1. Effects of heterogeneity in hosts and pathogens on effectiveness of vaccination Mirjam Kretzschmar RIVM, Department of Infectious Diseases Epidemiology The Netherlands

2. Populations are heterogeneous...

3. Why do we have to think about heterogeneity? Measles outbreak (almost 3000 cases) despite coverage of 96%

4. Host heterogeneity Disease independent (can be measured also for non-infected individuals): –Age, sex, other demographic variables –Behaviour (e.g. number of contacts, compliance with vaccination) Disease dependent (only for infected individuals): –Transmission route –Disease stage; primary versus secondary infection –Clininal symptoms or asymptomatic

5. Pathogen heterogeneity Heterogeneity between strains: –Virulence (defined as host mortality or severity of disease) –Vulnarability to host immune response –Competition via cross-immunity Within host heterogeneity: –Immunogenic variability (HIV) –Different location within host leads to different effects (invasive infection versus carrier)

6. Effects of heterogeneity on vaccination depend on vaccination strategy Universal vaccination –Rationale: create herd immunity such that unvaccinated individuals are also protected pockets of not vaccinated persons (MMR vaccination in the Netherlands) core groups of individuals with very many contacts (STD, Hepatitis B) non-homogeneous contact patterns, i.e. household contacts, spatial patterns, repeated contacts with same individuals (long term partnerships, networks)

7. Targetted vaccination of risk groups –Rationale: protect those individuals who are at greatest risk for being infected Takes heterogeneity in risk into account, but what are effects of mixing between risk groups? Critical coverage per risk group? Effects of vaccination on non-risk groups?

8. Ring vaccination –Rationale: vaccinate direct contacts of infected individuals to interrupt transmission chain Heterogeneity in contact patterns is taken into account, only persons at risk are included in vaccination. But: how to estimate fraction of contacts that have been found and vaccinated? Modelling: Contact tracing requires a network modelling approach

9. Contact patterns: who has contact with whom?

10. Contact and transmission route Influenza (airborne infection): –talking with each other at close distance –coughing at each other Gonorrhoea (sexually transmitted dis.): –sexual intercourse Hepatitis C (bloodborne infection): –sharing contaminated needles –blood transfusion

11. Knowledge about contact patterns leads to insight into transmission routes Contact network AIDS cases (Auerbach et al. 1984) –Probability that cluster of cases is connected by contact on the basis of random events –timing of contacts and onset of disease Hypothesis: AIDS is transmitted by homosexual contact

12. Cluster of AIDS patients A.S. Klovdahl. Social networks and the spread of infectious diseases: The AIDS example. Soc. Sci. Med. 21 (1985): 1203-1216. number: order of diagnosis 0 index case

13. Contacts are non-random Population heterogeneity –Age structure, social economic structure, education Social grouping –Families, working environment, recreation Geographical distribution –Cities, rural areas, mobility between regions  People are not the same and they choose contacts with certain preferences  these choices influence the way infectious diseases spread

14. Influence of contact patterns on epidemiological outcome Age distribution of cases in STDs for men and women Biannual measles epidemics in prevaccination era High prevalence of STDs in high activity core groups Widespread heterosexual transmission of HIV in sub- Saharan Africa Hepatitis A outbreaks in day care centers Increasing incidence of HIV in monogamous married women in Thailand Increasing incidence of malaria in Western Europe

15. Modelling heterogeneity Heterogeneity in number of contacts –Core groups –Stratification by activity –Mixing? Local/global contacts –Households –Metapopulation models Partnership duration: pair formation models, pair approximation models Networks

16. Vaccination in a population stratified by households Equalizing strategy: Choose individuals for vaccination sequentially from those households with largest number of susceptibles. Minimizes the number of vaccinations needed to reduce R to below 1. Ball, Mollison & Scalia-Tomba.Ann. Appl. Prob. 7 (1997) 46. global contacts local contacts

17. The basic reproduction number R 0 The expected number of secondary cases caused by one index case during his entire infectious period in a completely susceptible population. homogeneous population: R 0 =c  D heterogeneous population: number of secondary cases has to be averaged in the right way.

18. Heterogeneous population Diekmann, Heesterbeek, Metz. J. Math. Biol. 1990; 28:365-382 Diekmann, Heesterbeek. Mathematical Epidemiology of Infectious Diseases, Wiley, 2000. Next generation operator Number of cases in the (n+1)-th generation of infections given the distribution of infectious individuals (with respect to population structure) in the n-th generation. Basic reproduction number Dominant eigenvalue of the next-generation operator Explicit calculation of R 0 for separable mixing Contact funtion c(a,b)=f(a)g(b)

19. Host heterogeneity: example Hepatitis B vaccination Background: –Introduction of universal infant vaccination in the Netherlands? –Low prevalence, high costs of vaccination –How many cases of chronic hepatitis B infection can potentially be prevented? Project including case-control study, modelling and cost-effectiveness analysis

20. Hepatitis B: many types of heterogeneity Transmission routes: –Sexual transmission –Vertical to babies at birth –Horizontal close contact (household) Age: –Age dependent immune response (clinical symptoms and development of chronic carrier state) –Age dependent sexual activity level Behaviour: –High versus low activity within age groups Disease states: –Latent (1-2 months), acute (3-4 months), and chronic stages

21. Model structure Williams et al. (1996), Epidemiol & Infect. 116: 71-89 Kretzschmar et al. (2002) Epidemiol & Infect. 128: 229-244. Population stratified by age and sexual activity (6 activity classes) Two transmission routes (vertical and sexual) Different stages of infection (acute, chronic carrier) susceptiblelatent carrier vaccinated acute immune

