Dynamical behavior of a hepatitis B virus transmission model with vaccination

Pang, Jing; Cui, Jinǵan; Zhou, Xueyong

doi:10.1016/j.jtbi.2010.05.038

Cited by 108 publications

(68 citation statements)

References 14 publications

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“…However, it should be noted that for areas with low endemic HBV infection and a low proportion of vertical transmission such as in Western countries, such preventive strategies may neither be costsaving nor even cost-effective. It is hoped that our proposed five-state stochastic model can be extended to shed light on how vaccination and anti-virus treatment can stop the spread of HBV as they did in two prior studies (O'Leary et al 2010;Pang et al 2010) and can also assess how different transmission resources can lead to HBV infection or other cross-infection as seen in another previous study (Aylward et al 1995).…”

Section: Discussionmentioning

confidence: 88%

“…Numerous studies have been devoted to estimating this indicator for various infectious diseases (Pybus et al 2001;Yang et al 2009). Two studies have already focused on modeling the effect of vaccination or antivirus treatment on the transmission, the prevalence, and the incidence of HBV infection (O'Leary et al 2010;Pang et al 2010). The effect of unsafe injection on HBV infection and also HIV cross-infection has been also elucidated with a mathematical model (Aylward et al 1995).…”

Section: Introductionmentioning

confidence: 99%

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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

Hung

Wang

Yen

et al. 2013

Stoch Environ Res Risk Assess

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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 (R 0 ) 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 populationbased 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 R 0 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 n...

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Section: Discussionmentioning

confidence: 88%

Section: Introductionmentioning

confidence: 99%

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

Hung

Wang

Yen

et al. 2013

Stoch Environ Res Risk Assess

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“…An age structure model to predict the dynamics of HBV transmission and evaluate the long-term effectiveness of the vaccination program in China has been proposed by Zhao et al [8]. The mathematical model developed by Pang et al [9] allowed him to explore the impact of vaccination and other controlling measures of HBV infection while Bhattacharyya and Ghosh [10], Kar and Batabyal [11], and Kar and Jana [12] proposed optimal control of infectious diseases.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Logic Approach for Solving an Optimal Control Problem of an Uninfected Hepatitis B Virus Dynamics

Ntaganda¹,

Gahamanyi²

2015

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“…Malaria, Tuberculosis, Hepatitis B, HIV/AIDS and other sexually transmitted infections have all being mathematically accounted for (see [28,2,24,31,22,25] to mention just a few of them). Quite recently some authors [34,19] did analyse some general SIR and SEIRS models with interesting dynamics.…”

Section: Introductionmentioning

confidence: 99%

Transmission dynamics of Trichomonas vaginalis: A mathematical approach

Bhunu

Mushayabasa

2011

Journal of Mathematical Analysis and Applications

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Despite the availability of treatment that is effective, Trichomonas vaginalis infections are still high. A deterministic model for transmission dynamics of Trichomonas vaginalis is presented as a system of non-linear differential equations. Analysis of the reproduction number has shown that an increase in the number of straight women (non-lesbians) infected result in an increase in the number of lesbians infected. This suggests that straight women are turning into lesbians already infected. The disease-free equilibrium is shown to be globally asymptotically stable when the corresponding reproduction number is less than unity. Analytical results and numerical simulations both show that treatment is able to control Trichomonas vaginalis infections. This suggests an effective control of trichomoniasis rests in encouraging and persuading sexual partners of those displaying symptoms to seek treatment. Failure for the asymptomatic to seek treatment (mostly males given that the majority of males does not show symptoms) will continue to fuel the infection.

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Dynamical behavior of a hepatitis B virus transmission model with vaccination

Cited by 108 publications

References 14 publications

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

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

Fuzzy Logic Approach for Solving an Optimal Control Problem of an Uninfected Hepatitis B Virus Dynamics

Transmission dynamics of Trichomonas vaginalis: A mathematical approach

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