Tracking infectious diseases

Summary: Physicians and mathematicians have long worked together to develop and use models that track the spread of infectious diseases in order to develop appropriate countermeasures and responses to halt the disease spread.

The health of societies relies on quickly and correctly tracking and predicting the growth and spread of disease in populations. Epidemiology is a mathematically rich area. Exposure and infection are both probabilistic processes, and tracking infectious diseases is a dynamic application of mathematics. The World Health Organization (WHO) and other organizations concerned with public health use mathematical models in their decision-making, such as when WHO analyzed the risks and benefits of travel restrictions during the early twenty-first-century H1N1 (swine flu) epidemic. Epidemiologists using mathematical and statistical models have been influential in research, treatment, and some methods of prevention for potentially devastating diseases, like tuberculosis, smallpox, typhus, and malaria.

Epidemiology has a long history with important societal connections. Historians trace one early use of mathematical modeling for disease to eighteenth-century mathematician Daniel Bernoulli. He presented an analysis of smallpox morbidity and mortality to demonstrate the efficacy of vaccination. Nineteenth-century physician William Farr is often called the “father of epidemiology” and was responsible for the collection of official medical statistics in England and Wales. His most important contribution was to set up a system for routinely recording causes of death. Physician John Snow is frequently cited as using graphical methods to propose a mechanism of transmission and the source of a cholera epidemic in nineteenth century London.

Infectious diseases are a leading cause of death for humans. In order to understand the dynamics of tracking infectious disease at the population level, it is important to understand the responsible mechanisms at the individual level. Infectious disease is caused by a pathogenic agent (for example, a virus, bacterium, or parasite) transmitted through one of many methods, such as air or body fluids. One method scientists have developed for investigating why outbreaks of disease take place and how to contain or end them is to design a system of surveillance and data collection from individual cases, which can then be used to model the infection’s trajectory through a population. Other times, they may use data from past similar situations to extrapolate possible solutions.

Surveillance of Infectious Disease

Central public health institutions have created computer systems to monitor emerging outbreaks of infectious disease. Traditional notification has relied on disease reporting by laboratories and hospitals. However, the first indications of an outbreak usually occur before a formal diagnosis. People respond to illness with a variety of behaviors to illness that can often be tracked; for example, the number of visits to emergency rooms, or purchases of over-the-counter drugs. Other people’s behaviors are more difficult to track, such as those people who continue their daily routines even though they feel sick. Systems of surveillance may compile data from many sources to look for unusual patterns or significant increases in activities like emergency room visits.

Another approach, based on internet search queries, collects disease-related searches. The searches are linked to mapping tools such as geographic information systems (GIS) and are used to identify clusters of symptoms. Further analysis and modeling using mathematical and statistical methods are needed to estimate the potential impact of a disease outbreak.

Modeling Infectious Disease

Quantitative analysis describes probable disease trajectories for predicting impact over time. The parameters may include the variables of time, geographic location, population density, contact rate, and saturation, as well as the personal characteristics of those who contract the disease. For example, eighteenth-century mathematician Daniel Bernoulli created mathematical models for smallpox to support the use of inoculations. At the turn of the twentieth century, British physician Ronald Ross began to develop mathematical models to help him understand malaria’s trajectory, rate of progression, and probability of infection. He received the Nobel Prize in Physiology or Medicine in 1902, indicating the importance of his mathematical contributions to epidemic theory. Another early twentieth-century model is the Reed–Frost epidemic model, which was developed by scientists Lowell Reed and Wade Hampton Frost. It models disease transmission via person-to-person contact in a group and includes concepts like a fixed probability of any person coming into contact with any other individual in the group.

Quantitative research continued throughout the twentieth century and continues to be active in the twenty-first century. There are many large agencies that use epidemiological models, such as WHO and the US Centers for Disease Control and Prevention (CDC). As medicine and technology advance, new variables become important in models; for example, global air travel, which brings previously isolated populations into greater contact with one another, along with new vaccinations and vaccination policies. Differential use of longtime practices, like quarantining sick and potentially exposed individuals, may also be a factor. Other models incorporate seasonal information, such as varying contact rates, which can be affected by societal structures, such as school schedules.

From the late twentieth century, computer networking and the subsequent spread of computer viruses have led mathematicians and others to extend epidemiological models to research and model the spread of computers worms and viruses using mathematical techniques, such as directed graphs and simulation. Advanced computer systems, including artificial intelligence (AI) have also led to improved real-time tracking of disease outbreaks, making use of so-called big data with both more efficient application of traditional analysis methods and more novel ways. In such an active field of research, new technologies and methods for quickening the pace of identifying patterns of disease are consistently developed.

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