Mathematical Modelling of the Hepatitis B Virus.  Ms.Sirikalayanee Meritthi G 5337906  TMTM/D
Introduction
Hepatitis B Virus   (ICD10 : B16) <ul><li>According to WHO </li></ul><ul><li>Hepatitis B is a  majority of global health p...
Hepatitis B Virus (ICD10 : B16) <ul><li>~ 2  Billion  have been HVB infection. </li></ul><ul><li>~ 4  Million   have Acute...
Prevalence of chr . infection  with hepatitis B virus,  2006   ( Ref.CDC  :  Viral Hepatitis Statistics & Surveillance )
Hepatitis B Virus (Form 506 : B12) <ul><li>Year BE. 2549 :  </li></ul>( Ref. Bureau of Epidemiology,DDC,MOPH  : Hepatitis  )
Hepatitis B Virus (Form 506 : B12) ( Ref. Bureau of Epidemiology,DDC,MOPH  : Hepatitis  ) Prevalence of HepatitisB By year...
Hepatitis B Virus (Form 506 : B12) ( Ref. Bureau of Epidemiology,DDC,MOPH  : Hepatitis  ) Report case of Hepatitis B By re...
Province specific incidence 2006 ( Ref. Bureau of Epidemiology,DDC,MOPH  : Hepatitis  ) Report Case of Hepatitis per 100,0...
Thailand  : EPI for Children ( Ref. who.int/immunization_monitoring/en/globalsummary/countryprofileresult )
WHO,Unicef: EPI Thailand ( Ref. who.int/immunization_monitoring/en/globalsummary/countryprofileresult )
Literature Review
Hepatitis B <ul><li>Epidemic jaundice described by Hippocrates in 5th century BCE </li></ul><ul><li>Jaundice reported amon...
Hepatitis B Virus <ul><li>Hepadnaviridae family (DNA) </li></ul><ul><li>Numerous antigenic components </li></ul><ul><li>Hu...
Hepadnaviridae   Molecular biology Enveloped, spherical .  Diameter from about 42nm nm .  Icosahedric T = 4 capsid .  Ref....
GENOME Partially dsDNA circular genome, about 3.2 kb in size .  Encodes for 7 proteins .  Ref.   :  http :// viralzone . e...
GENE EXPRESSION <ul><li>REPLICATION </li></ul><ul><li>CYTOPLASMIC /NUCLEAR  </li></ul><ul><li>Virus attaches to host recep...
<ul><li>HBsAg </li></ul><ul><ul><li>Antigenic determinant found on the surface of the virus </li></ul></ul><ul><ul><li>Not...
Hepatitis B Clinical Features <ul><li>Incubation period 60-150 days (average 90 days) </li></ul><ul><li>Nonspecific prodro...
Hepatitis B Complications <ul><li>Fulminant hepatitis </li></ul><ul><li>Hospitalization </li></ul><ul><li>Cirrhosis </li><...
Chronic Hepatitis B  Virus Infection <ul><li>Chronic viremia </li></ul><ul><li>Responsible for most mortality </li></ul><u...
<ul><li>Risk of Chronic HBV Carriage by   Age of Infection </li></ul>Ref.  : CDC  http :// www . cdc . gov / hepatitis / H...
Global Patterns of  Chronic HBV Infection <ul><li>High ( > 8%): 45% of global population </li></ul><ul><ul><li>lifetime ri...
Global Patterns of  Chronic HBV Infection <ul><li>High ( > 8%): 45% of global population </li></ul><ul><ul><li>lifetime ri...
Hepatitis B Epidemiology <ul><li>Reservoir     Human </li></ul><ul><li>Transmission     Bloodborne     Asymptomatic infect...
<ul><li>Incubation period: Average 60-90 days </li></ul><ul><li>Range 45-180 days </li></ul><ul><li>Clinical illness (jaun...
Clinical outcomes of Hepatitis B infections Ref.  : CDC  http :// www . cdc . gov / hepatitis / HBV / index . htm
Outcomes of Hepatitis B Infection Acute HBV Infection Recovery  and  Immunity Fulminant Hepatitis Chronic Infection [carri...
Immunological events of acute vs. chronic HBV infection From Murray et. al., Medical Microbiology 5 th  edition, 2005, Cha...
