Transmission dynamics of hepatitis E among swine: potential impact upon human infection
© Satou and Nishiura; licensee BioMed Central Ltd. 2007
Received: 11 January 2007
Accepted: 10 May 2007
Published: 10 May 2007
Hepatitis E virus (HEV) infection is a zoonosis for which pigs play a role as a reservoir. In Japan, the infection has been enzootic in swine. Clarifying the detailed mechanisms of transmission within farms is required in order to facilitate an understanding of the age-specific patterns of infection, especially just prior to slaughter.
Here we reanalyze a large-scale seroprevalence survey dataset from Japanese pig farms to estimate the force of infection. The forces of infection of swine HEV were estimated to be 3.45 (95% confidence interval: 3.17, 3.75), 2.68 (2.28, 3.14) and 3.11 (2.76, 3.50) [×10-2 per day] in Hokkaido, Honshu and Kyushu, respectively. The estimates with our model assumptions indicated that the average ages at infection ranged from 59.0–67.3 days and that the basic reproduction number, R 0, was in the order of 4.02–5.17. Sensitivity analyses of age-specific incidence at different forces of infection revealed that a decline in the force of infection would elevate the age at infection and could increase the number of virus-excreting pigs at the age of 180 days.
Although our estimates imply that more than 95% of pigs are infected before the age of 150 days, the model shows that a decline in the force of infection could increase the risk of pig-to-human transmission. If the force of infection started to decline, it might be necessary to implement radical countermeasures (e.g. separation of uninfected pigs from infected herds beginning from the end of the suckling stage) to minimize the number of virus-positive pigs at the finishing stage.
Hepatitis E virus (HEV) is a positive-strand RNA virus without an envelope, which is classified as a member of the genus Hepevirus in the family Hepeviridae [1, 2]. The virus is distributed worldwide, especially in the tropical and subtropical regions of Asia, Africa and Latin America, causing acute hepatitis in humans and is thus an important public health problem . HEV infection is a zoonosis mainly seen in humans and pigs [4–8]. In addition to the maintenance of the virus in swine as a reservoir , the infection is also seen in other primates [10–12]. The virus is mainly transmitted via fecal-oral routes among swine [13, 14]. Whereas humans are also enterically infected mainly through contaminated foods, a water-borne outbreak can be caused if drinking water is contaminated with feces containing the virus .
HEV infection in humans is seen not only in developing countries but also in industrialized countries where sporadic cases of infection have been reported . In particular, sporadic cases in various places and settings have been reported in Japan [16–23]. Whereas deer have been suggested to be a source of human infection [17, 18], ingestion of uncooked liver from wild boar is also frequently reported as the cause of infection [19–23]. In addition to the habitual consumption of porcine liver in Japan, it is important to note that the HEV infection is enzootic in swine, facilitating the frequent occurrence of pig-to-human transmission [12, 24, 25]. Seroprevalence surveys in other industrialized countries have also demonstrated the occurrence of virus transmission in swine [14, 26–30]. Although it is still yet to be fully clarified, pigs are believed to be the natural host for the virus [5, 10, 16].
With these points in mind, it is essential to clarify the detailed mechanisms of HEV transmission in swine. For example, it would be very useful to know the average age of individuals acquiring infection in enzootic areas and the age-specific incidence, especially just prior to slaughter. Moreover, to identify effective control measures on the farm (e.g., potential vaccination strategy ), it would be necessary to quantify a key parameter of the transmission, the basic reproduction number, R 0, defined as the average number of secondary cases arising from a single primary case in a fully susceptible population. R 0 gives an indication of the transmission potential, and thus, is one of the most important epidemiologic determinants [32, 33]. For example, in a randomly mixing population, a critical coverage of vaccination to eradicate a disease, p c, can be derived by using R 0; p c > 1-1/R 0 . In enzootic areas, an estimate of R 0 can be approximately obtained by estimating the force of infection (i.e. the rate at which susceptible individuals become infected), λ, which is derived from age-specific seroprevalence data. For nearly half a century, a catalytic model, the most classic type of force of infection model , has been applied to seroprevalence and incidence data and various extensions have been proposed [36–40].
