Abstract
Background
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 agespecific patterns of infection, especially just prior to slaughter.
Results
Here we reanalyze a largescale 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 agespecific 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 virusexcreting pigs at the age of 180 days.
Conclusion
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 pigtohuman 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 viruspositive pigs at the finishing stage.
Background
Hepatitis E virus (HEV) is a positivestrand 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 [3]. HEV infection is a zoonosis mainly seen in humans and pigs [48]. In addition to the maintenance of the virus in swine as a reservoir [9], the infection is also seen in other primates [1012]. The virus is mainly transmitted via fecaloral routes among swine [13,14]. Whereas humans are also enterically infected mainly through contaminated foods, a waterborne outbreak can be caused if drinking water is contaminated with feces containing the virus [15].
HEV infection in humans is seen not only in developing countries but also in industrialized countries where sporadic cases of infection have been reported [16]. In particular, sporadic cases in various places and settings have been reported in Japan [1623]. 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 [1923]. 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 pigtohuman transmission [12,24,25]. Seroprevalence surveys in other industrialized countries have also demonstrated the occurrence of virus transmission in swine [14,2630]. 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 agespecific incidence, especially just prior to slaughter. Moreover, to identify effective control measures on the farm (e.g., potential vaccination strategy [31]), 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 }> 11/R_{0 }[34]. 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 agespecific seroprevalence data. For nearly half a century, a catalytic model, the most classic type of force of infection model [35], has been applied to seroprevalence and incidence data and various extensions have been proposed [3640].
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 agespecific mechanisms of transmission in swine raised for human consumption, published data [24] on agespecific seroprevalence on pig farms was reexamined. 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 shortlived 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 [9]. 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.
Results
Time required for seroconversion
A simple logit model was applied to the cumulative distribution of the time required for seroconversion of antiHEV antibody based on inoculation experiments using swine HEV [9]. Figure 1 compares the observed and predicted proportion of seroconversion with time postinoculation. The maximum likelihood estimate of the median time required for seroconversion was 25.0 (95% confidence interval (CI): 20.9, 31.3) days. The coefficient of the time after inoculation (for the logit model) was estimated as 0.19 (95% CI: 0.11, 0.30). The χ^{2 }goodnessoffit test did not reveal significant deviations between observed and predicted frequencies (χ^{2}_{5 }= 2.31, p = 0.81).
Figure 1. Observed and predicted time required for seroconversion of antiHEV antibody. Logit model (line) was applied to the observed cumulative distribution of the time required for seroconversion (dot), which revealed a sigmoid pattern. Data source: ref. [9].
Estimates of the force of infection
The total sample sizes of seroprevalence surveys were 1400, 400 and 700 for Hokkaido, Honshu and Kyushu, respectively [24]. The maximum likelihood estimates of the force of infection, λ, (and the corresponding 95% CI) of swine HEV for the three different geographic locations in Japan were 3.45 (3.17, 3.75), 2.68 (2.28, 3.14) and 3.11 (2.76, 3.50) [×10^{2 }per day]. Expected values of λ ranging from 2.68–3.45 ×10^{2 }day^{1 }indicate that the average time of infection ranged from 29.0–37.3 days after the age of 30 days when individuals were first exposed to the risk of infection (i.e. average age at infection was 59.0–67.3 days). Observed and predicted agespecific seroprevalence are compared in Figure 2, confirming good overall agreement of the model with the data. Although a significant deviation was seen in Hokkaido (χ^{2}_{4 }= 16.71, p < 0.01), this was not the case for Honshu (χ^{2}_{4 }= 1.49, p = 0.89) or Kyushu (χ^{2}_{4 }= 6.34, p = 0.17).
Figure 2. Observed and predicted agespecific seroprevalence against swine hepatitis E virus in Japan. Observed (gray bar) and predicted (black) seroprevalence are compared. Three discrete geographic areas, Hokkaido (A), Honshu (B) and Kyushu (C), are modeled separately. Data source: ref. [24].
The population structure on pig farms in Japan is specific in that individuals are slaughtered immediately after the age of 180 days (i.e., 150 days after pigs are first exposed to the risk of infection). This satisfied a reasonable approximation of a simple agespecific survivorship function, referred to as Type I survivorship [32], to the data:
where μ(a) denotes agespecific mortality rate at age a. The basic reproduction number, R_{0}, is approximated as the product of the force of infection, λ, and the time from first exposure to death, L (= 150 days) [32]:
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.
Agespecific incidence at different forces of infection
Figure 3A shows the cumulative proportion of infected individuals according to our simple assumptions with different forces of infection, λ, being 0.01, 0.03 and 0.05 (day^{1}). Accordingly, the average ages at infection, A (= 30 + 1/λ), are 130, 63 and 50 days, respectively. Using this range of λ, 0.03 (0.01, 0.05), it is predicted that 83.5 % (45.1, 95.0) of the herd would be infected at the age of 90 days, 93.3 % (59.3, 98.9) at 120 days and 97.3 % (69.9, 99.8) at 150 days. Based on the same assumptions, Figure 3B shows the agespecific absolute incidence (i.e. the number of newly infected individuals) at each given age in a hypothetical herd with a population size of 1000. Despite a few rough assumptions, the figure indicates that average age at infection directly influences the agespecific patterns of HEV incidence, enabling the prediction of incidence shortly before the age of finishing (i.e. 180 days). According to the above range of λ, the model predicts that 2.1 (4.1, 0.6) individuals would be newly infected at the age of 120 days, 0.8 (3.0, 0.1) at 150 days and 0.3 (2.3, 0.0) at 180 days. In other words, the smaller the force of infection is, higher the probability that virus excretion would occur at the finishing stage.
Figure 3. Cumulative frequency of infection and agespecific incidence at different forces of infection. A. Cumulative frequencies of HEV infection and B. agespecific incidence elicited by different forces of infection are compared. Assumed values for the forces of infection were 0.01 (thick black), 0.03 (thin black) and 0.05 (thick gray) days^{1}. See eqs. 6 and 7 for details of the model.
Discussion
