transovarial transmission, fecundity reduction, and infectivity in cattle). Transmission of B. bovis by B. annulatus is somewhat less sensitive to changes in these biotic variables. This difference in sensitivity is apparently attributable to higher numbers of engorging larvae available with B. annulatus than with B. microplus. Table 3 shows that inoculation rates for B. bigemina transmitted by B. microplus and B. annulatus are sensitive to deviations in all variables. However, the maximum-minimum ratios indicated that inoculation rates are somewhat less sensitive to changes in biotic and environmental variables with B. bigemina, than with B. bovis. One exception is variation in cattle replacement rate, which produced a higher maximum-minimum ratio with transmission of B.

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" Mean weekly number of larvae per calf transferring to the nymphal stage •=- 7. b Percentage infection of calves at 9 mo (39 wk) of age, unless otherwise indicated. Estimated by multiplying standard female ticks per calf per day on one side by four. d Values in parentheses: (simulated larvae/calf -r reported larvae/calf) x reported inoculation rate. c Percentage infection at mean age of =3.5 mo. •^Observed value (other reported values for percentage infection of larvae are calculated). s Percentage infection at mean age of =6 mo. c

252

Vol. 29, no. 2

JOURNAL OF MEDICAL ENTOMOLOGY

Table 2. Simulation of the effects of biological and environmental variables on epidemiological parameters for B. bovis transmitted by Boophilus ticks at equilibrium densities on Bos taurus cattle using historical weather for Monterrey, Nuevo Leon, Mexico Variable

Level

Transovarial transmission

0.0014 0.0042 0.285 0.855 0.065-0.195 0.195-0.585 0.0:0.4:0.6 0.4:0.4:0.2 0.577% 1.731% 0.192 0.576

Inoculation rate"

Max/min ratiob 7.24

21

0.0033 0.0239 0.0034 0.0237 0.0037 0.0228 0.0075 0.0191 0.0066 0.0151 0.0069 0.0156 0.0128

20 23 14 49 21 20 12 29 23 17 .22 19 20

0.0028 0.0656 0.0230 0.1007 0.0139 0.0583 0.0160 0.0604 0.0174 0.0526 0.0253 0.0443 0.0386

Standard no. 9 ticks/cow/d B. microplus

Fecundity reduction Infectivity in cattle Type of pasture

0

Replacement rate No. cattle/ha

21 21 21 21 21 20 18 24 21 21 18 22

Standard''

Type of pasture0 Transovarial transmission No. cattle/ha Infectivity in cattle Replacement rate

6.16 2.55 2.29 2.26 —

B. annulatus 0.285 0.855 0.0:0.4:0.6 0.4:0.4:0.2 0.0014 0.0042 0.192 0.576 0.065-0.195 0.195-0.585 0.577% 1.731%

Standard

5.13 4.38 4.19 3.78 3.02 1.75 —

" Daily proportion of calves infected. '' Inoculation rate of high level + inoculation rate of low level. c Ratio of improved dense/unimproved/improved light. d Standard variable levels are 0.0028 transovarial transmission rate, 0.57 fecundity reduction, 0.13—0.39 cattle infectivity range, 1.154% weekly cattle replacement rate, 0.384 cattle/ha, and 0.2 improved dense/0.4 unimproved/0.4 improved light pasture ratio.

bigemina by B. annulatus than B. bovis by B. annulatus. The somewhat decreased sensitivity of B. bigemina to changes in variables, compared with B. bovis, is due to higher transovarial and recovery rates for the former. Transmission Thresholds. The Babesia simulation model was used to determine tick density thresholds for disease transmission. For this study, we defined two transmission thresholds. The first threshold is the minimum density of Boophilus ticks required to maintain Babesia transmission in populations of ticks and cattle (maintenance threshold). Mahoney & Ross (1972) state that Babesia persists in the enzootic environment because enough ticks are present to replace each generation of infected cattle with a succeeding one at least of equal size. When tick densities are controlled below the maintenance threshold, parasites will eventually disappear from ticks and cattle. The second threshold is the minimum density of Boophilus ticks required to inoculate ^99.5% of calves with Babesia parasites by 9 mo of age (inoculation threshold).

