Thirty-Year Outcomes of the National Hepatitis B Immunization Program in Taiwan

Abstract

In this paper, we derive a formula to compute the solution of the linear matrix equation X = Af (X)B + C via finding any solution of a specific Stein matrix equation X = AX B + C, where the linear (or anti-linear) matrix operator f is period-n. According to this formula, we should pay much attention to solve the Stein matrix equation from recently famous numerical methods. For instance, Smith-type iterations, Bartels-Stewart algorithm, and etc.. Moreover, this transformation is used to provide necessary and sufficient conditions of the solvable of the linear matrix equation. On the other hand, it can be proven that the general solution of the linear matrix equation can be presented by the general solution of the Stein matrix equation. The necessary condition of the uniquely solvable of the linear matrix equation is developed. It is shown that several representations of this formula are coincident. Some examples are presented to illustrate and explain our results.

Treatment and Prognosis of Hepatitis B Virus Concomitant with Alcoholism

“…This is accompanied by a significant decrease in the incidence of infant fulminant hepatitis associated with chronic liver disease, mortality, and HCC [14,15].…”

Immunogenicity, effectiveness and safety of combined hepatitis A and B vaccine: a systematic literature review

“…On the other hand, the A&B combination vaccine is mostly recommended and used in individuals at risk of exposure, providing the opportunity to protect against Hepatitis A and B individuals that would suffer from higher morbidity and mortality, if infected. The impact of vaccination and longterm safety, immunogenicity, and effectiveness with this vaccine cannot be not measured in the context of national programs as it is the case for Hepatitis A [62]or B [63]. It is therefore key to continue monitoring how Hepatitis A&B combination vaccination performs from individual studies and to do so with and using a systematic and unbiased methodology seems to be the most appropriate approach.…”

Vaccination contre l’hépatite B

“…En 2013, 183 pays avaient adopté ce programme de vaccination ce qui a conduit à une diminution significative du taux d'infections chroniques chez les enfants et les adolescents. Ceci est particulièrement bien illustré à Taïwan où le taux des PC a diminué depuis 1984, de 10 % à moins de 1 % chez les adolescents et les jeunes adultes [12]. Mais le plus grand succès du vaccin contre l'hépatite B est certainement son impact sur l'incidence des carcinomes hépatocellulaires (CHC) qui AgHBe+), la transmission du virus conduit à une infection chronique de l'enfant dans 95 % des cas.…”