Stochastic model for hepatitis B virus infection through maternal (vertical) and environmental (horizontal) transmission with applications to basic reproductive number estimation and economic appraisal of preventive strategies

Hui Fang Hung, Ya Chuan Wang, Amy Ming Fang Yen, Hsiu Hsi Chen

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Elucidating the temporal natural history of Hepatitis B virus (HBV) infection provides not only useful information for assessing the spread of HBV infection but also a bedrock for economic appraisal of population-based preventive strategies (such as universal vaccination). HBV transmissions are transmitted through the maternal (vertical) route and environmental (horizontal) route. As the infection process from susceptible to active virus replication and finally to recovery state or to carrier state through both routes is not directly observable, mathematical models were therefore proposed to quantitatively elucidate the dynamic process of HBV infection with time. We began with a simple two-state model (from susceptible to infection) and further developed a five-state (including susceptible, latent phase, active viral replication, carrier, and recovery states) stochastic process to quantify the dynamics of HBV infection, making allowances for a mixed proportion of vertical and horizontal transmissions. The data used in the estimation, which were collected before implementation of a policy for universal HBV vaccination, were derived from several previous serum prevalence studies, including both low (northern) and high (southern) HBV prevalence areas, in Taiwan. The parameters obtained from stochastic models were converted to compute the basic reproductive number (R0) in each study to indicate the extent of the spread of HBV infection. By linking the temporal natural history of HBV infection with the previously established Markov process for the sequelae of HBV infection (chronic hepatitis infection, liver cirrhosis, and hepatocelluar carcinoma), we developed a Markov cycle decision tree to evaluate the two population-based preventive strategies related to vaccination and maternal lamivudine use with a cost-effectiveness analysis. In the five-state model, horizontal transmission was found to contribute more to HBV infection than vertical transmission in the northern area (59 vs. 41 %), whereas vertical transmission was more likely than horizontal transmission in the southern area (80 vs. 20 %). After considering the parameters of the two transmission routes, annual infection rate (person-years) for susceptible subjects was higher in the northern area (0.35) than the southern area (0.011). A similar finding was noted for annual rate of the transition from the latent period to active viral replications (1.12 in the northern area and 0.072 in the southern area). Annual rate of the conversion from active viral replication to the carrier state was higher in the southern area (0.184) than the northern area (0.119). Annual recovery rates were 0.014 in the northern area and 0.024 in the southern area for the carrier and 0.048 and 0.088 for transient viremia. The R0 at age 30 using the parameters obtained from the five-state stochastic model was estimated as 4.88 in the northern and 7.03 in the southern area. Regarding the findings of economic appraisal, both preventive strategies were cost-saving, yielding the negative value of incremental cost-effectiveness ratio, compared with the baseline group (no intervention), regardless of areas. The preventive strategies in the southern area were more cost-saving than those in the northern area. The consolidation of elucidating the temporal natural history of HBV infection, estimating basic reproductive number, and conducting an economic appraisal of population-based preventive strategy can aid health policy-makers in designing effective preventive strategies in other countries worldwide where HBV is still prevalent. However, the empirical findings on transmission routes and the temporal evolution of HBV infection varying with areas should be considered with great caution as only two studies were modeled.

Original languageEnglish
Pages (from-to)611-625
Number of pages15
JournalStochastic Environmental Research and Risk Assessment
Volume28
Issue number3
DOIs
Publication statusPublished - 2014

Fingerprint

horizontal transmission
hepatitis
Stochastic models
Viruses
virus
Economics
economics
vertical transmission
vaccination
appraisal
infection
Cost effectiveness
Recovery
history
cost
health policy
Lamivudine
cost analysis
stochasticity
Decision trees

Keywords

  • Hepatitis B
  • Infection
  • Reproductive number
  • Stochastic model

ASJC Scopus subject areas

  • Environmental Engineering
  • Environmental Science(all)
  • Environmental Chemistry
  • Water Science and Technology
  • Safety, Risk, Reliability and Quality