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 subregions in the large prefecture, the model adequately explained the basic aspects of the agespecific 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. fecaloral route), breeding methods and other determinants affecting exposure are likely to influence the agespecific 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 timespecificity of the force of infection to be derived due to limited data [3740], knowing the average age at infection enables clarification of the agespecific 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 postinoculation. 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 viruspositive 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 pigtohuman 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 virusexcreting 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 [4648], 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 }> 11/R_{0 }[34]. Although vaccines are currently under development [31], 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 pigtohuman 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 costbenefit 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 fourfifths 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 newlybuilt 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.
Conclusion
The force of infection of swine HEV was estimated from three discrete geographic locations in Japan using agespecific 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 agespecific 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 virusexcretion 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 pigtohuman 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 viruspositive 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.
Methods
Data
To estimate the force of infection, this study used two published datasets: (1) an experimental inoculation study of swine HEV [9], and (2) a largescale seroprevalence survey in Japan [24]. The experimental study recorded the time required for seroconversion of antiHEV antibody following inoculation. The seroepidemiologic study consisted of a survey of pig farms in three discrete geographic locations (Hokkaido, Honshu and Kyushu; see Figure 4A). AntiHEV IgG antibodies of 2500 pigs were measured by age group. The original study examined the agespecific seroprevalence by month, i.e., pigs at 60, 90, 120, 150 and 180 days of age (allowing ± 5 days variation for each) were sampled [24]. We used this data because the detailed breeding methods of the piggery in Japan were known and the sample size was sufficiently large to allow statistical analysis. On the farm, a proportion of the suckling herd has a very shortlived maternal antibody (Tsunemitsu H, personal communication) and is not exposed to infection due to separate housing during this stage. A seroepidemiologic study and an isolation study of HEV RNA during natural infection in other countries also roughly satisfied this assumption: the number of seropositive pigs was negligible at the age of 30 days on several farms [50] and HEV RNA started to be detected at the age of 30 days [51]. Since the pigs thereafter entered into weaning, growing and fattening stages, we assume that the risk of exposure starts at the age of 30 days. The pigs are slaughtered immediately after the age of 180 days.
Figure 4. Estimation of the force of infection of hepatitis E virus in Japan. A. The map of three geographic locations in Japan (drawn by the authors). B. Compartment of the catalytic model. Susceptibles at age a, S(a), are infected at a rate λ and then enter into the compartment, infected, I(a). C. Schematic illustration of the time delay to seroconvert. If the time of seroconversion t_{0 }and possible time of exposure t_{k }are given, probability of exposure at time t_{k }can be extracted by g(t_{0}t_{k}), where g(t) is the probability density of the time required for seroconversion at t days after infection. See eqs. 9 and 10 for statistical details.
Estimation of the time required for seroconversion
Cumulative distribution of the time required for seroconversion, G(t) at t days postinoculation was approximated by a simple logit model:
where l is a linear predictor given by:
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
For simplicity and due to limited data availability, we assumed that the force of infection, λ, was independent of time (i.e. endemic equilibrium). Furthermore, except for an assumption that no exposure occured during the suckling stage (i.e. until the age of 30 days), λ was also assumed to be ageindependent. Figure 4B shows a schematic illustration of the model. We denote the proportions of susceptible and infected individuals at age a days (for a ≥ 30) by S(a) and I(a), respectively. With an initial condition, S(30) = 1 and I(30) = 0, the model is given by the following ordinal differential equations:
for a ≥ 30. The analytical solution is given by:
for a ≥ 30. Under the same assumption, agespecific incidence, C(a), at age a, is given by product of λ and S(a):
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 agespecific patterns and clarify the practical implications of λ to farm management.
Convolution equation and maximum likelihood estimation
Since all individuals are slaughtered immediately after the age of 180 days, the time delay from infection to seroconversion was thought to be nonnegligible. That is, the agespecific seroprevalence data (at age a days) does not directly reflect all of those who were infected until age a, I(a), but rather indicates those infected until the age which is smaller than a. Thus, to account for the delay, we used probability density of the time to seroconvert (Figure 4C) in addition to the model of the cumulative distribution of HEV infection (Eq. 6). Considering the timescale of the distribution of time to seroconvert (Figure 1) and the cumulative incidence up to the age of 60 days (Figure 2), we assumed that those seropositive at the age of 60 days approximately reflected those who were infected until the age of 45 days. Under these assumptions, the agespecific incidence density, f_{i}, whose infection is reflected as seropositive at i months after starting to be exposed (i.e., a = 30(i + 1) days) is assumed to be:
Using the same midpoint of the timeinterval, the probability density of time to seroconvert, g_{j}, at j months after infection was also approximated by using G(t):
The density of those who newly showed seropositive results at the age of 60 days (i.e., at i = 1 month), k_{1}, is given by k_{1 }= f_{1}g_{1}. In the same way, the densities at the ages of 90 and 120 days, k_{2 }and k_{3}, are given by k_{2 }= f_{2}g_{1 }+ f_{1}g_{2 }and k_{3 }= f_{3}g_{1 }+ f_{2}g_{2 }+ f_{1}g_{3}. This can be generalized by using the following convolution equation [5254]:
Since the observed seroprevalence data shows the cumulative distribution of those seroconverted after infection until month i, K_{i}, which is given by , we get:
where . Suppose that there were N_{i }pigs who had been seropositive until month i (where i = a/30  1) and M_{i }who had not, the likelihood function is
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).
Abbreviations
HEV – Hepatitis E virus
CI – Confidence interval
Competing interests
The author(s) declare that they have no competing interests.
Authors' contributions
KS and HN carried out paper reviews, proposed the study, performed statistical analyses and drafted the manuscript together. The authors have read and approved the final manuscript.
Acknowledgements
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 GrantinAid for Young Scientists (#18810024, 2006).
References