The aim of this paper was to assess the transmission potential of HEV infection in swine using seroprevalence survey data from Japan. To clarify the age-specific mechanisms of transmission in swine raised for human consumption, published data  on age-specific seroprevalence on pig farms was re-examined. With respect to data from farms where pigs are slaughtered immediately after the age of 180 days, there are two specific characteristics which required close epidemiologic attention: (1) since the pigs at the suckling stage (i.e., younger than 30 days of age) are raised in separate housing from those in later stages, and due partly to a very short-lived maternal antibody, those younger than 30 days are not exposed to infection [24, 25], and (2) compared to the demographic time scale (i.e. life expectancy being 180 days), the time required for seroconversion is relatively long and is not insignificant . Thus, we propose our original modeling strategy assuming that exposure starts at the age of 30 days and combining the explicit estimate of the time required for seroconversion with a simple model of the force of infection.
Time required for seroconversion
Estimates of the force of infection
Thus, R 0 (and the 95% CI) was estimated to be 5.17 (4.76, 5.62), 4.02 (3.43, 4.71) and 4.66 (4.13, 5.25) for Hokkaido, Honshu and Kyushu, respectively.
Age-specific incidence at different forces of infection
This study estimated the force of infection of swine HEV for three geographic locations in Japan. For the estimation, we incorporated two realistic aspects of swine HEV transmission: (1) no exposure during the suckling stage and (2) time delay of seroconversion after exposure to the virus. As a result, the force of infection was estimated to be approximately 0.03 day-1 implying that the average age at infection is 63 days after birth. According to the estimates, the basic reproduction number, R 0, was in the order of 4–5, which is relatively high compared to other diseases [32, 41]. To the best of our knowledge, this study is the first to quantify the transmission potential of swine HEV infection. Although the model needs a few rough assumptions, and despite limited precision of the observed data (i.e. seroprevalence data was only collected monthly), our model successfully provides similar estimates of λ for 3 discrete locations. Except for a slight deviation seen in Hokkaido where the samples were taken from numerous sub-regions in the large prefecture, the model adequately explained the basic aspects of the age-specific pattern of HEV seroprevalence in swine. Estimated force of infection was highest in Hokkaido, the northernmost prefecture, while Honshu revealed the lowest estimate. The force of infection depends on various factors influencing transmission (e.g. biological, environmental and demographic factors). In particular, as the disease is transmitted through virus contamination (i.e. fecal-oral route), breeding methods and other determinants affecting exposure are likely to influence the age-specific patterns of prevalence. Whereas the farms in Hokkaido were partly infested with both genotypes III and IV, only genotype III was observed in the other two regions. However, since these two genotypes are immunologically crossreactive each other [5, 42], these could not be separately evaluated without detailed information with respect to differences in natural history and immune reaction.
There are two practical implications from our exercise. First, estimation of the force of infection permitted clarification of the average age at infection (being 63 days). Although our model did not allow more detailed age- and time-specificity of the force of infection to be derived due to limited data [37–40], knowing the average age at infection enables clarification of the age-specific incidence of infection (as shown in Figure 3), thereby providing a reasonable assessment of the risk of HEV excretion in slaughtered pigs. According to rigorous inoculation experiments [9, 13, 43], swine HEV RNA can be detected in the liver, feces, bile and other parts of the body as long as 30 days post-inoculation. In enzootic areas, therefore, pigs should ideally be infected sufficiently far in advance of reaching 150 days of age, so that the probability of virus excretion will be extremely low at 180 days. Although our estimates of the force of infection in Japan imply that the majority of individuals (i.e., more than 95%) are infected before the age of 150 days, it should be noted that any future decline in the force of infection would increase the number of virus-positive pigs at the age of 180 days. Thus, most importantly, it must be remembered that a slight decline in the force of infection could elevate the age at infection and increase the risk of pig-to-human transmission. In addition to consumption of contaminated pork by the general public, the increased risk of infection could also be a particularly risk for veterinarians and boar meat processing workers [44, 45]. If the force of infection is naturally reduced on the farm, this could necessitate radical control measures to minimize the number of virus-excreting pigs at the finishing stage and to eliminate the transmission from the farm. Since the population dynamics model can account for more detailed mechanisms of transmission [46–48], further explicit clarification on this point is a subject of our further studies. Although the time required for seroconversion may be slightly underestimated (because of the estimation using intravenous inoculation rather than that through oral routes), this underestimation would only result in slight underestimation of the force of infection, and thus, the above qualitative discussion of the results and their implications is still valid.
