The Role of Mathematical Modeling in Epidemiology: Analyzing and Predicting Disease Spread

1. DIMACS Special Focus on Computational and Mathematical Epidemiology

2. The Role of the Mathematical Sciences in Epidemiology Emergence of new infectious diseases: Lyme disease HIV/AIDS Hepatitis C West Nile Virus Evolution of antibiotic-resistant strains: tuberculosis pneumonia gonorrhea

3. Great concern about the deliberate introduction of diseases by bioterrorists anthrax smallpox plague Understanding infectious systems requires being able to reason about highly complex biological systems, with hundreds of demographic and epidemiological variables. Intuition alone is insufficient to fully understand the dynamics of such systems.

4. Experimentation or field trials are often prohibitively expensive or unethical and do not always lead to fundamental understanding. Therefore, mathematical modeling becomes an important experimental and analytical tool.

5. Mathematical models have become important tools in analyzing the spread and control of infectious diseases, especially when combined with powerful, modern computer methods for analyzing and/or simulating the models.

6. What Can Math Models Do For Us?

7. What Can Math Models Do For Us? Sharpen our understanding of fundamental processes Compare alternative policies and interventions Help make decisions. Prepare responses to bioterrorist attacks. Provide a guide for training exercises and scenario development. Guide risk assessment. Predict future trends.

8. In order for math. and CS to become more effectively utilized, we need to: • make better use of existing tools

9. In order for math. and CS to become more effectively utilized, we need to: • develop new tools • establish working partnerships between mathematical scientists and biological scientists; • introduce the two communities to each others’ problems, language, and tools; • .

10. introduce outstanding junior researchers from both sides to the issues, problems, and challenges of mathematical and computational epidemiology;

11. involve biological and mathematical scientists together to define the agenda and develop the tools of this field. • These are all fundamental goals of this special focus.

12. Methods of Math. and Comp. Epi. Math. models of infectious diseases go back to Daniel Bernoulli’s mathematical analysis of smallpox in 1760.

13. Hundreds of math. models since have: highlighted concepts like core population in STD’s;

14. Made explicit concepts such as herd immunity for vaccination policies;

15. Led to insights about drug resistance, rate of spread of infection, epidemic trends, effects of different kinds of treatments.

16. The size and overwhelming complexity of modern epidemiological problems calls for new approaches. New methods are needed for dealing with: dynamics of multiple interacting strains of viruses through construction and simulation of dynamic models; spatial spread of disease through pattern analysis and simulation; early detection of emerging diseases or bioterrorist acts through rapidly-responding surveillance systems.

17. Statistical Methods Long used in epidemiology. Used to evaluate role of chance and confounding associations. Used to ferret out sources of systematic error in observations. Role of statistical methods is changing due to the increasingly huge data sets involved, calling for new approaches.

18. Dynamical Systems

19. Dynamical Systems Used for modeling host-pathogen systems, phase transitions when a disease becomes epidemic, etc. Use difference and differential equations. Little systematic effort to apply today’s powerful computational tools to these dynamical systems and few computer scientists are involved. We hope to change this situation.

20. Probabilistic Methods Important role of stochastic processes, random walk models, percolation theory, Markov chain Monte Carlo methods.

21. Probabilistic Methods Continued Computational methods for simulating stochastic processes in complex spatial environments or on large networks have started to enable us to simulate more and more complex biological interactions.

22. Probabilistic Methods Continued However, few mathematicians and computer scientists have been involved in efforts to bring the power of modern computational methods to bear.

23. Discrete Math. and Theoretical Computer Science Many fields of science, in particular molecular biology, have made extensive use of DM broadly defined.

24. Discrete Math. and Theoretical Computer Science Cont’d Especially useful have been those tools that make use of the algorithms, models, and concepts of TCS. These tools remain largely unused and unknown in epidemiology and even mathematical epidemiology.

25. DM and TCS Continued These tools are made especially relevant to epidemiology because of: Geographic Information Systems

26. DM and TCS Continued Availability of large and disparate computerized databases on subjects relating to disease and the relevance of modern methods of data mining.

27. DM and TCS Continued The increasing importance of an evolutionary point of view in epidemiology and the relevance of DM/TCS methods of phylogenetic tree reconstruction.