Anderson DA, Cheng RH: Hepatitis E: structure and molecular virology. In Viral hepatitis. Edited by Thomas H, Lemon S, Zuckerman A. Oxford: Blackwell; 2005:603610.

Emerson SU, Purcell RH: Hepatitis E virus.
Rev Med Virol 2003, 13:145154. PubMed Abstract  Publisher Full Text

Labrique AB, Thomas DL, Stoszek SK, Nelson KE: Hepatitis E: an emerging infectious disease.
Epidemiol Rev 1999, 21:162179. PubMed Abstract  Publisher Full Text

Balayan MS, Usmanov RK, Zamyatina NA, Djumalieva DI, Karas FR: Brief report: experimental hepatitis E infection in domestic pigs.
J Med Virol 1990, 32:5859. PubMed Abstract  Publisher Full Text

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, 94:98609865. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Meng XJ, Halbur PG, Shapiro MS, Govindarajan S, Bruna JD, Mushahwar IK, Purcell RH, Emerson SU: Genetic and experimental evidence for crossspecies infection by swine hepatitis E virus.
J Virol 1998, 72:97149721. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Meng XJ: Novel strains of hepatitis E virus identified from humans and other animal species: is hepatitis E a zoonosis?
J Hepatol 2000, 33:842845. PubMed Abstract  Publisher Full Text

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, 37:38283834. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

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, 39:918923. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Goens SD, Perdue ML: Hepatitis E viruses in humans and animals.
Anim Health Res Rev 2004, 5:145156. PubMed Abstract  Publisher Full Text

Vitral CL, Pinto MA, LewisXimenez 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, 100:117122. PubMed Abstract  Publisher Full Text

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, 42:53715374. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

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, 42:50475052. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

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, 71:78317837. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

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, 42:16851691. PubMed Abstract  Publisher Full Text

Teo CG: Hepatitis E indigenous to economically developed countries: to what extent a zoonosis?
Curr Opin Infect Dis 2006, 19:460466. PubMed Abstract  Publisher Full Text

Tei S, Kitajima N, Takahashi K, Mishiro S: Zoonotic transmission of hepatitis E virus from deer to human beings.
Lancet 2003, 362:371373. PubMed Abstract  Publisher Full Text