We used an iterative procedure to determine transmission thresholds for Babesia parasites. Various densities of Boophilus ticks were simulated by adjustments in the base host-finding rate for unfed tick larvae. Maintenance thresholds were first estimated by simulations with decreasing tick densities until Babesia infections in cattle disappeared. Then iterative simulations with tick densities above and below the estimated threshold were run until the minimum number of ticks required to maintain Babesia infection in ticks and cattle for ^ 5 yr was determined. A similar process was used to determine the minimum number of ticks required to inoculate >99.5% of calves for >5 yr as the inoculation threshold. During each simulation run, all variables were held constant except host-finding. The constant variables for simulation included 1.154% weekly calving and removal rate (60% yearly calving rate), 0.2 improved dense/0.4 unimproved light/0.4 improved light pasture ratio, and 0.384 cows/ha (0.313 cows and 0.188 calves as 0.071 cow-equivalents). Historical weather for

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Fecundity reduction

6.97

March 1992

HAILE ET AL.: COMPUTER SIMULATION OF

Babesia

253

TRANSMISSION

Table 3. Simulation of the effects of biological and environmental variables on epidemiological parameters for B. bigemina transmitted by Boophilus ticks at equilibrium densities on Bos taurus cattle using historical weather for Monterrey, Nuevo Leon, Mexico Variable

Level

Transovarial transmission

0.0245 0.0735 0.285 0.855 0.577% 1.731% 0.035-0.105 0.105-0.315 0.0:0.4:0.6 0.4:0.4:0.2 0.192 0.576

Standard no. 9. ticks/cow/d

Inoculation rate"

Max/min ratio''

0.0206 0.0819 0.0208 0.0814 0.0245 0.0730 0.0265 0.0777 0.0409 0.0710 0.0406 0.0592 0.0520

3.98

0.0565 0.2383 0.0441 0.1604 0.0423 0.1373 0.0446 0.1304 0.0508 0.1167 0.0528 0.1214 0.0870

4.22

B. microplus Fecundity reduction Replacement rate Infectivity in cattle Type of pasture0 No. cattle/ha

21 21 21 21 21 21 21 21 19 27 18 23

Standard''

21

3.19 2.98 2.93 1.74 1.46 —

Type of pasture0 No. cattle/ha Fecundity reduction Transovarial transmission Replacement rate Infectivity in cattle

0.0:0.4:0.6 0.4:0.4:0.2 0.192 0.576 0.285 0.855 0.0245 0.0735 0.577% 1.731% 0.035-0.105 0.105-0.315

Standard^

16 69 13 45 23 26 24 24 25 23 25 23 24

3.64 3.25 2.92 2.30 2.30 —

" Daily proportion of calves infected. h Inoculation rate of high level -j- inoculation rate of low level. c Ratio of improved dense/unimproved/improved light. d Standard variable levels are 0.049 transovarial transmission rate, 0.57 fecundity reduction, 0.07—0.21 cattle infectivity range, 1.154% weekly cattle replacement rate, 0.384 cattle/ha, and 0.2 improved dense/0.4 unimproved/0.4 improved light pasture ratio.

each geographic location was used for the simulations. The simulations were started with 100,000 eggs of Boophilus ticks on week 16 (Northern Hemisphere) or week 42 (Southern Hemisphere) of the first year. During the second year of simulation, 100 or more engorged female ticks/ha infected with Babesia parasites were added during week 1 to start transmission in the tick and cattle populations. Five or more years of simulation were then run to achieve equilibrium levels of Boophilus ticks and Babesia parasites before transmission thresholds were determined. Simulations were run at 10 locations with B. microplus and for six locations with B. annulatus with B. taurus and B. taurus x B. indicus cattle. Maintenance thresholds and associated epidemiological parameters for each simulation are presented in Table 4 and similar data for inoculation thresholds are presented in Table 5. Transmission thresholds were determined at only three locations with each species of tick infesting B. indicus cattle. These locations were Brownsville, San Juan, and Townsville with B.

microplus; and Agadir, Monterrey, and San Antonio with B. annulatus. Results shown in Table 4 indicate that maintenance thresholds and associated epidemiological parameters are influenced mostly by species of Babesia parasite. Differences among geographic locations, type of cattle, and species of Boophilus tick were slight. The differences in maintenance thresholds (standard female ticks per cow per day), tick bites per host per day, infection rates in cattle and ticks, and inoculation rates are from differences in transovarial transmission rates, cattle infectivity, and cattle recovery between B. bovis and B. bigemina. Overall, tick bites per host per day are higher with B. bovis than with B. bigemina, and percentage infections in cattle and ticks are higher with B. bigemina than with B. bovis. Inoculation rates are similar for the two species of Babesia. Results shown in Table 5 indicate that inoculation thresholds (standard female ticks per cow per day) for B. bovis vary 2-fold from one geographic location to another. For example, the in-

