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Mathematical Modeling of Infectious
Diseases:
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Chairs
Co-chairs
Members
Partial list: as at 30 Aug 2005
Scientific background
The impact of infectious diseases on human and animal is enormous, both in terms of suffering and in terms of social and economic consequences. Mathematical modeling is an essential tool in studying a diverse range of such diseases. Basic aims in studying their spread, both in time and in space, are to gain a better understanding of transmission mechanisms and those features that are most influential in that spread, so as to enable predictions to be made, and to determine and evaluate control strategies. In this latter area, mathematical models have a particularly important role to play in making public health decisions about the control of infectious diseases better informed and more objective. To cite a successful example, adopting a culling proportion calculated based on a mathematical model, the Foot-and-Mouth Disease UK in 2001 was controlled successfully. With the outbreak of SARS last year and the avian flu this year, epidemic modeling has taken on even more significance from the perspective of public health and policy making. Today, mathematical modeling can even find applications in the war against biological terrorism.
Role of mathematics in modeling
For successful modeling, it is important to understand the course of infection within an individual and the patterns of infection within communities of people. Aspects of the model that require careful choice include the number of population variables and equations needed for a sensible characterization of the system, the typical relationships among the various rate parameters (e.g., between transmission and recovery rate), and the form of the mathematical expression that captures the essence of the transmission process. Key questions that a model should answer include the spatio-temporal dynamics of the infection, incubation and latent period, the infectivity of the disease, the effect of heterogeneity within populations including the varying degree of susceptibility between subgroups of people and possibly their genetic profile, the estimation of age-specific prevalence and incidence, and ultimately the effectiveness of vaccination and other preventive measures. Based on the compartmental analyses, many successful mathematical models have been proposed. Wide range of theories and methodologies in mathematics and statistics, such as differential equations, stochastic process and statistical estimation, have been used in epidemic modeling. In recent years, modern themes such as nonparametric or semiparametric methods and sophisticated MCMC methods are being applied in the modeling of infectious diseases.
Possible future developments
There are two different aspects: population epidemic models and molecular analysis. Incorporating possible control strategies and other factors into the SEIR model in order to design optimal control strategies and understand the role of the factors in the transmission is an important area. The population dynamics of many host-pathogen interactions are well characterized. However, the link between epidemic processes and pathogen evolution, within and among hosts, is not so well understood. This connection is central to many applied issues, from the evolution of drug resistance and virulence, to vaccine design and the emergence of new diseases. The evolution in host and pathogen genomics underlines the timeliness of this issue. Research on the dynamics of pathogen strains has illuminated the issues involved. However, linking pathogen dynamics and genetic diversity quantitatively at within-host and population levels is a more formidable problem, because it requires empirical information about the interplay of dynamics and genetics at both levels. Unifying the interacting epidemiological and evolutionary processes that drive spatio-temporal incidence and phylogenetic patterns at different scales is important. The present understanding of these patterns is incomplete, allowing only qualitative inference to be made. Some investigations have focused on RNA viruses, where high mutation rates together with large population sizes and short generation times mean that epidemiological and population genetic processes occur on a similar time scale.
There will be five topics covered by the proposed program. Each of them is allocated a one-week or two-week slot, during which a two-day tutorial is planned for background and other introductory materials. In addition to the tutorial, there will be a workshop consisting of seminars on recent developments and future directions. Also included in the plan, and of no less importance, are two oneweek breaks for free-style interaction amongst the participants. Such interaction could be in the form of group discussions, brainstorming or improvised talks. The emphasis will be on dialogue and bridging the gaps between mathematicians, statisticians, epidemiologists, biologists and medical scientists. The program consists of the following 5 sessions.
Session 1. New development of the SEIR models. Mathematical modeling of infectious disease can be dated back to 1760 when Daniel Bernoulli evaluated the effectiveness of variolation of healthy people with smallpox virus. At the beginning of last century, a series of deterministic compartment models such as MSEIR, MSEIRS, SEIR, SEIRS, SIR, SIRS, SEI, SEIS, SI and SIS have been proposed based on the flow patterns between the compartments. Most models developed later try to incorporate other factors into the models. These factors include variation of population size and age-structure. Two important developments recently are the discretization of the model so that statistical method can be applied directly in the estimation of the parameters, and spatiotemporal structure which is becoming very important as travels between cities and countries are much easier than ever before. Another important research area is to factor vaccination into the model. New tools in statistics and mathematics, such as semiparametric methods, MCMC and wavelet methods, are also being used in the modeling. This session will cover new developments in the modeling of population dynamics of diseases and new statistical and mathematical methods in estimating the basic reproductive number, contact rate, average of passive immunity, the time to extinction, incubation period, the critical community size and the decay function of immunity over time.