Cite this

@article{b6ce64b1918c45b185aaface8a6d0c09,
title = "Stochastic model for hepatitis B virus infection through maternal (vertical) and environmental (horizontal) transmission with applications to basic reproductive number estimation and economic appraisal of preventive strategies",
abstract = "Elucidating the temporal natural history of Hepatitis B virus (HBV) infection provides not only useful information for assessing the spread of HBV infection but also a bedrock for economic appraisal of population-based preventive strategies (such as universal vaccination). HBV transmissions are transmitted through the maternal (vertical) route and environmental (horizontal) route. As the infection process from susceptible to active virus replication and finally to recovery state or to carrier state through both routes is not directly observable, mathematical models were therefore proposed to quantitatively elucidate the dynamic process of HBV infection with time. We began with a simple two-state model (from susceptible to infection) and further developed a five-state (including susceptible, latent phase, active viral replication, carrier, and recovery states) stochastic process to quantify the dynamics of HBV infection, making allowances for a mixed proportion of vertical and horizontal transmissions. The data used in the estimation, which were collected before implementation of a policy for universal HBV vaccination, were derived from several previous serum prevalence studies, including both low (northern) and high (southern) HBV prevalence areas, in Taiwan. The parameters obtained from stochastic models were converted to compute the basic reproductive number (R0) in each study to indicate the extent of the spread of HBV infection. By linking the temporal natural history of HBV infection with the previously established Markov process for the sequelae of HBV infection (chronic hepatitis infection, liver cirrhosis, and hepatocelluar carcinoma), we developed a Markov cycle decision tree to evaluate the two population-based preventive strategies related to vaccination and maternal lamivudine use with a cost-effectiveness analysis. In the five-state model, horizontal transmission was found to contribute more to HBV infection than vertical transmission in the northern area (59 vs. 41 {\%}), whereas vertical transmission was more likely than horizontal transmission in the southern area (80 vs. 20 {\%}). After considering the parameters of the two transmission routes, annual infection rate (person-years) for susceptible subjects was higher in the northern area (0.35) than the southern area (0.011). A similar finding was noted for annual rate of the transition from the latent period to active viral replications (1.12 in the northern area and 0.072 in the southern area). Annual rate of the conversion from active viral replication to the carrier state was higher in the southern area (0.184) than the northern area (0.119). Annual recovery rates were 0.014 in the northern area and 0.024 in the southern area for the carrier and 0.048 and 0.088 for transient viremia. The R0 at age 30 using the parameters obtained from the five-state stochastic model was estimated as 4.88 in the northern and 7.03 in the southern area. Regarding the findings of economic appraisal, both preventive strategies were cost-saving, yielding the negative value of incremental cost-effectiveness ratio, compared with the baseline group (no intervention), regardless of areas. The preventive strategies in the southern area were more cost-saving than those in the northern area. The consolidation of elucidating the temporal natural history of HBV infection, estimating basic reproductive number, and conducting an economic appraisal of population-based preventive strategy can aid health policy-makers in designing effective preventive strategies in other countries worldwide where HBV is still prevalent. However, the empirical findings on transmission routes and the temporal evolution of HBV infection varying with areas should be considered with great caution as only two studies were modeled.",
keywords = "Hepatitis B, Infection, Reproductive number, Stochastic model",
author = "Hung, {Hui Fang} and Wang, {Ya Chuan} and Yen, {Amy Ming Fang} and Chen, {Hsiu Hsi}",
year = "2014",
doi = "10.1007/s00477-013-0776-0",
language = "English",
volume = "28",
pages = "611--625",
journal = "Stochastic Environmental Research and Risk Assessment",
issn = "1436-3240",
publisher = "Springer New York",
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}

TY - JOUR

T1 - Stochastic model for hepatitis B virus infection through maternal (vertical) and environmental (horizontal) transmission with applications to basic reproductive number estimation and economic appraisal of preventive strategies

