New Challenges for Modelers of Infectious Diseases of Africa

1. New Challenges for Modelers of Infectious Diseases of Africa Fred Roberts, DIMACS

2. Mathematical modeling of the spread of infectious disease has a long history. Bernoulli’s 1760 modeling of smallpox.

3. Endemic and emerging diseases of Africa provide new and complex challenges for mathematical modeling. HIV/AIDS Malaria Tuberculosis

4. Major new health threats such as avian influenza present especially complex challenges to modelers in the context of developing countries.

5. This workshop is aimed at: Studying challenges for mathematical models arising from the diseases of Africa Understanding special challenges from diseases in resource-poor countries. Bringing together U.S. and African researchers and students to collaborate in solving these problems. Laying the groundwork for future collaborations to address problems of public health and disease in Africa.

6. What are the challenges for mathematical scientists in the defense against disease? This question led DIMACS, the Center for Discrete Mathematics and Theoretical Computer Science, based at Rutgers University, to launch a “special focus” on this topic in Spring 2002.

7. DIMACS Special Focus on Computational and Mathematical Epidemiology • Special Focus: • Workshops • Tutorials • Research working groups • Visitor Exchanges

8. DIMACS Special Focus on Computational and Mathematical Epidemiology One workshop was instrumental in leading to the present one: “Evolutionary Aspects of Vaccine Use” DIMACS, June 2005 Organizers: Troy Day, Alison Galvani, Abba Gumel, Claudio Struchiner

9. DIMACS Special Focus on Computational and Mathematical Epidemiology The special problems of vaccination strategies in Africa that arose in this workshop were one of the primary motivations for Abba Gumel to propose that DIMACS sponsor a workshop on mathematical modeling of infectious diseases of Africa.

10. Snowbird Conference • “Modeling the Dynamics of Human Diseases: • Emerging Paradigms and Challenges” • July 2005, Snowbird, Utah • Organizers: Carlos Castillo-Chavez, Dominic • Clemence, Abba Gumel, Travette Jackson, • Ronald Mickens • One notable feature of conference: Recognition • of central role of developing nations in emergence • of novel pathogens.

11. Snowbird Conference • One notable feature of conference: Recognition • of central role of developing nations in emergence • of novel pathogens. • This led meeting participant Simon Levin to • suggest that we pursue ways to more directly • engage US and African researchers and students.

12. The Role of Mathematical Modeling Hundreds of math. models since Bernoulli’s work on smallpox have: highlighted concepts like core population in STD’s;

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

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

15. In recent years, modeling has had an increasing influence on the theory and practice of disease management and control. Modeling has played an important role in shaping public health policy decisions in a number of countries. Gonorrhea, HIV/AIDS, BSE, FMD, measles, rubella, pertussis (UK, US, Netherlands, Canada) measles FMD

16. Modeling has provided insights leading to “optimal” treatment strategies Immuno-pathogenesis of HIV/AIDS and use of highly active anti-retroviral therapy Modeling has played a role in shaping vaccine design and determining threshold coverage levels for vaccine-preventable diseases: measles, rubella, polio AIDS

17. During SARS outbreaks in 2003, modelers and public health officials worked hand-in-hand to devise effective control strategies in a number of countries. Earlier, similar importance of efforts to control FMD.

18. 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.

19. To maximize benefit from mathematical models, need to: specialize them test assumptions in specific contexts and populations gather local data to help define key parameters That is one of the motivations for this workshop and the plans we have for follow ups.

20. If scientists from Africa and outside Africa collaborate: Vitally-needed access to data can be provided Data can be interpreted with the help of individuals knowledgeable about local conditions Better and more realistic models can be developed. It is important for non-African researchers to: Understand effects of government policies in Africa Learn of modeling efforts in Africa Find key contacts knowledgeable about both endemic diseases and deadly emerging diseases

21. Themes of our Meeting • Current State of Infectious Diseases in Africa • Current state of different • diseases. • Epidemiological data. • Recent control initiatives: • failures and successes

22. Themes of our Meeting • Mathematical Modeling of Diseases that Inflict a Significant Burden on Africa • HIV/AIDS • TB • Malaria • Diseases of Animals AIDS orphans, Zambia