Prevention of Hepatitis B –prophylaxis and vaccination
Reference  : <ul><li>Hepatitis B  factsheet  : WHO  </li></ul><ul><li>The estimated coverage EPI Thailand  WHO & UNICEF. <...
The Studies: Cont. <ul><li>Clinical Virology of Hepatitis B Virus infection 2002  : Department of medicina interna , Italy...
Methodology
Aim :  <ul><li>To Investigation of mathematic models for the Hepatitis B virus (HVB) infection on the  disease dynamics fr...
Aim :  <ul><li>To propose general mathematical model for HVB with asymtomatic carriers to investigate the effects of carri...
Mathematic Model <ul><li>Assumption : </li></ul><ul><ul><li>Population densities </li></ul></ul><ul><ul><li>S usceptibles ...
Mathematic Model
Compartment HVB
Mathematic Model <ul><li>1. A single infective in an otherwise susceptible population will start an epidemic only if the d...
Basic Reproduction Ratio after Immunization <ul><li>R’ ≅ R (1 - v) to define threshold for eradication </li></ul><ul><li>E...
ThAnK yOu
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    1. 1. Mathematical Modelling of the Hepatitis B Virus. Ms.Sirikalayanee Meritthi G 5337906 TMTM/D
    2. 2. Introduction
    3. 3. Hepatitis B Virus (ICD10 : B16) <ul><li>According to WHO </li></ul><ul><li>Hepatitis B is a majority of global health problem </li></ul><ul><li>and potentially life-threatening liver infection . </li></ul><ul><li>The severe pathological of HBV </li></ul><ul><li>Hepatitis B is preventable with a safe and effective vaccine . </li></ul>( Ref. WHO : Global Alert Response: Hepatitis B)
    4. 4. Hepatitis B Virus (ICD10 : B16) <ul><li>~ 2 Billion have been HVB infection. </li></ul><ul><li>~ 4 Million have Acute clinical of HBV </li></ul><ul><li>< 350 M illion have chr . liver infection. </li></ul><ul><li>~ 600,000 die due to the acute or chronic consequences of hepatitis B. </li></ul><ul><li>Of 25% of adults chr . infected during childhood die from liver cancer or cirrhosis caused by the chronic infection. </li></ul>( Ref. WHO : Global Alert Response: Hepatitis B)
    5. 5. Prevalence of chr . infection with hepatitis B virus, 2006 ( Ref.CDC : Viral Hepatitis Statistics & Surveillance )
    6. 6. Hepatitis B Virus (Form 506 : B12) <ul><li>Year BE. 2549 : </li></ul>( Ref. Bureau of Epidemiology,DDC,MOPH : Hepatitis )
    7. 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. 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. 9. Province specific incidence 2006 ( Ref. Bureau of Epidemiology,DDC,MOPH : Hepatitis ) Report Case of Hepatitis per 100,000 population By Province , 2006
    10. 10. Thailand : EPI for Children ( Ref. who.int/immunization_monitoring/en/globalsummary/countryprofileresult )
    11. 11. WHO,Unicef: EPI Thailand ( Ref. who.int/immunization_monitoring/en/globalsummary/countryprofileresult )
    12. 12. Literature Review
    13. 13. Hepatitis B <ul><li>Epidemic jaundice described by Hippocrates in 5th century BCE </li></ul><ul><li>Jaundice reported among recipients of human serum and yellow fever vaccines in 1930s and 1940s </li></ul><ul><li>Australia antigen described in 1965 </li></ul><ul><li>Serologic tests developed in 1970s </li></ul>
    14. 14. Hepatitis B Virus <ul><li>Hepadnaviridae family (DNA) </li></ul><ul><li>Numerous antigenic components </li></ul><ul><li>Humans are only known host </li></ul><ul><li>May retain infectivity for more than 7 days at room temperature </li></ul>
    15. 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. 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. 17. GENE EXPRESSION <ul><li>REPLICATION </li></ul><ul><li>CYTOPLASMIC /NUCLEAR </li></ul><ul><li>Virus attaches to host receptors through major surface antigen and enters the cell by an unknown mechanism. </li></ul><ul><li>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 ). </li></ul><ul><li>Transcription by RNA polymerase II of the pregenomic RNA (pgRNA) and subgenomic mRNAs, inducing synthesis of all the viral proteins. </li></ul><ul><li>pgRNA is encapsidated, together with the P protein, and reverse-transcribed inside the nucleocapsid in (-)DNA covalently linked to P protein. </li></ul><ul><li>(+) DNA synthesis from the (-) DNA template generates new RC - DNA . </li></ul><ul><li>Transport to the nucleus of new RC - DNA leads to cccDNA amplification; alternatively, the RC - DNA containing nucleocapsids are enveloped and bud as virions . </li></ul>Ref. : http :// viralzone . expasy . org / all_by_species / 9 . html
