Modelling the testing and contact-tracing needed to suppress COVID-19

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Over the past year, countries have developed testing, tracing, and isolation systems as part of a COVID-19 elimination strategy of varying efficacy and accessibility. The test, trace, and isolate approach is a key part of a pandemic control plan that has been around for centuries, but how can we ensure it is implemented effectively around the world? Dr Victor Wang has developed the first mathematical model to calculate the specific number of tests and traces needed to suppress the coronavirus. This model has the potential to help governments suppress future outbreaks and other pandemics.

For many nations, it has now been well over a year since the monumental announcement of the first COVID-19 lockdowns. Government reputations have been made or broken by their response to the pandemic, as highlighted by countries like New Zealand – whose population elected Jacinda Ardern with an outright majority in 2020, primarily due to her success in curtailing the number of cases. But what is the most effective method for managing and combating the pandemic? The answer has actually been around for some time.

Between 2014 and 2016, when the Ebola virus was decimating communities in West Africa, healthcare workers extinguished the epidemic by finding and quarantining contacts of anyone who caught the disease. The idea of ‘contact tracing’ as a pandemic control, ie, identifying and isolating anyone who has been in contact with another person with confirmed disease, is much older than this though. In 1854, John Snow attempted to trace the origin of a cholera outbreak in London, and was able to trace its source to a district in Soho, and then to a single specific water-pump. By the late 19th century, whilst bacteriology was a new science in itself, a vast infectious disease surveillance system of notification, isolation, disinfection, and case finding was established in several Western countries, most notably the United Kingdom. ‘Sanitary inspectors’ would visit and inspect the home of infected persons, arrange for their removal, look for potential disease sources, schedule disinfection and find out about patient contacts.

In the case of smallpox (now eradicated), these inspectors were tasked to apply compulsory on-the-spot vaccination to any patient contacts. By the early 20th century, contact tracing was a public health tactic for a wide range of infectious diseases. In a more rudimentary form though, contact tracing and isolation can be tracked as far back as the medieval period in Europe; whilst the Black Death (plague) raged through towns and cities across the continent, sufferers were not only impelled to quarantine in their homes, but their houses were marked with crosses on the door to let others know not to attempt contact with the infected individuals.

In the past year and a half, contact tracing strategies of varying sophistication have been applied by nations across the globe, and these strategies have been proven effective, as shown by the reduction or elimination in cases in those countries that have closely adhered to them. In fact, for any new pandemic, until new vaccines and antiviral treatments can be developed to prevent infection and treat symptomatic people, these measures are the only ones proven effective.

“What is the most effective method for managing and combating the pandemic? The answer has actually been around for some time.”

The success stories

Many nations have been very successful at controlling the pandemic by following this blueprint of testing, contact tracing and isolation. Increasing testing capacity requires providing enough coverage for any given population, including fast antigen testing, and ensuring that these tests are free and easily accessible. People living in Western nations, Australia and New Zealand have been the high-profile case studies for successfully controlling the pandemic, yet nations in East Asia have enjoyed even greater success. As the subcontinent at the epicentre of the SARS outbreak in 2002, the people and their institutions were acutely aware of the danger posed by COVID-19’s predecessor

Over the past year, testing, tracing, and isolation systems have been developed as part of a COVID-19 elimination strategy.

Japan, an island nation just off the coast of a continent, has had nearly 500,000 cases, resulting in 9,311 deaths; the UK by contrast has had 4.37 million cases and 127,000 deaths. China, the unfortunate Patient Zero for the pandemic, was able to mobilise quickly and limit itself to around 90,000 cases and less than 5,000 deaths. Even if you are sceptical of China’s numbers, one is forced to concede that they have suppressed the pandemic far more effectively than their European and North American counterparts.

But one of the most remarkable success stories is Taiwan, at least before the recent breakout due to the new virus variant. As of the 15 March 2021, Taiwan has recorded ten deaths and less than a thousand cases, accounting for 40 cases per million. After the Taiwanese government was made aware of SARS-CoV-2 virus, they were quick to invest in public infrastructure for testing, tracing and isolation. The Taiwanese government rapidly created online travel reports and QR codes to identify citizens and travellers at risk of infection, as well as actively finding and testing patients showing symptoms.

Consequently, Taiwan have been able to insulate themselves from the economic and social damage wrought by the pandemic. Their thorough testing and tracing for initial cases meant that Taiwan avoided the lockdown measures that have defined the pandemic for most nations. Because of this, Taiwan’s gross domestic profit (GDP) grew by 2.98% in 2020, maintaining rates of GDP growth seen in its last five years, an impressive achievement in an otherwise shrinking global economy with entire economic sectors frozen. It was also the first time in over 30 years that Taiwan could boast higher GDP growth than China.

Taiwan has had remarkable success in its fight against the coronavirus. As of the 15 March 2021, it recorded ten deaths and less than a thousand cases, accounting for 40 cases per million.

Modelling testing and tracing

Despite the success stories described above, however, a great challenge remains. For a virus like SARS-CoV-2 that has a high reproduction number, a long incubation period inside an infected individual and a high chance of asymptomatic infection, the potential for its exponential spread is enormous, and cutting off transmission pathways needs to be done swiftly. The faster potential spreaders are isolated, tested and have transmission lines traced, the fewer the cases. To act decisively and efficiently, epidemiologists, public health officials and scientists need to understand the scientific basis of testing, tracing and isolation; and although we all know vaguely what works, we do not yet understand this quantitively. Nobody yet knows what specific level of testing and tracing needs to be applied to effectively suppress this pandemic.