Session 2. Influenza-like diseases. It is said that influenza is a master of disguise. With many diseases, one infection is enough: we become immune and are never infected by that disease again. However, influenza has the capacity of gradually changing its appearance over time so that our immune system can no longer recognize it. This is why we can be infected next time again, and also why the vaccine must be changed from year to year. This is also why flu is still the major threat to human and animals. It is important to explore the dynamics of influenza and the continual emergence of new strains using mathematic models. Some tools of mathematics and statistics are valuable to tackle the complexities of influenza. Some investigations are also carried out to model mutation, influenza drift, and strain-structure. This session will cover investigations on most flu-like diseases such as SARS and the Avian influenza. Assessing the risk to human health associated with outbreaks of highly pathogenic H5N1 avian influenza in poultry will also be included.
Session 3. Immunity, vaccination, and other control strategies. Vaccination has proven to be a powerful defence against a wide range of viral infectious diseases for humans and animals. Successful examples are the mass vaccination of Measles Mumps Rubella (MMR) Vaccine around the world and the strategy adopted by UK to control the major epidemics of foot-and-mouth disease in livestock in 2001. Given sufficient resources and preparation, a combination of reactive vaccination and quarantine (or culling) might control ongoing epidemics. These analyses have broader implications for the control of human and livestock infectious diseases in heterogeneous spatial landscapes and can be applied to the recent avian flu outbreaks. Another important area is the safety studies on vaccinations. Even for the MMR vaccination, people begin to worry about its long-term side effect. Most such studies are limited to short time periods only: from several days to several weeks. There are no long term (months or years) safety studies on any vaccination or immunization. For this reason, there are valid grounds for suspecting that many delayed-type vaccine reactions might be taking place unnoticed and their true nature has not been studied.
Session 4. Molecular analysis of infectious diseases. The ubiquity of parasites and pathogens has driven the evolution of various means of defence among host populations. These range from simple gene-for-gene to complex immune systems and to behavioural defences. While some of these mechanisms have long been known, scientists have recently become aware that life-history traits could act as defences or interact with other defence traits. A key priority for infectious disease research is to clarify how pathogen genetic variation, modulated by host immunity, transmission bottlenecks, and epidemic dynamics, determines the wide variety of pathogen phylogenies observed at scales that range from individual host to population. Scientists have introduced a phylodynamic framework for the dissection of dynamic forces that determine the diversity of epidemiological and phylogenetic patterns observed in RNA viruses of vertebrates. A central pillar of this model is the Evolutionary Infectivity Profile, which captures the relationship between immune selection and pathogen transmission.
Session 5. Clinical and public health applications of mathematical modeling. Collaboration between theoreticians and applied workers is vital, to ensure that mathematicians continue to tackle problems of genuine applied 5 interest, and that data are effectively collected and analysed to maximise the available empirical information about the processes under study. This session will focus on how mathematical models can and have been applied to guide clinical and public health practice. Using real-world examples of key infectious diseases ranging from nosocomial pathogens, vector-borne disease, SARS, tuberculosis and HIV, the session will also address how mathematical models can be used to assess the validity of observational studies, measure the burden of undetected disease, model the impact of potential interventions, predict the course of ongoing epidemics, and postulate possible outcomes for acts of bioterrorism or outbreaks of emerging infectious diseases.
Week |
Period |
Session |
Program |
1 |
1 |
New development of the SEIR models for |
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2 |
2 |
Influenza-like diseases |
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3 |
29 Aug - 2 Sep 2005 |
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Break for interaction and discussion |
4 |
3 |
Immunity, vaccination, and other
control |
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5 |
4 |
Molecular analysis of infectious diseases |
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6 |
19 - 23 Sep 2005 |
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Break for interaction and discussion |
7 |
5 |
Clinical and public health applications
of |
|
8 |
3 - 7 Oct 2005 |
|
Break for interaction and discussion |
Public Lecture
IMS Membership is not required for participation in above activities. For attendance at these activities, please complete the registration form (MSWord|PDF|PS) and fax it to us at (65) 6873 8292 or email it to us at ims@nus.edu.sg.
If you are an IMS member or are applying for IMS membership, you do not need to register for these activities.
The Institute for Mathematical Sciences invites applications for membership for participation in the above program. Limited funds to cover travel and living expenses are available to young scientists. Applications should be received at least three (3) months before the commencement of membership. Application form is available in (MSWord|PDF|PS) format for download.
For enquiries on scientific aspects of the program, please email Yingcun Xia at staxyc@nus.edu.sg.
Organizing Committee · Confirmed Visitors · Overview · Activities · Membership Application
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