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B. annulatus

0.0169 0.0244

23 33

13 41 24 38 28 33

6 5 6 5 5 5

0.00031 0.00043

0.00047 0.00032 0.00050 0.00014 0.00053 0.00037 0.00044 0.00080 0.00113

0.00123 0.00083 0.00133 0.00038 0.00139 0.00099 0.00114

0.0047 0.0297 0.0112 0.0242 0.0151 0.0232

2 13 5 18 10 12

0.00028 0.00041

0.00011 0.00056 0.00025 0.00045

0.00075 0.00108

0.00030 0.00148 0.00066 0.00119

5 0.0110 0.00020 0.00053 B. bigemina transmitted by B. annulatus

0.0268 0.0184 0.0277 0.0079 0.0304 0.0211 0.0237

35 32 34 15 36 32 37

16

0.00131 0.00082 0.00014 0.00058

3 0.0009 0.00006 0.00014 1 0.0006 0.00004 0.00012 B. bigemina transmitted by B. microplus

0.00050 0.00031 0.00005 0.00022

7 5

0.0049 0.0035 0.0008 0.0029

17 20

0.00055 0.00030

13 9 2 7

0.00021 0.00011

0.00027 0.00038 0.00028 0.00016 0.00031 0.00020 0.00035

41 30 7 24

0.0027 0.0017

0.00010 0.00014 0.00011 0.00006 0.00012 0.00008 0.00013

29 25 19 22

4 3

0.0018 0.0022 0.0014 0.0009 0.0015 0.0011 0.0020

No. Standard 9 ticks

6 6 7 6 6 6

19 30

5 5

24 36

23 44 41 35

16

43 34 19 28 41 33 36

5 5 5 5 5 5 5

8 14

5 15 14 14

0.0108 0.0216

7 14

0.0113 0.0254

0.0088 0.0326 0.0191 0.0191

0.0093

0.0333 0.0204 0.0115 0.0157 0.0347 0.0214 0.0258

19 13 6 7 18 11 13

0.0007 0.0024

2 11 7 30

21 36

2 2 3 2

2 2

2 2 2 2 2 2 2

8 14

0.0013 0.0045 0.0011 0.0024

0.0007

0.0015 0.0015

0.00023 0.00049

0.00023 0.00067 0.00048 0.00039

0.00019

0.00022 0.00040

0.00065 0.00039 0.00021 0.00030 0.00067 0.00041 0.00049

0.00005 0.00031

0.00014 0.00069 0.00011 0.00025

0.00007

0.00017 0.00014

0.00100 0.00063 0.00004 0.00062 0.00008 0.00098 0.00009

0.0013 0.0008 0.0005 0.0007 0.0009 0.0011 0.0010

0.00061 0.00129

0.00060 0.00175 0.00125 0.00102

0.00051

0.00059 0.00106

0.00171 0.00102 0.00056 0.00078 0.00176 0.00108 0.00128

0.00014 0.00082

0.00037 0.00180 0.00028 0.00064

0.00018

0.00045 0.00036

0.00025 0.00017 0.00011 0.00016 0.00022 0.00026 0.00024

Inoculation rate Calves Cows

Larvae

3 16 3 8 18 47 13 26

24 42 27 29

9 16 10 11

3

7

10

5 3 2 3 3 4 3

26

30 26

11 10

12 8 6 7 10 11 1

Calves

3 3

21 22 23 27 26 26 26

8 8 9 10 10 10 10

Herd

15 13

Cows

B. taunts X B. indicus cattle Tick bites* % Infection Calves

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° Minimum number of standard female ticks for maintenance of parasites in cattle herd and tick population. Tick bites indicate number of successfully engorging larvae (B. bovtis) or nymphs (B. bigemina) per host per day.

Americas Jackson, Miss. Monterrey, Nuevo Leon, Mexico Nashville, Tenn. San Antonio, Tex. Africa Agadir, Morocco Malakal, Sudan

Americas Arauca, Arauca, Colombia Brownsville, Tex. Formosa, Goias, Brazil Monterrey, Nuevo Leon, Mexico San Juan, Puerto Rico San Salvador, El Salvador Tampico, Tamaulipas, Mexico Australia Brisbane, Queensland Townsville, Queensland South Africa Durban

Americas Nashville, Tenn. Jackson, Miss. Monterrey, Nuevo Leon, Mexico San Antonio, Tex. Africa Malakal, Sudan Agadir, Morocco

18 12

3 4 3 4 5 9 3

2 0.0007 0.00055 0.00014 B. bovis transmitted by B. annulatus

22 19

8 7

11 15 13 7 14 7 15

5

16 19 20 19 21 19 19

6 7 8 7 8 7 7

Calves

Inoculation rate Calves Cows

B. bovis transmitted by B. microplus

B. taunts cattle % Infection Cows Herd Calves Larvae

Tick bites 6

to to

Americas San Juan, Puerto Rico Arauca, Arauca, Colombia Brownsville, Tex. Formosa, Goias, Brazil Monterrey, Nuevo Leon, Mexico San Salvador, El Salvador Tampico, Tamaulipas, Mexico Australia Brisbane, Queensland Townsville, Queensland South Africa Durban

No. Standard 9 ticks

Table 4. Simulated standard female Boophilus ticks per cow per day, tick, bites per calf or per cow-day, and other epidemiological parameters for Bubesia parasite maintenance thresholds'* at various geographic locations

0

r 0

0

o

o r W

0

tn

0

c

0

N3

to CD 3 O

Vol.

