1. Case study (or epidemic modelling in real life) BGC Netword: Epidemic modelling, simulation and statistical analysis – Stockholm 2012. Sharon Kühlmann-Berenzon 2012-09-21

2. Outline for the day 1.Epidemic modelling: what is it for, extension, real life 2.SARS case study (Jia and Tsui, 2005): –Background on SARS outbreak 2003 –Deterministic modeling –Stochastic modeling 3.Classroom exercises: mental modeling and conceptualization –In groups –Paper and pen –Oral presentation

3. 1. Epidemic modelling: what is it good for for? 1.Understand mechanisms of the spread –What are key factors speeding/breaking the spread –Human contact, international travel, mass movement 2.Control: how, what intervention is more effective –Plan interventions –Optimize interventions 3.Prediction, preparedeness –Can it happen again –What are realistic scenarios –Burden and consequences in society –Preventive measures All models are wrong but some are useful. (Box, 1979)

4. Extensions to the SIR model

5. Basic reprodcution number: R0 DiseaseTransmissionR0R0 Measles Airborne12–18 PertussisAirborne droplet12–17 DiphtheriaSaliva6–7 SmallpoxSocial contact5–7 PolioFecal-oral route5–7 RubellaAirborne droplet5–7 MumpsAirborne droplet4–7 HIV/AIDSSexual contact2–5 SARSAirborne droplet2–5 Influenza (1918 pandemic strain) Airborne droplet2–3 Wikipedia, 20120920

6. 1. Real life applications Pandemic influenza 2009: possible scenarios for health care and vital services, vaccination strategy, R0 UK food-and-mouth outbreak 2001: vaccination strategy, preparedeness for future outbreak by understanding spread of the disease Dengue in Taiwan: understanding effect of temperature, preparedeness HIV and XDRTB: understand interaction for control measures of TB Cost-effectiveness of Chlamydia systematic screening in the Netherlands: predict epidemic and other outcomes as input in a cost analysis Outbreak in camel population of unknown aethiology: Understand spread and possible key factors

7. 2. SARS (Severe acute respiratory syndrom) Viral respiratory disease (coronavirus) Unknown until 2003 Symptoms: fever, myalgia, lethargy symptoms, cough, sore throat. The patient has symptoms as with a cold in the first stage, but later on they resemble influenza. Nov 2002 – July 2003: 8422 cases, 916 deaths Treatment: Isolation, fever-reducing drugs, oxygen Source: Wikipedia 2012-09-20

8. SARS outbreak 2003 Nov 16, 2002: First case of a typical pneumonia reported in Guandong, China Feb 26, 2003: First case of a typical pneumonia reported in Vietnam March 10, 2003 -- Urbani reports an unusual outbreak of the illness, which he calls sudden acute respiratory syndrome or SARS, to WHO. He notes that the disease has infected an usually high number of healthcare workers (22) at the hospital. March 11, 2003 -- A similar outbreak of a mysterious respiratory disease is reported among healthcare workers in Hong Kong. March 12, 2003 -- WHO issues a global alert cases in Vietnam and Hong Kong. March 15, 2003 -- WHO issues a heightened global health alert cases in Singapore and Canada. March 24, 2003 -- CDC officials present the first evidence that a new strain of a virus may cause SARS.

9. March 29, 2003 -- Carlo Urbani, who identified the first cases of SARS, dies as a result of the disease. April 2, 2003 -- WHO issues its first travel warning Hong Kong and Guangdong province April 3, 2003 -- WHO-sponsored team Guangdong province to investigate the outbreak April 9, 2003 -- WHO investigative team gives initial report on Guangdong outbreak: "super spreaders" who were capable of infecting as many of 100 persons. April 16, 2003 -- A new form of a coronavirus never before seen in humans is confirmed as the cause of SARS. April 23, 2003 -- WHO adds Toronto, Beijing, and the Shanxi province of China to the list of regions travelers should avoid. April 28, 2003 -- WHO removes Vietnam from list of SARS affected areas, making it the first country to contain SARS successfully. WHO also lifts travel advisory to Hanoi, Vietnam. (…) July 8, 2003 -- CDC lifts its SARS travel alert for Toronto, Canada after more than 30 days had elapsed since the date of onset of symptoms for the last SARS case. Source: WebMD.com from WHO and CDC.

