Mathematical Modelling of Infectious Diseases. Raina MacIntyre

Transcription

1 Mathematical Modelling of Infectious Diseases Raina MacIntyre

2 A little bit of EBM is a dangerous thing Research question: Does smoking cause lung cancer? Answer: I couldn t find a meta-analysis or even a single RCT, therefore the level of evidence is low.

3 Research question: Is school closure effective in a pandemic? Answer: I couldn t find a meta-analysis or even a single RCT

4 Levels of Evidence Are specific to types of research questions Research questions can be about: Therapy Screening Diagnostic tests Aetiology Harm Cost-effectiveness Future events

5 Modelling The use of mathematical models to predict the dynamics and behaviour of infectious diseases Useful when prediction of future outcomes and impact of control strategies is needed When an RCT is not possible because the disease of interest that you wish to prevent or treat has not yet occurred

6 Examples How should Australia respond to emerging infections such as SARS, an influenza pandemic or deliberatelyreleased smallpox? What is the population effect of introducing a new vaccine and what is the best age to administer it?

7 Isn t surveillance enough? Surveillance is based on past data and gives static/2-dimensional results Modelling allows forecasting Gives dynamic picture

8 What data are required? seroepidemiologic data (serosurveys) (enhanced) surveillance data vaccine coverage data (ACIR) vaccine or drug efficacy estimates (clinical trials)

9 The meaning of R- the n of secondary cases generated from one index case The lower the Ro, the easier it is to eradicate the disease

10 Factors affecting Ro Characteristics of the organism Infectivity of organism Duration of infectiousness Population characteristics Demographics Social mixing patterns Population density

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12 Examples of R (Anderson & May 1982, 1988) Pertussis Measles Mumps Varicella 7-12 Rubella 6-10 Scarlet fever 5-8 Polio 5-7 Diphtheria 4-5 HIV 2-5 (men who have sex with men in UK) (heterosexuals in Uganda and Kenya)

13 Interpreting R If R>1 the number of cases increases (an epidemic will occur) If R<1 the number of cases decreases (infection cannot be sustained and dies out) R=1 is the epidemic threshold This threshold at R=1 defines the critical proportion susceptible, x*=1/r 0

14 Elimination graph % Herd Immunity required for elimination 93 Measles 60 Small pox 3 15 R

15 Oscillation of incidence over time R=1 R=1 Disease incidence R<1 R>1 R=1 Average R over time is=1

16 Mumps notifications Jan-93 Jan-94 Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 notifications

17 Simple compartmental model Susceptible Infected Recovered (Immune) Source: births, immigration, waning immunity

18 Special issues for vaccination Changes in disease epidemiology (R-shift of age specific incidence) Herd immunity Cross-protection Strain replacement Super-infection

19 A local example: measles control in Australia A mathematical model, using serosurvey results & ACIR coverage data, was used to calculate the change in R, the reproductive number, pre- and post MCC. ACIR coverage data used as worst case scenario and compared to ideal coverage levels ( best case scenario).

20 Measles notifications, Australia MCC 20 0 Jan-97 Apr-97 Jul-97 Oct-97 Jan-98 Apr-98 Jul-98 Oct-98 Jan-99 Apr-99 Jul-99 Oct-99 Jan-00 Apr-00 Jul-00 Oct-00

21 Effect of varying vaccination coverage at 5 years of age on R for measles R Year ACIR (70%) mid (77%) best (84%)

22 Projected R for selected Divisions of GP R value Year Data source: ACIR

23 Modelling study: measles elimination in Australia Endemic transmission of measles in Australia has been eliminated..??? This raises some questions Q1: Will our current vaccination strategies be sufficient to maintain elimination Q2: What if we changed the timing of the 2 nd dose of MMR vaccine? Q3: How sensitive is elimination status to other factors?

24 Can we monitor R? If we can predict the value of R into the future, then we can predict elimination status This requires an estimate of R0 for Australia and Estimates of the immune proportion in different age groups

25 Predictions of R Serological data Coverage data r s Immunity model v sv Base-case

26 Effects of waning/improved 1-dose coverage Serological data Coverage data r s Immunity model v sv Waning immunity...targeting those who miss dose 1 Vaccine distribution

27 Modelling the impact of one-dose versus two-dose vaccination schedules on the epidemiology of varicella zoster virus (VZV) in Australia Dr Zhanhai Gao

28 Varicella cases at low coverage (50%) Both one-dose and two-dose strategies are expected to produce similar numbers of natural varicella. But the breakthrough varicella cases of onedose strategy are more than three times of two-dose strategy. One dose strategy, 50% coverage Two dose strategy, 50% coverage

29 Varicella cases at high coverage (90%) At equilibrium, VE (vaccine effectiveness) is 66% for one dose strategy and 92% for twodose strategy. A two dose vaccination is expected to not only produce less natural varicella cases but also fewer varicella breakthrough cases. Breakthrough varicella cases in one dose vaccinees are 7 times higher than two dose vaccinees. One dose strategy, 90% coverage Two dose strategy, 90% coverage

30 Age-specific natural varicella incidence for one-dose strategy

31 Age-specific zoster cases One-dose strategy Two-dose strategy

32 Good science for modelling Multidisciplinary Underpinned by good data and sound assumptions Transparent and easily reproducible Not black box models

33 Modelling Modelling is useful in the design of VPD control and elimination strategies Informing policy and funding decisions Useful in anticipation of emergencies ensures that rational planning, not chaos, ensues. Gives additional information to routine surveillance data, and allows forecasting

34 Acknowledgments Dr James Wood Dr Zhanhai Gao Dr Tony Newall Dr Rob Menzies Prof Peter McIntyre NCIRS/UNSW modelling collaboration

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