Infectious disease
From NECSIWiki
Statement of Problem
An emerging infectious disease can pose a great threat to human society given that no one will have immunity against it. The SARS epidemic during 2002-2003 is an example. Much of recent concern for an emerging infection has been focused on the possible pandemic of influenzae, should the circulating avian influenzae virus evolve in a way that human-to-human transmission can occur. A fundamental concept in describing the transmissibility of an infectious disease is the basic reproductive number, Ro, which is the average number of secondary cases generated when an index case enters a totally susceptible population. When Ro is greater than one, the disease will spread out in the population, and there will be an epidemic. When Ro is lesser than one, the disease will die out. The concept of Ro can be easily applied to an emerging infectious disease, since the whole human population will be susceptible to this new disease. Previous studies have suggested that the mean Ro of SARS in the range of 2.2~3.7(Riley et al, 2003) and 2.2~3.6 (Lipsitch et al, 2003). Using the data from 1918 pandemic influenzae, Mills et al (2004) obtained an estimated Ro of between 2 and 3, which is very similar to that of SARS.
With respect to epidemic control, an infectious disease with a higher value of Ro generally implies that it will be harder to control than an outbreak with a lower Ro value. The Ro of measles, for example, is estimated to be around 15. Therefore, it is almost impossible to contain measles in a population without vaccination. On the other hand, an infectious disease with a Ro of 2~3 allows a chance of using public health measures other than vaccination (e.g., isolation, quarantine) to bring down the epidemic. A real life example is the success of SARS control using these public health measures. Given the similar values of Ro and similar route of transmission between SARS and pandemic influenzae, an optimistic view is that pandemic influenzae, should it happen again, can be controlled using similar methods to those employed with SARS.
There is, however, a major difference between SARS and pandemic influenzae in terms of epidemic control. Epidemiological studies and laboratory viral shedding studies have shown that the transmission of SARS generally occurs after one develops symptoms (Fraser et al, 2004). The lag period, which is estimated to be 5~10 days, provides a chance of early recognition and isolation of infected cases. On the other hand, the transmission of pandemic influenzae occurs 1 day before the onset of symptoms, which makes early isolation extremely difficult. Therefore, we hypothesize that, despite similar values of Ro, pandemic influenzae will be much more difficult to control than SARS due to the increased difficulty of providing timely intervention.
Literature Review
Some of the more traditional computer models used in epidemiology draw upon the principle of homogeneous mixing, wherein all individuals represented by the model have an equal chance of coming into contact with all other individuals. These models are referred to as SIR models (standing for susceptible, infected, and removed). Some versions of this model, known as Structured Population SIR models, in an effort to address the shortcomings of traditional SIR models, allow for heterogeneous mixing among larger populations, but only by creating sub-groups among which there is still only homogeneous mixing. Therefore, an accurate picture of the real world is still not achieved (Eubank 2005).
One example of what these models fail to take into account was seen in Canada in 2003 during the SARS outbreak. Two separate cities, Toronto and Vancouver, each experienced the introduction of SARS into their populations via an index case, however the disease progressed very differently from that point in each locale. In Vancouver, the infected man, who lived with only one other person, went directly to the hospital, where he was diagnosed, isolated, and treated. It is believed that only four people were ultimately infected. Conversely, in Toronto, the index case was a woman who shared a home with a very large, multi-generational family. She died at home, undiagnosed. In the coming weeks in Toronto, 209 other probable SARS cases occurred, all stemming from this original patient in one way or another (Meyers, et al, 2005). From these two examples, it becomes clear that not all people are equal in an infectious disease outbreak situation. Indeed, the contact patterns of the first few cases within an outbreak often determine whether an epidemic will occur or not (Meyers, et al, 2005).
A better model for the accurate examination of infectious disease outbreak dynamics can be found in that of the network model. In a network model, person to person interactions become paramount. Another benefit of using the network model in this instance is the ability to determine the relative benefits of different interventions. In the case of SARS in Toronto, authorities knew that something had to be done, but did not know whether that something was to close schools, provide better protections (such as facemasks) to the medical professionals, or to intervene in some other way entirely (Meyere, et al, 2005). With an appropriate network model, this information could more easily be determined.
