Measure If You Can, Simulate If You Must

1. Measure If You Can, Simulate If You Must Joseph S. Y. LEE Pierce K. H. CHOW Jorgen SELDRUP T. K. TAN Joseph S. Y. LEE Pierce K. H. CHOW Jorgen SELDRUP T. K. TAN

2. The Questions • How long do patients remain infectious? • How infectious is SARS? • How many people will get infected during the epidemic? • Are there better public health measures to contain the spread of the virus?

3. Common Approaches • Traditional methods involving complex analytic/computational ODE and/or PDE models are inadequate. • Cellular automata • Uniform • Non-uniform

4. The Model • Each individual is modeled as a node in a simple,undirected graph. • An arc linking 2 nodes represents a connection between the two persons.

5. Simple Undirected Graph

6. An Example Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10

7. Graph Abstraction Node 1 Node 2 Node 3 Node 4 Node 5 Node 6 Node 7 Node 8 Node 9 Node 10

8. Modeling Social Cliques Node 1 Node 4 Node 5 Node 7 Node 8 Node 9 Node 10

9. Parameters Node 1 Node 2 • Global Parameters • Basic Infectivity • Basic Incubation Period • Basic Infection Period • Clinical Probability • … • Per-Edge Parameters • Connectivity • Family Clique is strong. • Work Clique is moderate. • Casual Clique is very weak. • Per-Node Parameters • Immunity Level • Recovery Rate

10. State Transition Diagram Dead Clinical Normal Infected Recovered Fully Recovered Subclinical

11. The Situation • 6 April 2003, 70 patients in 2 surgical wards in SGH were believed to have been exposed to the SARS virus. • They were quarantined in 3 isolated wards in TTSH.

12. The Situation • Temperature readings were taken 4-hourly. • Patients with temperature above a certain threshold were isolated. • They were observed over a period of three weeks.

13. Objective • To see whether it is likely that there is no sub-clinical case for SARS. • If sub-clinical cases are likely, what is the sub-clinical rate.

14. Edge Setting for the graph • Patients in the same room have strong edges. • Patients in the same ward have weak edges. • Patients in different ward have no edge at all.

15. Assumptions • The incubation period is set to follow a Gamma distribution (with  = 6.4 days). • Infection is independent of previous encounters. • There is no vehicular transmission. • Detection rate: 0.9

16. Assumptions • Medical staff are not carriers/vectors. • Existing medical condition does not alter the basic parameters significantly. • Infectious period (normal  = 5 days,  = 1 day).

17. Experiment Setup • We implement our model using Python running on FreeBSD. • Each simulation is run 1,000 times for a set of parameters. • The epidemic curve generated from the simulation is compared with the observed data.

18. A Sample Run

19. Result (1) If there is no sub-clinical case, and the virus does not survive for more than one day, then the clinical-infection rate for the patients in the ward is lower than 10%.

20. If the clinical probability is set to 1.0, many more people would have been infected.

21. Second Objective We run 9000 sets of different parameter sets to find reasonable range of clinical-infection rate and clinical probability.

22. Our Result (2) Possible range of parameters are in the blue region:

23. Our Result (3) • Result consistent with observed data • If Clinical prob < 0.3 • Else • Inter-room connectivity = 0.1, clinical infectivity < 0.2 • Inter-room connectivity = 0.3, clinical infectivity < 0.1

24. Future Refinement More refined individual modeling: Just as the community acquired pneumonia, mortality rate of SARS varies across different age group. For example, death rate from SARS in Hong Kong is • 43% (35-52%) for those over 60 years old. • 13% (10-17%) for those under 60s.

25. Future Refinement • Confidence level estimation of each parameter set. • Time-series analysis. • Application of the model on larger populations.

26. Thank You