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HBV modelling

HBV modelling

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  • 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