10. http://www.iasa.com.au/folders/Safety_Issues/Cabin_Safety/virally-yours.html

11. http://www.scientific- computing.com/features/feature.php?feature_id=166

12. SARS outbreak in Hong Kong http://www.chp.gov.hk/en/data/1/10/26/43/7.html# Hung (2009) JSM

13. Epidemic modelling using SARS as a Case Study (Jia & Tsui, 2005) a.Deterministic model b.Stochastic model

14. 2a. Deterministic model

15. Modifications to SEIR 1.Different patterns of infection at hospital => infectives are divided: –Infectives but not admitted to hospital (I-A) (rate ) –Admitted to hospital (A) (rate ) –Total rate of infection: 2.Parameters –Fitted to Gamma distributions from real data: E to I I-A to A –A to R/D Death = (SARS mort rate) x (total deaths and recoveries) Recoveries = (1-SARS mort rate) x (total deaths and recoveries) 3.N: cannot be assumed constant due to awareness, quarantines and restriction; to be estimated.

16. Super-Spreading Events (SSE) 1 case many cases Here: Amoy Gardens outbreak

17. Assumptions 20 Feb – 20 June 2003 20 Feb: 24 index cases (backward calculation) = 0 from 28 March Case fatality rate: 17.5%

18. Parameters With Amoy Gardens case – = 0.25 – = 0.365 (0 after 28/3) –N = 2 396 Without Amoy Gardens cases – = 0.22 – = 0.28 (0 after 28/3) –N = 2 368 –Days from onset to admission = 4.85 –Days from admisstion to death/recovery = 28.32 –R 0 = 6.23 (no hospital or SSE)

19. Control of outbreak Reduce : difficult Reduce : easier Increase A/I by shortening lag from onset to hospital: not effective Reduce N: possible Number secondary cases

20. R0 over life of epidemic

21. 2b. Stochastic Model Range of outcomes from same start point Probability of an epidemic Effect of interventions in future epidemics Determinstic to Stochastic S to E: Poisson E to (I-A): Binomial A to P/D: Binomal 0.5% chance of SSE on any given day See Table 5-6

23. Minnesota Health #3: I think we need to consider closing schools down. Minnesota Health #4: And who stays home with the kids? People that work on stores, government workers, people that work in hospitals. When will we know what this is? What causes it? What cures it? Things to keep people calm. Dr. Erin Mears: What we need to determine is this; for every person who gets sick, how many other people are they likely to infect? So, for seasonal flu that's usually about one. Smallpox on the other hand, it's over three. Now, before we had vaccine, Polio spread at a rate between four and six. Now, we call that number the R-not. R stands for the reproductive rate of the virus. Minnesota Health #3: Any ideas what that might be for this? Dr. Erin Mears: How fast it multiplies depends on the variety of factors; the incubation period, how long a person is contagious. Sometimes people can be contagious without even having symptoms, you need to know that too. And we need to know how big the population of people susceptible to the virus might be. Minnesota Health #4: So far that appears to be everyone with hands, a mouth and a nose.

24. Minnesota Health #3: I think we need to consider closing schools down. Minnesota Health #4: And who stays home with the kids? People that work on stores, government workers, people that work in hospitals. When will we know what this is? What causes it? What cures it? Things to keep people calm. Dr. Erin Mears: What we need to determine is this; for every person who gets sick, how many other people are they likely to infect? So, for seasonal flu that's usually about one. Smallpox on the other hand, it's over three. Now, before we had vaccine, Polio spread at a rate between four and six. Now, we call that number the R-not. R stands for the reproductive rate of the virus. Minnesota Health #3: Any ideas what that might be for this? Dr. Erin Mears: How fast it multiplies depends on the variety of factors; the incubation period, how long a person is contagious. Sometimes people can be contagious without even having symptoms, you need to know that too. And we need to know how big the population of people susceptible to the virus might be. Minnesota Health #4: So far that appears to be everyone with hands, a mouth and a nose. Contagion, 2011. Film. Directed by Steven Soderbergh. USA: Warner Bros.

25. 3. Classroom exercise: Mental model Purpose: choose one or several objectives for the model (Mechanism, Control, Preparedness) Stochastic vs Deterministic: which and why Conceive and sketch a mental/conceptual model Data: what is needed, how to get it Limitations: what is not accounted for, what has been simplified Present max 10 min Use internet as needed (eg. Wikipedia, CDC.gov)

26. Outbreaks 1.MRSA in a hospital 2.Cholera in a refugee camp 3.Rotavirus outbreak at preschool 4.Mutation of Chlamydia bacteria goes undetected in the lab (false negatives) 5.Vector-borne disease (malaria, dengue, West Nile)