Second, the critical coverage of vaccination required for eradication, p c, is obtained from R 0, using p c > 1-1/R 0 . Although vaccines are currently under development , our estimate of R 0, ranging from 4.02–5.17, suggests that the HEV transmission on the farm could be prevented if more than 75.1–80.7 % of the pigs were successfully immunized. However, since HEV infection in man is likely to result in asymptomatic or mild disease [3, 16, 49], and because pig-to-human transmission could be partly prevented by dietary changes of humans (i.e. avoiding consumption of fresh liver), potential future vaccination policies for swine need to take account of cost-benefit analyses and the biological feasibility of elimination. For example, the maintenance of the virus by other primates could prevent the elimination of virus transmission in swine [3, 10]. Rather, if it becomes necessary to implement radical control measures, it may be more realistic and less costly to control the transmission within a herd at specific stages; considering that more than four-fifths of infection had happened between the ages of 30 and 90 days, temporal separation of uninfected young pigs from infected herds beginning from the end of suckling stage (e.g. for a certain time period, breed the individuals in a new house) could limit the chance of continued transmission. In this case, tight management of newly-built pig farms (i.e. prevention of contamination from other locations and animals) combined with the possibility of vaccination in the future might be necessary to reduce transmission within the herd.
The force of infection of swine HEV was estimated from three discrete geographic locations in Japan using age-specific seroprevalence data. The estimates ranged from 2.68–3.45 ×10-2 (day-1), indicating that R 0 ranges from 4.02–5.17. The estimates permitted a reasonable prediction of the age-specific incidence including that at the finishing stage. Although our estimates of the force of infection imply that more than 95% are infected before the age of 150 days and the probability of virus-excretion is small at 180 days, the model suggests that a decline in the force of infection could elevate the average age at infection and increase the risk of pig-to-human transmission. If the force of infection started to decline, it might be necessary to implement radical countermeasures (e.g. separation of uninfected pigs from infected herds beginning from the end of the suckling stage) to minimize the number of virus-positive pigs at the finishing stage. As this study showed a reasonable estimation in Japan which is an enzootic area for swine HEV infection, similar seroprevalence survey would be extremely useful to decipher the mechanisms of transmission. Thus, seroepidemiologic studies of swine, human and other animals with time, space and age as well as among specific groups [44, 45] could shed further light on the transmission dynamics of HEV.
Estimation of the time required for seroconversion
where b is the coefficient of the time since inoculation and t m is the median time required for seroconversion. In order to apply a logistic curve to the cumulative distribution, the model has to satisfy G(0) ≈ 0 and G(∞) = 1. The maximum likelihood estimates of b and t m were obtained by minimizing the binomial deviance of the model from the observed data. The 95% CI were determined by using the profile likelihood.
Force of infection
In addition to the estimation of λ, we examined the sensitivity of I(a) and C(a) to the different values of λ to explore the age-specific patterns and clarify the practical implications of λ to farm management.
Convolution equation and maximum likelihood estimation
The maximum likelihood estimate of λ is obtained by minimizing the negative logarithm of Eq. 12. The 95% CI were derived from the profile likelihood. All statistical data were analyzed using the statistical software JMP IN ver. 5.1 (SAS Institute Inc., Cary, NC).
Hepatitis E virus
We thank Prof. Hiroaki Okamoto, Jichi Medical School, for permitting us to reanalyze the seroprevalence data with model. HN thanks to the Banyu Life Science Foundation International for supporting his research in Germany. This study was also supported by the Japanese Ministry of Education, Science, Sports and Culture in the form of a Grant-in-Aid for Young Scientists (#18810024, 2006).