The model designed by Meyers and her group in response to the SARS outbreak in Toronto was based upon patterns of interaction found to be true within the city. The model takes into account many data points, such as number of households, size of households, and distribution of schools, hospitals, and offices. The model was designed specifically to be unique to Toronto, to capture the actual patterns of interaction that take place within the city. While this method of design could be made to fit other cities, each model would have to first be tailored to the particular location before it would be effective (Meyers, et al, 2005). This fact is both a strength and a drawback to this model. Designing the model in this way allows the identification of both high risk areas and high risk activities within the city. The next mathematical model effort that Meyers’ team has lined up involves looking at the patterns of transmission seen on an international scale due to air travel (Meyers, et al, 2005). This next project will be much larger in scale, but is an essential piece of the transmission and epidemiological puzzle in modern times.
Others are also designing network models in an effort to better understand the dynamics of an epidemic. Epidemiological Simulation System (EpiSims), one of three models put together by the Modeling Infectious Disease Agent Study (MIDAS) of the National Institute for General Medical Sciences within the U.S. National Institute of Health (NIH), is one such model. EpiSims is a time-dependent bipartite labeled graph, which creates an individual graph for each time interval in the model. It is capable of generating graphs at one-minute intervals, or as many as 1,440 graphs per day (Eubanks, 2005).
Extreme detail was used in designing the EpiSims model, drawing upon actual U.S. census data and statistical fitting techniques to come up with accurate information for the creation of “synthetic” households that are assigned to the appropriate locations within a chosen U.S. locale. Many demographics available from census information, such as age, gender, etc., remain tied to the individuals in this simulated population. From here, activities are assigned to each member of the household, such as work, home, school, and so on. The appropriate activities for each individual based off of their census data was generated by another mathematical model known as Transportation Analysis and Simulation System (TRANSIMS). TRANSIMS’ accuracy and fidelity is currently the subject of another study. Along with activity assignment is the assignment of location, arrival, and departure times. In this way, not only is activity location information captured and taken into account, but so is information regarding transportation choices to and from the activity. Activities taking place at a large enough location, for example a large office building or a university, end up requiring their own sub-location models, with EpiSims takes into account (Eubanks).
One of the many benefits of EpiSims is its amazing levels of complexity. Through its various parameters for health interactions, EpiSims designers established the ability to predict altered patterns of interaction that occur during an outbreak, including those of seeking medical treatment, obtaining OTC medications, confining themselves at home, or fleeing a geographic location. One of the downsides to this complexity, however, is the difficulty in generating data that can be worked with when using the model in its entirety. In the network configuration of this model, both people and locations represented as nodes and edges between them indicating the presence of a person at a particular location. Edges contain information of arrival and departure times, at a minimum. With all of this data, for Portland, Oregon, (a moderately sized city) the EpiSims model has 1.6 million people vertices and 160,000 location vertices with tens of millions of edges (Eubanks 2005).
In order to work around this issue of scale, one must take the model a few pieces at a time. This is done by using time-frozen sub-graphs of EpiSims, made to include person-to-person links for determining whether people were present at the same location at the same time, and the resulting likelihood of their interaction. The initial goals of analysis included determining which vertices (people and places) and edges (interactions) contribute most to disease propagation, and determining and measuring the structural properties of disease networks that are most central to propagation. The EpiSims model also lends itself to answering other questions, as well, for example how interaction patterns, including duration of contact, affect transmission (Eubanks, 2005).
References
1. Lipsitch M, Cohen T, Cooper B, et al. Transmission dynamics and control of severe acute respiratory syndrome. Science. 300(5627):1966-70, 2003
2. Riley S, Fraser C, Donnelly CA, et al. Transmission dynamics of the etiological agent of SARS in Hong Kong: impact of public health interventions. Science. 200(5627):1961-6, 2003
3. Fraser C, Riley S, Anderson RM, Ferguson NM. Factors that make an infectious disease outbreak controllable. Proc Natl Acad Sci USA. 101(16):6146-51, 2003
4. Meyers LA, Pourbohloul B, Newman MEJ, Skowronskic DM, Brunham RC. Network theory and SARS: predicting outbreak diversity. Journal of Theoretical Biology. 232, 71–81, 2005.
5. Eubank S. Network based models of infectious disease spread. Jpn. J. Infect. Dis. 58, 2005.
6. Sarama J, Kaski K. Modelling development of epidemicswith dynamic small-world networks. Journal of Theoretical Biology. 234: 413-21, 2005.
7. Liu Z, Lai YC, Ye N. Propagation and immunization of infection on general networks with both homogeneous and heterogeneous components. Physical Review E. 67(031911): 1-5, 2003.