    18. 18. <ul><li>HBsAg </li></ul><ul><ul><li>Antigenic determinant found on the surface of the virus </li></ul></ul><ul><ul><li>Not infectious; only the complete virus (Dane particle) is infectious </li></ul></ul><ul><ul><li>When HBsAg is present, complete virus is also present </li></ul></ul><ul><ul><li>During replication, HBV produces HBsAg in excess of that needed for production of the Dane particles </li></ul></ul><ul><li>HBcAg </li></ul><ul><ul><li>Nucleocapsid protein core of the HBV </li></ul></ul><ul><ul><li>Not detectable in serum by conventional techniques </li></ul></ul><ul><ul><li>Found in liver tissue of persons with acute or chronic HBV infection </li></ul></ul><ul><li>HBeAg </li></ul><ul><ul><li>A soluble protein found in the core of HBV </li></ul></ul><ul><ul><li>Found in serum of person with high virus titers </li></ul></ul><ul><li>Anti-HBs </li></ul><ul><ul><li>Develops during convalescence to acute HBV or after vaccination </li></ul></ul><ul><li>Anti-HBc </li></ul><ul><ul><li>Indicates infection with HBV at an undefined time in the past </li></ul></ul><ul><li>Anti-HBe </li></ul><ul><ul><li>Associated with low infectivity of serum </li></ul></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    19. 19. Hepatitis B Clinical Features <ul><li>Incubation period 60-150 days (average 90 days) </li></ul><ul><li>Nonspecific prodrome of malaise, fever, headache, myalgia </li></ul><ul><li>Illness not specific for hepatitis B </li></ul><ul><li>At least 50% of infections asymptomatic </li></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    20. 20. Hepatitis B Complications <ul><li>Fulminant hepatitis </li></ul><ul><li>Hospitalization </li></ul><ul><li>Cirrhosis </li></ul><ul><li>Hepatocellular carcinoma </li></ul><ul><li>Death </li></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    21. 21. Chronic Hepatitis B Virus Infection <ul><li>Chronic viremia </li></ul><ul><li>Responsible for most mortality </li></ul><ul><li>Overall risk 5% </li></ul><ul><li>Higher risk with early infection </li></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    22. 22. <ul><li>Risk of Chronic HBV Carriage by Age of Infection </li></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    23. 23. Global Patterns of Chronic HBV Infection <ul><li>High ( > 8%): 45% of global population </li></ul><ul><ul><li>lifetime risk of infection >60% </li></ul></ul><ul><ul><li>early childhood infections common </li></ul></ul><ul><li>Intermediate (2%-7%): 43% of global population </li></ul><ul><ul><li>lifetime risk of infection 20%-60% </li></ul></ul><ul><ul><li>infections occur in all age groups </li></ul></ul><ul><li>Low (<2%): 12% of global population </li></ul><ul><ul><li>lifetime risk of infection <20% </li></ul></ul><ul><ul><li>most infections occur in adult risk groups </li></ul></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    24. 24. Global Patterns of Chronic HBV Infection <ul><li>High ( > 8%): 45% of global population </li></ul><ul><ul><li>lifetime risk of infection >60% </li></ul></ul><ul><ul><li>early childhood infections common </li></ul></ul><ul><li>Intermediate (2%-7%): 43% of global population </li></ul><ul><ul><li>lifetime risk of infection 20%-60% </li></ul></ul><ul><ul><li>infections occur in all age groups </li></ul></ul><ul><li>Low (<2%): 12% of global population </li></ul><ul><ul><li>lifetime risk of infection <20% </li></ul></ul><ul><ul><li>most infections occur in adult risk groups </li></ul></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    25. 