23. Mathematical Modeling of Diseases that Inflict a Significant Burden on Africa • HIV/AIDS • Modeling/evaluation of preventive and therapeutic strategies • Allocation of anti-retroviral drugs • Evolution and transmission of drug-resistant strains • Interaction with other infections: TB, malaria Themes of our Meeting

24. Mathematical Modeling of Diseases that Inflict a Significant Burden on Africa • Malaria • New methods of control (e.g., insecticide-treated cattle) • Climate and disease (e.g., global warming and effect on mosquito populations) Themes of our Meeting

25. Mathematical Modeling of Diseases that Inflict a Significant Burden on Africa • Diseases of Animals • Bovine tuberculosis (in domestic and wild populations) • Avian influenza • Trypanosomiasis Themes of our Meeting

26. Modeling Issues from Threat of Emerging Diseases in Resource-poor Countries • Special issues arising from: • Slow communication • Short supplies of vaccines and prophylactics • Difficulty of imposing quarantines • Special emphasis on problems arising from avian or pandemic influenza Themes of our Meeting

27. Optimization of Scarce Public Health Resources • How to handle shortages of drugs and vaccines, physical facilities, and trained personnel. • Mathematical methods to: • Allocate medicines to optimize impact • Assign trained personnel to most critical jobs • Design efficient transportation plans. • Design efficient dispensing plans. Themes of our Meeting

28. Vaccination Strategies • Explore protocols for vaccination • for major diseases in Africa • Discuss potential for vaccines for HIV, malaria • Use of computer simulations to allow comparison of vaccination strategies when field trials are prohibitively expensive • Identify major modeling challenges unique to Africa: e.g., age-structured, health-status-related models Themes of our Meeting

29. Next Steps • Identify future research challenges for African and non-African scientists in collaboration • Identify training programs for African and non-African students • Identify future initiatives Themes of our Meeting

30. Methods of Mathematical Epidemiology • Many mathematical tools used in epidemiological modeling. • Not so widely known: Usefulness of newer tools of discrete mathematics and algorithmic methods of theoretical computer science.

31. 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.

32. Dynamical Systems

33. Dynamical Systems Used for modeling host-pathogen systems, phase transitions when a disease becomes epidemic, etc. Use difference and differential equations. Need for new methods to apply today’s powerful computational tools to these dynamical systems.

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

35. 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.

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

37. 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.

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

39. 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.

40. 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.

41. Challenges for Discrete Math and Theoretical Computer Science

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

43. 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.

44. DM and TCS have found extensive use in many areas of science and public policy, for example in Molecular Biology. These tools, which seem especially relevant to problems of epidemiology, are not well known to those working on public health problems.

45. So How are DM/TCS Relevant to the Fight Against Disease?

46. Detection/Surveillance Streaming Data Analysis: When you only have one shot at the data Widely used to detect trends and sound alarms in applications in telecommunications and finance AT&T uses this to detect fraudulent use of credit cards or impending billing defaults Columbia has developed methods for detecting fraudulent behavior in financial systems Uses algorithms based in TCS Needs modification to apply to disease detection DIMACS/CDC Adverse Events Detection Group

47. Research Issues: • Modify methods of data collection, transmission, processing, and visualization • Explore use of decision trees, vector-space methods, Bayesian and neural nets • How are the results of monitoring systems best reported and visualized? • To what extent can they incur fast and safe automated responses? • How are relevant queries best expressed, giving the user sufficient power while implicitly restraining him/her from incurring unwanted computational overhead?

48. Cluster Analysis Used to extract patterns from complex data Application of traditional clustering algorithms hindered by extreme heterogeneity of the data Newer clustering methods based on TCS for clustering heterogeneous data need to be modified for infectious disease applications.

49. Visualization Large data sets are sometimes best understood by visualizing them.

50. Visualization Sheer data sizes require new visualization regimes, which require suitable external memory data structures to reorganize tabular data to facilitate access, usage, and analysis. Visualization algorithms become harder when data arises from various sources and each source contains only partial information.