28. How does a Special Focus Work? Get researchers with different backgrounds and approaches together. Stimulate new collaborations. Set the agenda for future research. Act as a catalyst for new developments at the interface among disciplines. DIMACS has been doing this for a long time.

29. Components of a Special Focus Working Groups Tutorials Workshops Visitor Programs Graduate Student Programs Postdoc Programs Dissemination

30. Working Groups

31. Working Groups Continued Interdisciplinary, international groups of researchers. Come together at DIMACS. Informal presentations, lots of time for discussion. Emphasis on collaboration. Return as a full group or in subgroups to pursue problems/approaches identified in first meeting. By invitation; but contact the organizer. Junior researchers welcomed. Nominate them.

32. Tutorials

33. Tutorials Continued Integrate research and education. Introduce mathematical scientists to relevant topics in epidemiology and biology Introduce epidemiologists and biologists to relevant methods of math., CS, statistics, operations research. Financial support available by application.

34. Workshops

35. Workshops Continued More formal programs. Widely publicized. One-time programs. Some educational component: encourage participation by graduate students; tutorials. Interdisciplinary flavor. Can spawn new working groups. Financial support available in limited amounts;contact the organizer.

36. Visitor Programs

37. Visitor Programs Continued Interdisciplinary groups of researchers will return after working group meetings. Workshop participants can come early or stay late. Visits can be arranged independent of workshops or working group meetings. Contact DIMACS Visitor Coordinator. Visits by junior researchers and students will be encouraged. We want to make DIMACS a center for collaboration in mathematical and computational epidemiology for the next 5 years (and beyond).

38. Grad. Student/Postdoc Programs

39. Grad. Student/Postdoc Programs Each working group, workshop, tutorial will support students/postdocs. Contact organizer. Students/postdocs visiting for longer will have a host/mentor. Contact DIMACS visitor coordinator. Local graduate students will get involved through participation in working groups and small research projects. We hope to raise funds for postdoctoral fellows to participate by spending a year or more at DIMACS.

40. Dissemination DIMACS technical report series. Working group and workshop websites. DIMACS book series.

41. Working Groups WG’s on Large Data Sets: Adverse Event/Disease Reporting, Surveillance & Analysis. Data Mining and Epidemiology. WG’s on Analogies between Computers and Humans: Analogies between Computer Viruses/Immune Systems and Human Viruses/Immune Systems Distributed Computing, Social Networks, and Disease Spread Processes

42. WG’s on Methods/Tools of TCS Phylogenetic Trees and Rapidly Evolving Diseases Order-Theoretic Aspects of Epidemiology WG’s on Computational Methods for Analyzing Large Models for Spread/Control of Disease Spatio-temporal and Network Modeling of Diseases Methodologies for Comparing Vaccination Strategies

43. WG’s on Mathematical Sciences Methodologies Mathematical Models and Defense Against Bioterrorism Predictive Methodologies for Infectious Diseases Statistical, Mathematical, and Modeling Issues in the Analysis of Marine Diseases WG on Noninfectious Diseases Computational Biology of Tumor Progression

44. Workshops on Modeling of Infectious Diseases The Pathogenesis of Infectious Diseases Models/Methodological Problems of Botanical Epidemiology WS on Modeling of Non-Infectious Diseases Disease Clusters

45. Workshops on Evolution and Epidemiology Genetics and Evolution of Pathogens The Epidemiology and Evolution of Influenza The Evolution and Control of Drug Resistance Models of Co-Evolution of Hosts and Pathogens

46. Workshops on Methodological Issues Capture-recapture Models in Epidemiology Spatial Epidemiology and Geographic Information Systems Ecologic Inference Combinatorial Group Testing Other Topics: Suggestions are encouraged.

47. Tutorials Dynamic Models of Epidemiological Problems The Foundations of Molecular Genetics for Non-Biologists Introduction to Epidemiological Studies DM and TCS for Epidemiologists and Biologists Promising Statistical Methods for Epidemiology for Epidemiologists and Biologists

48. Challenges for Discrete Math and Theoretical Computer Science

49. What are DM and TCS? DM deals with: arrangements designs codes patterns schedules assignments

50. TCS deals with the theory of computer algorithms. During the first 30-40 years of the computer age, TCS, aided by powerful mathematical methods, especially DM, probability, and logic, had a direct impact on technology, by developing models, data structures, algorithms, and lower bounds that are now at the core of computing.