- Anderson DA, Cheng RH: Hepatitis E: structure and molecular virology. Viral hepatitis. Edited by: Thomas H, Lemon S, Zuckerman A. Oxford: Blackwell; 2005:603-610.Google Scholar
- Emerson SU, Purcell RH: Hepatitis E virus. Rev Med Virol. 2003, 13: 145-154. 10.1002/rmv.384.PubMedView ArticleGoogle Scholar
- Labrique AB, Thomas DL, Stoszek SK, Nelson KE: Hepatitis E: an emerging infectious disease. Epidemiol Rev. 1999, 21: 162-179.PubMedView ArticleGoogle Scholar
- Balayan MS, Usmanov RK, Zamyatina NA, Djumalieva DI, Karas FR: Brief report: experimental hepatitis E infection in domestic pigs. J Med Virol. 1990, 32: 58-59. 10.1002/jmv.1890320110.PubMedView ArticleGoogle Scholar
- Meng XJ, Purcell RH, Halbur PG, Lehman JR, Webb DM, Tsareva TS, Haynes JS, Thacker BJ, Emerson SU: A novel virus in swine is closely related to the human hepatitis E virus. Proc Natl Acad Sci USA. 1997, 94: 9860-9865. 10.1073/pnas.94.18.9860.PubMedPubMed CentralView ArticleGoogle Scholar
- Meng XJ, Halbur PG, Shapiro MS, Govindarajan S, Bruna JD, Mushahwar IK, Purcell RH, Emerson SU: Genetic and experimental evidence for cross-species infection by swine hepatitis E virus. J Virol. 1998, 72: 9714-9721.PubMedPubMed CentralGoogle Scholar
- Meng XJ: Novel strains of hepatitis E virus identified from humans and other animal species: is hepatitis E a zoonosis?. J Hepatol. 2000, 33: 842-845. 10.1016/S0168-8278(00)80319-0.PubMedView ArticleGoogle Scholar
- Hsieh SY, Meng XJ, Wu YH, Liu ST, Tam AW, Lin DY, Liaw YF: Identity of a novel swine hepatitis E virus in Taiwan forming a monophyletic group with Taiwan isolates of human hepatitis E virus. J Clin Microbiol. 1999, 37: 3828-3834.PubMedPubMed CentralGoogle Scholar
- Halbur PG, Kasorndorkbua C, Gilbert C, Guenette D, Potters MB, Purcell RH, Emerson SU, Toth TE, Meng XJ: Comparative pathogenesis of infection of pigs with hepatitis E viruses recovered from a pig and a human. J Clin Microbiol. 2001, 39: 918-923. 10.1128/JCM.39.3.918-923.2001.PubMedPubMed CentralView ArticleGoogle Scholar
- Goens SD, Perdue ML: Hepatitis E viruses in humans and animals. Anim Health Res Rev. 2004, 5: 145-156. 10.1079/AHR200495.PubMedView ArticleGoogle Scholar
- Vitral CL, Pinto MA, Lewis-Ximenez LL, Khudyakov YE, dos Santos DR, Gaspar AM: Serological evidence of hepatitis E virus infection in different animal species from the Southeast of Brazil. Mem Inst Oswaldo Cruz. 2005, 100: 117-122. 10.1590/S0074-02762005000200003.PubMedView ArticleGoogle Scholar
- Sonoda H, Abe M, Sugimoto T, Sato Y, Bando M, Fukui E, Mizuo H, Takahashi M, Nishizawa T, Okamoto H: Prevalence of hepatitis E virus (HEV) Infection in wild boars and deer and genetic identification of a genotype 3 HEV from a boar in Japan. J Clin Microbiol. 2004, 42: 5371-5374. 10.1128/JCM.42.11.5371-5374.2004.PubMedPubMed CentralView ArticleGoogle Scholar
- Kasorndorkbua C, Guenette DK, Huang FF, Thomas PJ, Meng XJ, Halbur PG: Routes of transmission of swine hepatitis E virus in pigs. J Clin Microbiol. 2004, 42: 5047-5052. 10.1128/JCM.42.11.5047-5052.2004.PubMedPubMed CentralView ArticleGoogle Scholar