20 30

11 13

19

13 21 22 38 25

22 19

14 15

10 12 16* 10*

19 17 21 15 17 17 21

14 14 14 14 14 15 16

89 133

20 28

105

35 65 87 71 46

69 120

24 39

14 19 15* 10*

53 58 65 69 70 87 97

53 78

55 59 99 65

49

57 50

51 44 56 39 44 46 56

235 349

171 228 188 120

275

182 315

139 152 172 182 185 228 256

96 99

97 97 93 92

86

85 92

97 93 97 94 95 96 97

97 99

97 97 90 87

88

90 83

93 96 96 97 92 98 97

Inoculation rate Calves Cows

19 20 21" 21 24 13 C 13"

0.0363 0.0357 0.0178 0.0158

0.0323 0.0296 0.0125 0.0072

0.0606 0.0737 0.0316 0.0184

0.1467 0.1472

99.5 + 99.5+ 0.0282 0.0266

0.0273 0.0209 0.0270 0.0210 0.0209 0.0226 0.0299 0.0713 0.0697

0.0709 0.0549 0.0696 0.0553 0.0550 0.0596 0.0783

99.5+ 99.5+

99 93

99.5 + 99.5 +

0.1352 0.1334

0.1452 0.1518 0.1270 0.1218

0.0257 0.0332

0.0292 0.0330 0.0444 0.0283

0.0664 0.0832

0.0738 0.0857 0.0989 0.0645

0.0233 0.0602 99.5+ 0.1386 B. bigemina transmitted by B. annulatus

0.1503 0.1304 0.1389 0.1475 0.1313 0.1385 0.1479

99.5+ 99.5+ 99.5+ 99.5+ 99.5+ 99.5+ 99.5 +

0.0342 0.0292 99.5 + 0.0743 0.0969 0.0358 0.0394 99.5+ B. bigemina transmitted by B. microplus

90 79

99.5+ 99.5 +

io c

8* 10 8* 7*

15

14* 12

12 12 11 12 12 13 12

10* 8*

14" 8" 8* 7*

19"

0.0545 0.0509 0.0570 0.0679 0.0601 0.0768 0.0748

0.0346 0.0361 0.0869 99.5+ B. bovis transmitted by B. annulatus

0.0250 0.0368

0.0207 0.0193 0.0218 0.0260 0.0230 0.0301 0.0297 25 14"

0.0375 0.0340

0.0407 0.0357 0.0349 0.0391 0.0342 0.0363 0.0336

No. Standard 9 ticks

0.0650 0.0900

99.5 + 99.5 +

99.5+ 99.5+ 99.5 + 99.5+ 99.5+ 99.5+ 99.5+

B. bovis transmitted by B. microplus

B. taurus cattle % Infection Tick bites* Calves Cows Herd Calves Larvae

16 20 23 23 24 29 32

No. Standard 9 ticks

204 214 219 225 248 121 108 270 117 175 199 99 94 79 106 88 62 60 51 37 51 65 51 69 52 78 53 66 50 42 57 48

78 81 83 86 94 46 41 103 45 67 76 38 36 30 40 33 24 23 20 14 19 25 19 26 20 29 20 25 19 16 22 18