22. Model System of partial differential equations (age structure) Proportionate mixing Separate models for hetero/homosexual populations Included immigration and age dependence in probability to become carrier Explicit formula for R 0

23. Calculation of R 0 Individuals can be infected via two routes. R 0 is the dominant eigenvalue of next generation matrix s sexual transmission v vertical transmission

24. Calculation of R 0 ss with L maximum lifetime  k fraction in activity class k =1,...6 c k (a) age dependent contact rate in activity class k  time since infection  i transmission probability per partnership

25. Age-dependence of becoming carrier P C ( ,a) has factor p(a), the probability of becoming carrier when infected at age a for a=0 for a>0 Edmunds et al. 1993: Point estimate of parameters  1 and  2 from data from 29 different studies

26. Probability of becoming carrier after infection

27. Partner change rates from sexual behaviour surveys (UK and NL)

28. Estimates for R 0 (heterosexual population)

29. Estimate R 0 Homosexual men R 0 >1: –Hepatitis B virus can persist –Immigration of infected persons has little influence Heterosexual population R 0 <1: –short transmission chains –immigration of infected persons determines prevalence

30. Compare with data Case control study: –heterosexual cases (N=41): 60% of cases infected by immigrant from high endemic country –homosexual cases (N=44): 16% infected by immigrant from medium or high endemic country

31. Conclusions for vaccination Vaccinating general population can reduce incidence of new infections within the country, but has little influence on prevalence of carriers. Vaccination of risk groups is being intensified Vaccination is offered to children of whom at least one parent is an immigrant from country with higher prevalence

32. Vertical transmission In highly endemic countries it is believed that vertical transmission and horizontal transmission to children are the most important transmission routes. In low endemic countries the role of horizontal transmission to children is not known. Can we use R 0 to analyse importance of those transmission routes? Assume sexual behaviour comparable to UK data

33. Consider R 0 vv with (  )fertility rate at age  b i transmission probabilities per offspring (b 1 =0.724, b 2 =0.115)

34. Fertility distributions

35. Horizontal transmission Horizontal transmission in households can be approximately described by increasing b i The fertility function can vary in age distribution and total number of offspring during lifetime. Example: mean offspring number 3, b 2 =0.5 R 0 = 1.29  Neither of the transmission modes alone could sustain endemic prevalence, together they can

36. Horizontal transmission as main transmission mode?

37. Conclusions Explicit expression for R 0 in heterogeneous populations can help to get insight into influence of different types of heterogeneity on transmission dynamics and their interaction Drawback: proportionate mixing assumption How does R 0 depend on underlying model assumptions? How well does R 0 reflect heterogeneity? Hepatitis B: different vaccination strategies depending on population heterogeneity?

38. Heterogeneity in the pathogen population and vaccination When can serotype replacement occur? Indirect effects of serotype replacement: partial immunisation by replacing strains? Optimal composition of vaccine (trade-off between breadth and effectiveness)? Evolution to higher virulence? Vaccination against disease or against infection?

39. Competition of 2 strains Model McLean: Assumptions: –2 strains, total cross-immunity –Vaccinated individuals can become infected with a small probability, vaccine efficacy differs between strains –after infection permanent immunity –Strain 1 outcompetes 2 in absence of vaccination A.R. McLean. Proc R Soc Lond B (1995) 261: 389-393.

40. McLean model S I2I2 I1I1 V recovery + death birth death vaccination death 1I1S1I1S 2I2S2I2S (1-r)  2 I 2 V (1- s)  1 I 1 V transmission

41. Effects of vaccination Vaccination reduces competitive pressure on weaker strain 2 -> outbreaks indirect effect: more herd immunity against strain 1

42. Superinfection Model Lipsitch: Assumptions: –no immunity, after recovery susceptible again –Individual can be infected by 2 strains simultaneously –Cross-immunity –vaccine 100% effectiv for target strain M. Lipsitch. Emerging Infectious Diseases (1999) 5: 336-345

43. Model with superinfection S I 1v I1I1 V birth death vaccination  1 (I 1 +I 1v +I 12 )S  2 (I 2 +I 12 )S (1- s)  1 (I 1 +I 1v +I 12 )V I2I2 aI 1 I 2 I 12 transmission recovery c 2  2 (I 2 +I 12 )I 1 c 1  1 (I 1 +I 1v +I 12 )I 2  I 1v

44. Effects of vaccination Vaccination enables coexistence of strains serotype replacement can occur If vaccine is also effective for other than the target strains, higher coverage is needed for eradication

45. Example pertussis Since middle of the 90‘s increase in incidence of pertussis in NL Increase in incidence among vaccinated children Large incidence of subclinical infections in adults Hypothesis: vaccine not as effective against presently circulating strains

46. Model with 2 strains

47. Assumptions Full cross immunity after natural infection vaccine protects fully against strain 1, partly against strain 2 vaccine induced immunity lasts shorter than natural immunity

48. Equilibrium under vaccination primary infection more transmissible, R 0 1 >R 0 2

49. Dynamics with vaccination

50. Conclusions Strains can coexist for certain range of vaccination coverage for high coverages strain 2 is dominant total prevalence of infection decreases with increasing coverage elimination for p larger than critical vaccination coverage

51. Equilibrium under vaccination secondary infection more transmissible

52. Dynamics with vaccination

53. Conclusions For high coverages coexistence of both strains total prevalence of infection increases when 2 strains are present infection remains present even with 100% vaccination coverage

54. Summary Vaccination can lead to coexistence of strains Contribution of secondary infections determines success of vaccination Even very high coverage might not suffice for elimination Changes of transmission rate of primary infections may lead to sudden shifts in prevalence Need more empirical data about secondary infections