The document summarizes information about the Hepatitis B virus (HBV) from multiple sources. It describes HBV as a major global health problem that is transmitted through blood and body fluids. Mathematical models are proposed to study the transmission dynamics of HBV and the effects of asymptomatic carriers on infection rates. The models examine thresholds for disease eradication based on variables like basic reproduction number and vaccination levels.

1. Mathematical Modelling of the Hepatitis B Virus. Ms.Sirikalayanee Meritthi G 5337906 TMTM/D

2. Introduction

3. Hepatitis B Virus (ICD10 : B16) According to WHO Hepatitis B is a majority of global health problem and potentially life-threatening liver infection . The severe pathological of HBV Hepatitis B is preventable with a safe and effective vaccine . ( Ref. WHO : Global Alert Response: Hepatitis B)

4. Hepatitis B Virus (ICD10 : B16) ~ 2 Billion have been HVB infection. ~ 4 Million have Acute clinical of HBV < 350 M illion have chr . liver infection. ~ 600,000 die due to the acute or chronic consequences of hepatitis B. Of 25% of adults chr . infected during childhood die from liver cancer or cirrhosis caused by the chronic infection. ( Ref. WHO : Global Alert Response: Hepatitis B)

5. Prevalence of chr . infection with hepatitis B virus, 2006 ( Ref.CDC : Viral Hepatitis Statistics & Surveillance )

6. Hepatitis B Virus (Form 506 : B12) Year BE. 2549 : ( Ref. Bureau of Epidemiology,DDC,MOPH : Hepatitis )

7. Hepatitis B Virus (Form 506 : B12) ( Ref. Bureau of Epidemiology,DDC,MOPH : Hepatitis ) Prevalence of HepatitisB By year 1997 to 2006 Per 100,000 population Report Case of Hepatitis By year 2006 Age group Per 100,000 population

8. Hepatitis B Virus (Form 506 : B12) ( Ref. Bureau of Epidemiology,DDC,MOPH : Hepatitis ) Report case of Hepatitis B By region year 2006 Per 100,000 population Report Case of Hepatitis By Type of HAV , HVB Year 1997 to 2006 Per 100,000 population

9. Province specific incidence 2006 ( Ref. Bureau of Epidemiology,DDC,MOPH : Hepatitis ) Report Case of Hepatitis per 100,000 population By Province , 2006

10. Thailand : EPI for Children ( Ref. who.int/immunization_monitoring/en/globalsummary/countryprofileresult )

11. WHO,Unicef: EPI Thailand ( Ref. who.int/immunization_monitoring/en/globalsummary/countryprofileresult )

12. Literature Review

13. Hepatitis B Epidemic jaundice described by Hippocrates in 5th century BCE Jaundice reported among recipients of human serum and yellow fever vaccines in 1930s and 1940s Australia antigen described in 1965 Serologic tests developed in 1970s

14. Hepatitis B Virus Hepadnaviridae family (DNA) Numerous antigenic components Humans are only known host May retain infectivity for more than 7 days at room temperature

15. Hepadnaviridae Molecular biology Enveloped, spherical . Diameter from about 42nm nm . Icosahedric T = 4 capsid . Ref. : http :// viralzone . expasy . org / all_by_species / 9 . html

16. GENOME Partially dsDNA circular genome, about 3.2 kb in size . Encodes for 7 proteins . Ref. : http :// viralzone . expasy . org / all_by_species / 9 . html

17. GENE EXPRESSION REPLICATION CYTOPLASMIC /NUCLEAR Virus attaches to host receptors through major surface antigen and enters the cell by an unknown mechanism. Relaxed circular DNA ( RC - DNA ) and capsid are transported via microtubules to the nucleus where DNA is released through the nuclear pore, and repaired to form covalently closed circular DNA ( cccDNA ). Transcription by RNA polymerase II of the pregenomic RNA (pgRNA) and subgenomic mRNAs, inducing synthesis of all the viral proteins. pgRNA is encapsidated, together with the P protein, and reverse-transcribed inside the nucleocapsid in (-)DNA covalently linked to P protein. (+) DNA synthesis from the (-) DNA template generates new RC - DNA . Transport to the nucleus of new RC - DNA leads to cccDNA amplification; alternatively, the RC - DNA containing nucleocapsids are enveloped and bud as virions . Ref. : http :// viralzone . expasy . org / all_by_species / 9 . html

18. HBsAg Antigenic determinant found on the surface of the virus Not infectious; only the complete virus (Dane particle) is infectious When HBsAg is present, complete virus is also present During replication, HBV produces HBsAg in excess of that needed for production of the Dane particles HBcAg Nucleocapsid protein core of the HBV Not detectable in serum by conventional techniques Found in liver tissue of persons with acute or chronic HBV infection HBeAg A soluble protein found in the core of HBV Found in serum of person with high virus titers Anti-HBs Develops during convalescence to acute HBV or after vaccination Anti-HBc Indicates infection with HBV at an undefined time in the past Anti-HBe Associated with low infectivity of serum Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