Takahashi K, Kitajima N, Abe N, Mishiro S: Complete or nearcomplete nucleotide sequences of hepatitis E virus genome recovered from a wild boar, a deer, and four patients who ate the deer.
Virology 2004, 330:501505. PubMed Abstract  Publisher Full Text

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 foodborne, as suggested by the presence of hepatitis E virus in pig liver as food.
J Gen Virol 2003, 84:23512357. PubMed Abstract  Publisher Full Text

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. PubMed Abstract  Publisher Full Text

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, 39:292298. PubMed Abstract  Publisher Full Text

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, 40:869870. PubMed Abstract  Publisher Full Text

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, 31:178183. PubMed Abstract  Publisher Full Text

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, 84:851862. PubMed Abstract  Publisher Full Text

Takahashi M, Nishizawa T, Tanaka T, TsatsraltOd 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, 86:18071813. PubMed Abstract  Publisher Full Text

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, 68:95105. PubMed Abstract  Publisher Full Text

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, 8:12131219. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

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, 65:525529. PubMed Abstract  Publisher Full Text

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, 154:223227. PubMed Abstract

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, 43:30423048. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

Emerson SU, Purcell RH: Recombinant vaccines for hepatitis E.
Trends Mol Med 2001, 7:462466. PubMed Abstract  Publisher Full Text

Anderson RM, May RM: Infectious Diseases of Humans: Dynamics and Control. Oxford: Oxford University Press; 1991.

Diekmann O, Heesterbeek JAP: Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. New York: Wiley Series in Mathematical and Computational Biology; 2000.

Smith CE: Factors in the transmission of virus infections from animal to man.
Sci Basis Med Annu Rev 1964, :125150. PubMed Abstract

Muench H: Catalytic Models in Epidemiology. Cambridge, Massachusetts: Harvard University Press; 1959.

Schenzle D, Dietz K, Frosner GG: Antibody against hepatitis A in seven European countries. II. Statistical analysis of crosssectional surveys.
Am J Epidemiol 1979, 110:7076. PubMed Abstract  Publisher Full Text

Farrington CP: Modelling forces of infection for measles, mumps and rubella.
Stat Med 1990, 9:953967. PubMed Abstract  Publisher Full Text

Keiding N: Agespecific incidence and prevalence: a statistical perspective.
J R Stat Soc A 1991, 154:371412. Publisher Full Text

Ades AE, Nokes DJ: Modeling age and timespecific incidence from seroprevalence:toxoplasmosis.
Am J Epidemiol 1993, 137:10221034. PubMed Abstract  Publisher Full Text

Whitaker HJ, Farrington CP: Estimation of infectious disease parameters from serological survey data: the impact of regular epidemics.
Stat Med 2004, 23:24292443. PubMed Abstract  Publisher Full Text

Satou K, Nishiura H: Basic reproduction number for equine2 influenza virus A (H3N8) epidemic in racehorse facilities in Japan, 1971.
J Equine Vet Sci 2006, 26:310316. Publisher Full Text

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, 81:16751686. PubMed Abstract  Publisher Full Text

Kasorndorkbua C, Halbur PG, Thomas PJ, Guenette DK, Toth TE, Meng XJ: Use of a swine bioassay and a RTPCR assay to assess the risk of transmission of swine hepatitis E virus in pigs.
J Virol Methods 2002, 101:7178. PubMed Abstract  Publisher Full Text

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, 40:117122. PubMed Abstract  Publisher Full Text  PubMed Central Full Text

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, nonswine workers, swine, and murids.
Am J Trop Med Hyg 2002, 66:384388. PubMed Abstract  Publisher Full Text

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, 23:163172. Publisher Full Text

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, 33:3958. PubMed Abstract  Publisher Full Text

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, 126:119128. PubMed Abstract

Okamoto H, Takahashi M, Nishizawa T: Features of hepatitis E virus infection in Japan.
Intern Med 2003, 42:10651071. PubMed Abstract  Publisher Full Text

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, 59:297302. PubMed Abstract  Publisher Full Text

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, in press.
(doi:10.1016/j.vetmic.2006.08.027)
PubMed Abstract  Publisher Full Text 
Brookmeyer R, Gail MH: A method for obtaining shortterm projections and lower bounds on the size of the AIDS epidemic.
J Am Stat Assoc 1988, 83:301308. Publisher Full Text

Nishiura H, Eichner M: Infectiousness of smallpox relative to disease age: estimates based on transmission network and incubation period.
Epidemiol Infect 2006, :16. PubMed Abstract  Publisher Full Text

Karlin S, Taylor HM: A first course in stochastic process. 2nd edition. New York: Academic Press; 1975.