AU - Hung, Hui Fang

AU - Wang, Ya Chuan

AU - Yen, Amy Ming Fang

AU - Chen, Hsiu Hsi

PY - 2014

Y1 - 2014

N2 - Elucidating the temporal natural history of Hepatitis B virus (HBV) infection provides not only useful information for assessing the spread of HBV infection but also a bedrock for economic appraisal of population-based preventive strategies (such as universal vaccination). HBV transmissions are transmitted through the maternal (vertical) route and environmental (horizontal) route. As the infection process from susceptible to active virus replication and finally to recovery state or to carrier state through both routes is not directly observable, mathematical models were therefore proposed to quantitatively elucidate the dynamic process of HBV infection with time. We began with a simple two-state model (from susceptible to infection) and further developed a five-state (including susceptible, latent phase, active viral replication, carrier, and recovery states) stochastic process to quantify the dynamics of HBV infection, making allowances for a mixed proportion of vertical and horizontal transmissions. The data used in the estimation, which were collected before implementation of a policy for universal HBV vaccination, were derived from several previous serum prevalence studies, including both low (northern) and high (southern) HBV prevalence areas, in Taiwan. The parameters obtained from stochastic models were converted to compute the basic reproductive number (R0) in each study to indicate the extent of the spread of HBV infection. By linking the temporal natural history of HBV infection with the previously established Markov process for the sequelae of HBV infection (chronic hepatitis infection, liver cirrhosis, and hepatocelluar carcinoma), we developed a Markov cycle decision tree to evaluate the two population-based preventive strategies related to vaccination and maternal lamivudine use with a cost-effectiveness analysis. In the five-state model, horizontal transmission was found to contribute more to HBV infection than vertical transmission in the northern area (59 vs. 41 %), whereas vertical transmission was more likely than horizontal transmission in the southern area (80 vs. 20 %). After considering the parameters of the two transmission routes, annual infection rate (person-years) for susceptible subjects was higher in the northern area (0.35) than the southern area (0.011). A similar finding was noted for annual rate of the transition from the latent period to active viral replications (1.12 in the northern area and 0.072 in the southern area). Annual rate of the conversion from active viral replication to the carrier state was higher in the southern area (0.184) than the northern area (0.119). Annual recovery rates were 0.014 in the northern area and 0.024 in the southern area for the carrier and 0.048 and 0.088 for transient viremia. The R0 at age 30 using the parameters obtained from the five-state stochastic model was estimated as 4.88 in the northern and 7.03 in the southern area. Regarding the findings of economic appraisal, both preventive strategies were cost-saving, yielding the negative value of incremental cost-effectiveness ratio, compared with the baseline group (no intervention), regardless of areas. The preventive strategies in the southern area were more cost-saving than those in the northern area. The consolidation of elucidating the temporal natural history of HBV infection, estimating basic reproductive number, and conducting an economic appraisal of population-based preventive strategy can aid health policy-makers in designing effective preventive strategies in other countries worldwide where HBV is still prevalent. However, the empirical findings on transmission routes and the temporal evolution of HBV infection varying with areas should be considered with great caution as only two studies were modeled.

AB - Elucidating the temporal natural history of Hepatitis B virus (HBV) infection provides not only useful information for assessing the spread of HBV infection but also a bedrock for economic appraisal of population-based preventive strategies (such as universal vaccination). HBV transmissions are transmitted through the maternal (vertical) route and environmental (horizontal) route. As the infection process from susceptible to active virus replication and finally to recovery state or to carrier state through both routes is not directly observable, mathematical models were therefore proposed to quantitatively elucidate the dynamic process of HBV infection with time. We began with a simple two-state model (from susceptible to infection) and further developed a five-state (including susceptible, latent phase, active viral replication, carrier, and recovery states) stochastic process to quantify the dynamics of HBV infection, making allowances for a mixed proportion of vertical and horizontal transmissions. The data used in the estimation, which were collected before implementation of a policy for universal HBV vaccination, were derived from several previous serum prevalence studies, including both low (northern) and high (southern) HBV prevalence areas, in Taiwan. The parameters obtained from stochastic models were converted to compute the basic reproductive number (R0) in each study to indicate the extent of the spread of HBV infection. By linking the temporal natural history of HBV infection with the previously established Markov process for the sequelae of HBV infection (chronic hepatitis infection, liver cirrhosis, and hepatocelluar carcinoma), we developed a Markov cycle decision tree to evaluate the two population-based preventive strategies related to vaccination and maternal lamivudine use with a cost-effectiveness analysis. In the five-state model, horizontal transmission was found to contribute more to HBV infection than vertical transmission in the northern area (59 vs. 41 %), whereas vertical transmission was more likely than horizontal transmission in the southern area (80 vs. 20 %). After considering the parameters of the two transmission routes, annual infection rate (person-years) for susceptible subjects was higher in the northern area (0.35) than the southern area (0.011). A similar finding was noted for annual rate of the transition from the latent period to active viral replications (1.12 in the northern area and 0.072 in the southern area). Annual rate of the conversion from active viral replication to the carrier state was higher in the southern area (0.184) than the northern area (0.119). Annual recovery rates were 0.014 in the northern area and 0.024 in the southern area for the carrier and 0.048 and 0.088 for transient viremia. The R0 at age 30 using the parameters obtained from the five-state stochastic model was estimated as 4.88 in the northern and 7.03 in the southern area. Regarding the findings of economic appraisal, both preventive strategies were cost-saving, yielding the negative value of incremental cost-effectiveness ratio, compared with the baseline group (no intervention), regardless of areas. The preventive strategies in the southern area were more cost-saving than those in the northern area. The consolidation of elucidating the temporal natural history of HBV infection, estimating basic reproductive number, and conducting an economic appraisal of population-based preventive strategy can aid health policy-makers in designing effective preventive strategies in other countries worldwide where HBV is still prevalent. However, the empirical findings on transmission routes and the temporal evolution of HBV infection varying with areas should be considered with great caution as only two studies were modeled.

KW - Hepatitis B

KW - Infection

KW - Reproductive number

KW - Stochastic model

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