19. Hepatitis B Clinical Features Incubation period 60-150 days (average 90 days) Nonspecific prodrome of malaise, fever, headache, myalgia Illness not specific for hepatitis B At least 50% of infections asymptomatic Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

20. Hepatitis B Complications Fulminant hepatitis Hospitalization Cirrhosis Hepatocellular carcinoma Death Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

21. Chronic Hepatitis B Virus Infection Chronic viremia Responsible for most mortality Overall risk 5% Higher risk with early infection Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

22. Risk of Chronic HBV Carriage by Age of Infection Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

23. Global Patterns of Chronic HBV Infection High ( > 8%): 45% of global population lifetime risk of infection >60% early childhood infections common Intermediate (2%-7%): 43% of global population lifetime risk of infection 20%-60% infections occur in all age groups Low (<2%): 12% of global population lifetime risk of infection <20% most infections occur in adult risk groups Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

24. Global Patterns of Chronic HBV Infection High ( > 8%): 45% of global population lifetime risk of infection >60% early childhood infections common Intermediate (2%-7%): 43% of global population lifetime risk of infection 20%-60% infections occur in all age groups Low (<2%): 12% of global population lifetime risk of infection <20% most infections occur in adult risk groups Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

25. Hepatitis B Epidemiology Reservoir Human Transmission Bloodborne Asymptomatic infections transmit Communicability 1-2 months before and after onset of symptoms Chronic infection Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

26. Incubation period: Average 60-90 days Range 45-180 days Clinical illness (jaundice): <5 yrs, <10% 5 yrs, 30%-50% Acute case-fatality rate: 0.5%-1% Chronic infection: <5 yrs, 30%-90% 5 yrs, 2%-10% Premature mortality from chronic liver disease: 15%-25% Clinical Features Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

27. Clinical outcomes of Hepatitis B infections Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

28. Outcomes of Hepatitis B Infection Acute HBV Infection Recovery and Immunity Fulminant Hepatitis Chronic Infection [carrier] Chronic Active Hepatitis cirrhosis hepatocellular carcinoma Death 10% 25% 63-93% 1-2% Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm

29. Immunological events of acute vs. chronic HBV infection From Murray et. al., Medical Microbiology 5 th edition, 2005, Chapter 66, published by Mosby Philadelphia,, A) Acute B) Chronic

30. Prevention of Hepatitis B –prophylaxis and vaccination

31. Reference : Hepatitis B factsheet : WHO The estimated coverage EPI Thailand WHO & UNICEF. Viral Hepatitis Prevention Board. :CDC. Background media information Viral Hepatitis : European association for the study of the liver.

32. The Studies: Cont. Clinical Virology of Hepatitis B Virus infection 2002 : Department of medicina interna , Italy Viral Hepatitis : CDC . Viral Hepatitis Blood-Borne Hepatitis : Atsu/faculty Modeling the effect of carrier on transmission dynamic infection disease. : Mathematical Biosciences and engineering. Hepatitis Virus and Human Hepatocellular Carcinoma : Yale Journal

33. Methodology

34. Aim : To Investigation of mathematic models for the Hepatitis B virus (HVB) infection on the disease dynamics from prevalence of THAI population.

35. Aim : To propose general mathematical model for HVB with asymtomatic carriers to investigate the effects of carriers on the transmission dynamic.

36. Mathematic Model Assumption : Population densities S usceptibles (X) I nfectives (Y) R emovals (Z) - immune or dead SIR model (Age structural) populaion (X + Y + Z = N) Direct transmission and mass-action mixing (βXY) transfers X to Y Removal of infectives(γY) transfers Y to Z

37. Mathematic Model

38. Compartment HVB

39. Mathematic Model 1. A single infective in an otherwise susceptible population will start an epidemic only if the density of susceptibles exceeds a threshold At t = 0, dY/dt = (βX - γ) Y > 0 if X > γ / β (Note: X ≅ N) The rate at which susceptibles become infectives (βXY) must exceed the rate at which infectives are removed (γY) 2. At the end of the epidemic (if there is one), the population consists of… i. Susceptibles below threshold density ii. No infectives iii. Removals

40. Basic Reproduction Ratio after Immunization R’ ≅ R (1 - v) to define threshold for eradication Eradication if R’ < 1; immunization level v > 1 - (1/R) R = 2; v > 50% R = 5; v > 80% R = 10; v > 90% R = 20; v > 95% If 1 < R’ < R, infection persists in the population with reduced incidence and higher mean age Herd immunity

41. ThAnK yOu