Thankfully, this is a challenge that has been confronted by Dr Victor Wang, entrepreneur and founder of AimTop Ventures. Along with other scientists once based at Stanford University, Wang has developed the first mathematical model to calculate the number of tests and the level of tracing required to control virus spread within a given set of conditions. The vision was that once the model was available, calculating exact numbers would not be hard at all; anyone could fill in the parameters and statistics associated with the pandemic on a Microsoft Excel spreadsheet. During the height of COVID-19 in 2020, Dr Wang sent his suggestions of number of tests and tracing needed to California state government.

The numbers behind the model

Dr Wang’s equation begins with the ‘R number’ – the number which represents the basic rate of reproduction for a virus. The ‘Re rate’ is the effective reproduction number, which calculates the reproductive rate of the virus when considering the public health measures currently in place. Every government aiming to suppress the spread of COVID-19 has had a primary goal of getting this number below 1. It is also the starting point chosen by Dr Wang for his research; the aim was to describe mathematically how to bring the R number below one.

The math equations describing how fast infectious diseases may spread and when they will be dying out have been around for decades. But these equations describe only the “natural course” of the infectious disease without considering intervention measures such as testing, contact tracing and isolation. Dr Victor Wang’s model is the first to consider these measures. The model also takes into consideration other measures – such as social distancing, hand washing and face coverings – which are being implemented by governments and followed by people. Dr Wang’s equations give two important numbers as the results: the percentage of infectious people that need to be detected through testing daily and the percentage of close contacts that need to be traced daily. These two numbers are interdependent to each other: if you can detect more infectious people and isolate them, you may afford to trace fewer numbers of close contacts, or vice versa. Knowing the relationship of the two numbers, public health authorities can optimally deploy their resources (eg, if testing is easier than tracing you can choose to do more testing). The number of people that need to be tested is determined by the current attack rate of the virus (the proportion of the population who contract the disease), the positive test rate (the proportion of positive COVID-19 tests) compared with the size of the population, and the percentage of infectious people that need to be detected.

Ythlev, CC BY-SA 4.0, via Wikimedia Commons

Calculating some of these factors requires understanding some basic characteristics of the virus. Alongside its basic R number, it includes understanding the length of time it takes for an individual to become infected and become infectious (the latency period), the replication and release of new viral cells into the environment (viral shedding), and how long it takes for antibodies to develop (seroconversion rate). The model also takes into consideration the percentage of susceptible people within the population, thus the effect of vaccination. This means that the model can be applied to any infectious disease. The model can provide quantitative guidance to suppress the spreading of the disease with test and trace schemes and/or vaccination. In addition, the recent outbreaks of the Delta variant indicate that when the R number is too high, it is extremely difficult to rely only on testing and tracing; this fact is is evidenced by the recent outbreaks in Taiwan, Japan, and China, and can be fully explained by Dr Wang’s model.

“The model is a powerful tool for estimating the number of tests and traces a particular outbreak requires.”

It is worth noting there are still some limitations. As Dr Wang noted, the model works more accurately for a community which is in some way isolated, such as an island nation. In certain situations, such as the analysis of a city with high levels of travel between areas, the model may not be able to provide as clear a picture.

A model for the future

Nonetheless, the model is a powerful tool for estimating the number of tests and traces a particular outbreak requires. Government and public health officials can calculate this with the well-documented scientific parameters of any particular virus and local data from their own healthcare authorities, e.g. number of positive tests.

Dr Wang himself hopes that the model will become a guide for government and public health officials, allowing them to efficiently allocate resources for testing and tracing, helping public officials organise the logistics of suppressing COVID-19. As most nations will be waiting months or even years before they can fully vaccinate their populations, testing and tracing will undoubtedly continue to be important in curtailing new waves of COVID-19 and safely allowing countries to lift lockdowns. And, perhaps the real value of this research lies in the fact that this model can be directly applied for any infectious disease that can be suppressed with a test, trace, and isolation measures. It could lead to a much wider preparedness for future pandemics than seen at the outbreak of COVID-19. Dr Wang’s model might just provide a truly qualifiable and quantifiable model for a better understanding of the nuances of virus suppression.

Could you explain more about the different viruses and infectious diseases this model could be applied towards, and how this could work?

This model can be applied to any infectious disease or future pandemic without any restriction or modification, as long as these infectious diseases can be characterised by its reproduction number, latent period, and infectious period.



  • Lewis, D (2020). Why many countries failed at COVID contact-tracing — but some got it right. [online] Nature.
  • Mooney, G (2020). “A Menace to the Public Health” — Contact Tracing and the Limits of Persuasion. N Engl J Med, [online] 383:1806–1808.
  • Wang, V (2020). A Model for the Testing and Tracing Needed to Suppress COVID-19. medRxiv preprint.
  • Wang, C Ng, CY and Brook, R (2020). Response to COVID-19 in Taiwan: Big Data Analytics, New Technology, and Proactive Testing. The Journal of the American Medical Association, 323 (12), 1341–1342.
  • Unknown. (2020). What is the History of Contact Tracing? [online] Daily History. Available at: [Accessed 25 July 2021].

Research Objectives

Dr Wang presents the first model for calculating how many tests and tracing are needed to suppress transmission of COVID-19.


Dr Jing Liu


Victor Wang got his PhD from Stanford University in signal processing and artificial neural networks. He was a research scientist at various institutions before he became a high-tech entrepreneur and investor. He is the author of a best-selling book “Dark Knowledge” on AI and the epistemology behind it.

Victor Wang

543 Bryant Street, Palo Alto, CA94301 USA

T: +1 408 219 7159

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