- Kasorndorkbua C, Opriessnig T, Huang FF, Guenette DK, Thomas PJ, Meng XJ, Halbur PG: Infectious swine hepatitis E virus is present in pig manure storage facilities on United States farms, but evidence of water contamination is lacking. Appl Environ Microbiol. 2005, 71: 7831-7837. 10.1128/AEM.71.12.7831-7837.2005.PubMedPubMed CentralView ArticleGoogle Scholar
- Guthmann JP, Klovstad H, Boccia D, Hamid N, Pinoges L, Nizou JY, Tatay M, Diaz F, Moren A, Grais RF, Ciglenecki I, Nicand E, Guerin PJ: A large outbreak of hepatitis E among a displaced population in Darfur, Sudan, 2004: the role of water treatment methods. Clin Infect Dis. 2006, 42: 1685-1691. 10.1086/504321.PubMedView ArticleGoogle Scholar
- Teo CG: Hepatitis E indigenous to economically developed countries: to what extent a zoonosis?. Curr Opin Infect Dis. 2006, 19: 460-466. 10.1097/01.qco.0000244052.61629.49.PubMedView ArticleGoogle Scholar
- Tei S, Kitajima N, Takahashi K, Mishiro S: Zoonotic transmission of hepatitis E virus from deer to human beings. Lancet. 2003, 362: 371-373. 10.1016/S0140-6736(03)14025-1.PubMedView ArticleGoogle Scholar
- Takahashi K, Kitajima N, Abe N, Mishiro S: Complete or near-complete nucleotide sequences of hepatitis E virus genome recovered from a wild boar, a deer, and four patients who ate the deer. Virology. 2004, 330: 501-505. 10.1016/j.virol.2004.10.006.PubMedView ArticleGoogle Scholar
- Yazaki Y, Mizuo H, Takahashi M, Nishizawa T, Sasaki N, Gotanda Y, Okamoto H: Sporadic acute or fulminant hepatitis E in Hokkaido, Japan, may be food-borne, as suggested by the presence of hepatitis E virus in pig liver as food. J Gen Virol. 2003, 84: 2351-2357. 10.1099/vir.0.19242-0.PubMedView ArticleGoogle Scholar
- Matsuda H, Okada K, Takahashi K, Mishiro S: Severe hepatitis E virus infection after ingestion of uncooked liver from a wild boar. J Infect Dis. 2003, 188: 944-10.1086/378074.PubMedView ArticleGoogle Scholar
- Yamamoto T, Suzuki H, Toyota T, Takahashi M, Okamoto H: Three male patients with sporadic acute hepatitis E in Sendai, Japan, who were domestically infected with hepatitis E virus of genotype III or IV. J Gastroenterol. 2004, 39: 292-298. 10.1007/s00535-003-1292-7.PubMedView ArticleGoogle Scholar
- Tamada Y, Yano K, Yatsuhashi H, Inoue O, Mawatari F, Ishibashi H: Consumption of wild boar linked to cases of hepatitis E. J Hepatol. 2004, 40: 869-870. 10.1016/j.jhep.2003.12.026.PubMedView ArticleGoogle Scholar
- Masuda J, Yano K, Tamada Y, Takii Y, Ito M, Omagari K, Kohno S: Acute hepatitis E of a man who consumed wild boar meat prior to the onset of illness in Nagasaki, Japan. Hepatol Res. 2005, 31: 178-183. 10.1016/j.hepres.2005.01.008.PubMedView ArticleGoogle Scholar
- Takahashi M, Nishizawa T, Miyajima H, Gotanda Y, Iita T, Tsuda F, Okamoto H: Swine hepatitis E virus strains in Japan form four phylogenetic clusters comparable with those of Japanese isolates of human hepatitis E virus. J Gen Virol. 2003, 84: 851-862. 10.1099/vir.0.18918-0.PubMedView ArticleGoogle Scholar
- Takahashi M, Nishizawa T, Tanaka T, Tsatsralt-Od B, Inoue J, Okamoto H: Correlation between positivity for immunoglobulin A antibodies and viraemia of swine hepatitis E virus observed among farm pigs in Japan. J Gen Virol. 2005, 86: 1807-1813. 10.1099/vir.0.80909-0.PubMedView ArticleGoogle Scholar