25. Hepatitis B Epidemiology <ul><li>Reservoir Human </li></ul><ul><li>Transmission Bloodborne Asymptomatic infections transmit </li></ul><ul><li>Communicability 1-2 months before and after onset of symptoms Chronic infection </li></ul>Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    26. 26. <ul><li>Incubation period: Average 60-90 days </li></ul><ul><li>Range 45-180 days </li></ul><ul><li>Clinical illness (jaundice): <5 yrs, <10% 5 yrs, 30%-50% </li></ul><ul><li>Acute case-fatality rate: 0.5%-1% </li></ul><ul><li>Chronic infection: <5 yrs, 30%-90% 5 yrs, 2%-10% </li></ul><ul><li>Premature mortality from chronic liver disease: 15%-25% </li></ul>Clinical Features Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    27. 27. Clinical outcomes of Hepatitis B infections Ref. : CDC http :// www . cdc . gov / hepatitis / HBV / index . htm
    28. 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. 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. 30. Prevention of Hepatitis B –prophylaxis and vaccination
    31. 31. Reference : <ul><li>Hepatitis B factsheet : WHO </li></ul><ul><li>The estimated coverage EPI Thailand WHO & UNICEF. </li></ul><ul><li>Viral Hepatitis Prevention Board. :CDC. </li></ul><ul><li>Background media information Viral Hepatitis : European association for the study of the liver. </li></ul>
    32. 32. The Studies: Cont. <ul><li>Clinical Virology of Hepatitis B Virus infection 2002 : Department of medicina interna , Italy </li></ul><ul><li>Viral Hepatitis : CDC . </li></ul><ul><li>Viral Hepatitis Blood-Borne Hepatitis : Atsu/faculty </li></ul><ul><li>Modeling the effect of carrier on transmission dynamic infection disease. : Mathematical Biosciences and engineering. </li></ul><ul><li>Hepatitis Virus and Human Hepatocellular Carcinoma : Yale Journal </li></ul>
    33. 33. Methodology
    34. 34. Aim : <ul><li>To Investigation of mathematic models for the Hepatitis B virus (HVB) infection on the disease dynamics from prevalence of THAI population. </li></ul>
    35. 35. Aim : <ul><li>To propose general mathematical model for HVB with asymtomatic carriers to investigate the effects of carriers on the transmission dynamic. </li></ul>
    36. 36. Mathematic Model <ul><li>Assumption : </li></ul><ul><ul><li>Population densities </li></ul></ul><ul><ul><li>S usceptibles (X) </li></ul></ul><ul><ul><li>I nfectives (Y) </li></ul></ul><ul><ul><li>R emovals (Z) - immune or dead </li></ul></ul><ul><ul><li>SIR model </li></ul></ul><ul><ul><li>(Age structural) populaion (X + Y + Z = N) </li></ul></ul><ul><li>Direct transmission and mass-action mixing (βXY) transfers X to Y </li></ul><ul><li>Removal of infectives(γY) transfers Y to Z </li></ul>
    37. 37. Mathematic Model
    38. 38. Compartment HVB
    39. 39. Mathematic Model <ul><li>1. A single infective in an otherwise susceptible population will start an epidemic only if the density of susceptibles exceeds a threshold </li></ul><ul><li>At t = 0, dY/dt = (βX - γ) Y > 0 if X > γ / β (Note: X ≅ N) </li></ul><ul><li>The rate at which susceptibles become infectives (βXY) must exceed the rate at which infectives are removed (γY) </li></ul><ul><li>2. At the end of the epidemic (if there is one), the population consists of… </li></ul><ul><ul><li>i. Susceptibles below threshold density </li></ul></ul><ul><ul><li>ii. No infectives </li></ul></ul><ul><li>iii. Removals </li></ul>
    40. 40. Basic Reproduction Ratio after Immunization <ul><li>R’ ≅ R (1 - v) to define threshold for eradication </li></ul><ul><li>Eradication if R’ < 1; immunization level v > 1 - (1/R) </li></ul><ul><li>R = 2; v > 50% </li></ul><ul><li>R = 5; v > 80% </li></ul><ul><li>R = 10; v > 90% </li></ul><ul><li>R = 20; v > 95% </li></ul><ul><li>If 1 < R’ < R, infection persists in the population with </li></ul><ul><li>reduced incidence and higher mean age </li></ul><ul><li>Herd immunity </li></ul>
    41. 41. ThAnK yOu

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