Mathematical Modeling for understanding and predicting communicable diseases: a tool for evidence-based health policies Antoine Flahault Geneva, May 20, 2015

2 True world Theory (models) Observation calibration Simulation of scenarios Understanding Early warning Prevision validation Model = simplified miroring of true world Model = « drawing board »

Better Understanding Early Warning

1927: Kermack & McKendrick susceptibleInfectiousRemoved  c  d Simple Compartmental Model Mathematical Theory of Communicable Diseases

SIR : deterministic formulation

Threshold Theorem Probability of transmission Number of contacts per unit of time Duration of Infectious period Basic Reproductive Rate Doubling time Epidemic

Ro: Early warning signal for outbreak e.g. Seasonal Influenza (Sentinelles, France) A doubling of incidence in 3 days => Ro > 1 detection of an outbreak

Measles: What is optimal age for vaccination? Example: Measles in developing countries, D=6 months, A=18 months, then T = 10 months (Katzmann & Dietz, 1984) Duration of protection from maternal antibodies Mean age of wild cases Applying the threshold theorem to vaccination schedule

Ro: « Richter scale » for communicable diseases? MeaslesRo= 15 à 20 InfluenzaRo= 1.4 à 2 SmallpoxRo= 3 SARSRo= 2 Hepatitis B - High risk groupsRo= 4 à General Population e Ro= 1.1 SARS at Singapore (Lloyd-Smith, 2005)

Immunization Strategies: heard immunity –What proportion of population needs to be immunized to prevent an outbreak? Measles(R0 = 15-20) p = 93-95% Influenza(R0 = 2-4) p = 50-75% Hepatitis B -High risk groups(R0 = 4)p = 75% -Low risk groups(R0 = 1.1) p = 10% -Very high risk groups(R0 = 8.8) p = 89%

Measles in France Source : réseau Sentinelles, Inserm Governmental Media campaign 1988 Change in Vacc Schd 2 nd dose at yrs Sept nd dose at yrs April. 1998

Modeling: Scenarios simulating decrease in vaccine coverage No change Linear decrease in 5% up to 2010 Linear decrease in 20% up to 2010 (H. Sarter, 2004) Linear decrease in 10% up to 2010

Agent centered models

Ferguson et al. : the largest simulation on computer ever published Simulation of an 85 Mn population living in Thailand 10 high capacity computers in parallel > 1 month of CPU time

Prevention and Control of pandemic influenza Basic Reproductive Rate R 0 = .c.d probability of contactduration of transmission rateinfectious period Threshold Theorem, pandemic when R 0 > 1

Antivirals (curative, preventive) Protective masks Hand washing Vaccines (when available)

Increase « social distance » – Quarantine of patients – Closing schools – Reduction of transport Flahault A et coll, Vaccine 2006

Decrease in duration of infectious period (2.6d) – Antivirals – Anti coughing Cauchemez S, Stat Med, 2004 Ferguson N, Nature 2005

Expected pattern of spread of an uncontrolled epidemic Ro=1.5. (a) Spread of a single simulation. Red = infectives, green = recovered from infection or died. (b) Daily incidence of infection. Thick blue line = average, grey shading = 95% envelope of incidence timeseries. Multiple coloured = a sample of realisations. (c) Root Mean Square (RMS) distance from seed infective of all individuals infected since the start of the epidemic as a function of time. (d) Attack rate by age (mean = 33%). (e) Number of secondary cases per primary case

Understanding better, detection=ok, but what about prediction?

Ebola

Ebola

The black swan ! Nassim Nicholas Taleb, 2010

27 Smallpox (bioterrorism) : modeling Duration 235 [190;310] days Doses of vaccine [3 910;6 840] Isolated people 550 [415;686] Legrand J, Epidemiol Infect 2004 Cumul. No Cases Number of days after the attack

28 Key role of time to intervention (in terms of epidemic size) Reference scenario Isolation rate (%)Tracking rate (%) Time to intervention (days) Cumul. No Cases

To detect and forecast seasonal influenza

A series of epidemics Each winter An average of 2.5 M cases 6 M influenza cases 6000 deaths

Method of Analogues: Forecasting Time-Series

Time-Space Prediction of Influenza Method of Analogues Viboud C. et coll. Am J Epidemiol, 2003

Viboud C. et coll., 2003

H1N1pdm: predictions? R0 < 2 Gen. Time Interval= 3d

And what next? Flahault et al. BMC Inf Dis, August 2009 New-Zealand (May-Oct./2009) Scenario without immunization

Chikungunya, Indian Ocean

Why such a strong second wave (en 2006)?

DateSequences A226V226 March to June September to December270 January to March Mutation from A226 to V226 between the 2 waves Indian Ocean : 92 sequences from 89 patients Schuffenecker I et al., PLoS Medicine, 2006 Genome sequencing of chikungunya virus

Boelle et al., Vect Born Zoon Dis, < R < 4 Two waves but a unique epidemic force

The convergence model (Source IOM, 2003)

Conclusion Modelling = Math Epidemiology Mathematical models Allow for targeting epidemiologic surveillance (observation) Help better understanding communicable diseases Provide tools for early warning Aid public decisions (vaccination, interventions for prevention and control) Help designing/assessing various scenarios for the future However they deliver previsions… which remain previsions!

PhD in Global Health