- Chandler JD, Riddell MA, Li F, Love RJ, Anderson DA: Serological evidence for swine hepatitis E virus infection in Australian pig herds. Vet Microbiol. 1999, 68: 95-105. 10.1016/S0378-1135(99)00065-6.PubMedView ArticleGoogle Scholar
- Yoo D, Willson P, Pei Y, Hayes MA, Deckert A, Dewey CE, Friendship RM, Yoon Y, Gottschalk M, Yason C, Giulivi A: Prevalence of hepatitis E virus antibodies in Canadian swine herds and identification of a novel variant of swine hepatitis E virus. Clin Diagn Lab Immunol. 2001, 8: 1213-1219. 10.1128/CDLI.8.6.1213-1219.2001.PubMedPubMed CentralGoogle Scholar
- Garkavenko O, Obriadina A, Meng J, Anderson DA, Benard HJ, Schroeder BA, Khudyakov YE, Fields HA, Croxson MC: Detection and characterisation of swine hepatitis E virus in New Zealand. J Med Virol. 2001, 65: 525-529. 10.1002/jmv.2067.PubMedView ArticleGoogle Scholar
- Banks M, Heath GS, Grierson SS, King DP, Gresham A, Girones R, Widen F, Harrison TJ: Evidence for the presence of hepatitis E virus in pigs in the United Kingdom. Vet Rec. 2004, 154: 223-227.PubMedView ArticleGoogle Scholar
- Ahn JM, Kang SG, Lee DY, Shin SJ, Yoo HS: Identification of novel human hepatitis E virus (HEV) isolates and determination of the seroprevalence of HEV in Korea. J Clin Microbiol. 2005, 43: 3042-3048. 10.1128/JCM.43.7.3042-3048.2005.PubMedPubMed CentralView ArticleGoogle Scholar
- Emerson SU, Purcell RH: Recombinant vaccines for hepatitis E. Trends Mol Med. 2001, 7: 462-466. 10.1016/S1471-4914(01)02106-2.PubMedView ArticleGoogle Scholar
- Anderson RM, May RM: Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press: 1991.Google Scholar
- Diekmann O, Heesterbeek JAP: Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. New York: Wiley Series in Mathematical and Computational Biology:2000.Google Scholar
- Smith CE: Factors in the transmission of virus infections from animal to man. Sci Basis Med Annu Rev. 1964, : 125-150.Google Scholar
- Muench H: Catalytic Models in Epidemiology. Cambridge, Massachusetts: Harvard University Press: 1959.View ArticleGoogle Scholar
- Schenzle D, Dietz K, Frosner GG: Antibody against hepatitis A in seven European countries. II. Statistical analysis of cross-sectional surveys. Am J Epidemiol. 1979, 110: 70-76.PubMedGoogle Scholar
- Farrington CP: Modelling forces of infection for measles, mumps and rubella. Stat Med. 1990, 9: 953-967. 10.1002/sim.4780090811.PubMedView ArticleGoogle Scholar
- Keiding N: Age-specific incidence and prevalence: a statistical perspective. J R Stat Soc A. 1991, 154: 371-412. 10.2307/2983150.View ArticleGoogle Scholar
- Ades AE, Nokes DJ: Modeling age- and time-specific incidence from seroprevalence:toxoplasmosis. Am J Epidemiol. 1993, 137: 1022-1034.PubMedGoogle Scholar
- Whitaker HJ, Farrington CP: Estimation of infectious disease parameters from serological survey data: the impact of regular epidemics. Stat Med. 2004, 23: 2429-2443. 10.1002/sim.1819.PubMedView ArticleGoogle Scholar
- Satou K, Nishiura H: Basic reproduction number for equine-2 influenza virus A (H3N8) epidemic in racehorse facilities in Japan, 1971. J Equine Vet Sci. 2006, 26: 310-316. 10.1016/j.jevs.2006.05.003.View ArticleGoogle Scholar