99.5 + 99

92 96 98 90 90 95 97

0.1438 0.1526 0.0745 0.0899

99.5+

98

99.5+

91 91

99.5+

0.1468

99

84 93

0.1404 0.1130

0.1244 0.1513

0.1499 0.1515 0.1374 0.1484 0.1441 0.1508 0.1471

99.5+ 99.5+ 99.5+ 99.5+ 99.5 + 99.5 + 99.5 + 98 96 96 93 96 97 96

0.0302 0.0170

0.0276 0.0369 0.0137 0.0136

0.0405

0.0305 0.0286

0.0770 0.0445

0.0691 0.0495 0.0345 0.0336

0.0999

0.0750 0.0749

0.0861 0.0862 0.0626 0.0522 0.0697 0.0934 0.0731

0.0108 0.0078

0.0041 0.0030 0.0106 0.0098 72 57 80 77

0.0339 0.0333 0.0243 0.0198 0.0266 0.0359 0.0278

0.0458 0.0104 0.0066 0.0056 0.0175 0.0397 0.0025 0.0021

0.0233 0.0110 0.0074 0.0073

99 66 53 51

0.0206

0.0728 0.0104

0.0611 0.0566 0.0518 0.0603 0.0612 0.0143 0.0108

96 83 74 72

0.0078

0.0283 0.0039

0.0236 0.0216 0.0198 0.0231 0.0236 0.0055 0.0041

0.0124

0.0287 0.0091

0.0312 0.0281 0.0252 0.0281 0.0263 0.0124 0.0110

89

68

99.5+

80 68

99.5+ 99.5+

99

99.5+ 99.5 +

Inoculation rate Calves Cows

75

90 64

94 96 96 97 91 86 83

B. taurus x B. indicus cattle % Infection Tick bites* Calves Cows Herd Calves Larvae

Downloaded from http://jme.oxfordjournals.org/ by guest on June 7, 2016

" Minimum tick density required for inoculation of 99.5—100% of calves by 9 mo of age. b Tick bites indicate number of successfully engorging larvae (B. bovis) or (B. bigemina) per host per day. c Inoculation threshold (>99.5% inoculation of calves at 9 mo of age) was not achieved; epidemiological parameters are for equilibrium tick density at 2.0 x base host-finding rate.

Americas San Antonio, Tex. Monterrey, Nuevo Leon, Mexico Jackson, Miss. Nashville, Tenn. Africa Agadir, Morocco Malakal, Sudan

Americas Brownsville, Tex. Formosa, Goias, Brazil Monterrey, Nuevo Leon, Mexico San Juan, Puerto Rico San Salvador, El Salvador Arauca, Arauca, Colombia Tampico, Tamaulipas, Mexico Australia Brisbane, Queensland Townsville, Queensland South Africa Durban

Americas Monterrey, Nuevo Leon, Mexico San Antonio, Tex. Jackson, Miss. Nashville, Tenn. Africa Agadir, Morocco Malakal, Sudan

Americas San Juan, Puerto Rico Arauca, Arauca, Colombia San Salvador, El Salvador Tampico, Tamaulipas, Mexico Formosa, Goias, Brazil Brownsville, Tex. Monterrey, Nuevo Leon, Mexico Australia Townsville, Queensland Brisbane, Queensland South Africa Durban

Location

Table 5. Simulated standard female Boophilus ticks per cow per day, tick bites per calf or per cow-day, and other epidemiological parameters for Babesia parasite inoculation thresholds" at various geographic locations

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Vol. 29, no. 2

Mean maintenance and inoculation threshold densities (standard female ticks per cow per day) for all

Parasite species

Tick species

Cattle type"

B. boots

B. microplus

B. Bt B. B. Bt B. B. Bt B. B. Bt B.

B. annulatus

B. bigemina

B. microplus B. annulatus

taurus x Bt indicusb taurus x Bt indicusb taurus x Bt indicusb taurus x Bt indicusb

Mean maintenance threshold

Mean inoculation threshold

7 7 7 5 6 5

24 22

to to to to to to

Table 6. locations

JOURNAL OF MEDICAL ENTOMOLOGY

14 12 10 12 10

20 c

oculation threshold for B. bovis transmitted by B. microplus to B. taurus cattle varied from 16 standard ticks at San Juan, a tropical location in Puerto Rico with highly favorable weather for B. microplus, to 39 standard ticks at Brisbane, a subtropical location in southeastern Queensland with marginal weather for B. microplus. Thus, with B. bovis, higher yearly densities of ticks are required for inoculation thresholds at locations with shorter seasons of tick activity than at locations with year long tick activity. Inoculation thresholds for B. bigemina varied less from one location to another than those for B. bovis. Overall, inoculation thresholds are higher for B. bovis than for B. bigemina. Also, tick bites per host per day are higher for B. bovis inoculation thresholds than those for B. bigemina and percentage infections in ticks are higher for B. bigemina than for B. bovis. Inoculation rates for inoculation thresholds are similar regardless of species of Babesia, species of Boophilus, or type of cattle. Table 5 shows that the simulated percentage infection in herds at the end of a calendar year is consistently

Computer simulation of Babesia bovis (Babes) and B. bigemina (Smith & Kilborne) transmission by Boophilus cattle ticks (Acari: Ixodidae).

A computer model was developed to simulate the processes involved in transmission of the cattle fever parasites Babesia bovis (Babes) and Babesia bige...
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