- Wang Y, Zhang H, Ling R, Li H, Harrison TJ: The complete sequence of hepatitis E virus genotype 4 reveals an alternative strategy for translation of open reading frames 2 and 3. J Gen Virol. 2000, 81: 1675-1686.PubMedView ArticleGoogle Scholar
- Kasorndorkbua C, Halbur PG, Thomas PJ, Guenette DK, Toth TE, Meng XJ: Use of a swine bioassay and a RT-PCR assay to assess the risk of transmission of swine hepatitis E virus in pigs. J Virol Methods. 2002, 101: 71-78. 10.1016/S0166-0934(01)00420-7.PubMedView ArticleGoogle Scholar
- Meng XJ, Wiseman B, Elvinger F, Guenette DK, Toth TE, Engle RE, Emerson SU, Purcell RH: Prevalence of antibodies to hepatitis E virus in veterinarians working with swine and in normal blood donors in the United States and other countries. J Clin Microbiol. 2002, 40: 117-122. 10.1128/JCM.40.1.117-122.2002.PubMedPubMed CentralView ArticleGoogle Scholar
- Withers MR, Correa MT, Morrow M, Stebbins ME, Seriwatana J, Webster WD, Boak MB, Vaughn DW: Antibody levels to hepatitis E virus in North Carolina swine workers, non-swine workers, swine, and murids. Am J Trop Med Hyg. 2002, 66: 384-388.PubMedGoogle Scholar
- Bouma A, de Jong MCM, Kimman TG: Transmission of pseudorabies virus within pig populations is independent of the size of the population. Prev Vet Med. 1995, 23: 163-172. 10.1016/0167-5877(94)00442-L.View ArticleGoogle Scholar
- van Nes A, de Jong MC, Buijtels JA, Verheijden JH: Implications derived from a mathematical model for eradication of pseudorabies virus. Prev Vet Med. 1998, 33: 39-58. 10.1016/S0167-5877(97)00058-5.PubMedView ArticleGoogle Scholar
- van Nes A, de Jong MC, Kersten AJ, Kimman TG, Verheijden JH: An analysis of a presumed major outbreak of pseudorabies virus in a vaccinated sow herd. Epidemiol Infect. 2001, 126: 119-128.PubMedPubMed CentralGoogle Scholar
- Okamoto H, Takahashi M, Nishizawa T: Features of hepatitis E virus infection in Japan. Intern Med. 2003, 42: 1065-1071.PubMedView ArticleGoogle Scholar
- Meng XJ, Dea S, Engle RE, Friendship R, Lyoo YS, Sirinarumitr T, Urairong K, Wang D, Wong D, Yoo D, Zhang Y, Purcell RH, Emerson SU: Prevalence of antibodies to the hepatitis E virus in pigs from countries where hepatitis E is common or is rare in the human population. J Med Virol. 1999, 59: 297-302. 10.1002/(SICI)1096-9071(199911)59:3<297::AID-JMV6>3.0.CO;2-3.PubMedView ArticleGoogle Scholar
- de Deus N, Seminati C, Pina S, Mateu E, Martin M, Segales J: Detection of hepatitis E virus in liver, mesenteric lymph node, serum, bile and faeces of naturally infected pigs affected by different pathological conditions. Vet Microbiol. 2006, (doi:10.1016/j.vetmic.2006.08.027),Google Scholar
- Brookmeyer R, Gail MH: A method for obtaining short-term projections and lower bounds on the size of the AIDS epidemic. J Am Stat Assoc. 1988, 83: 301-308. 10.2307/2288844.View ArticleGoogle Scholar
- Nishiura H, Eichner M: Infectiousness of smallpox relative to disease age: estimates based on transmission network and incubation period. Epidemiol Infect. 2006, : 1-6.Google Scholar
- Karlin S, Taylor HM: A first course in stochastic process 2nd edition. New York: Academic Press: 1975.Google Scholar