How disease models overlook human behaviour factor
By Faith Awa Maji The South African mathematicians have devised a disease model that seeks to explain the gap between vaccine uptake and COVID-19 infection rates.
Using a new disease model, a team of mathematicians at the University of the Western Cape (UWC) in South Africa found that while social distancing and vaccinations played a significant part in slowing the spread of COVID-19, even maths can be flummoxed by human behaviour.
The pandemic produced unprecedented real-time data, explains Peter Witbooi of the Department of Mathematics and Applied Mathematics at UWC, bringing new predictive models almost every day, which showed that interventions like social distancing, and mask wearing were key to slowing disease spread.
Few models, however, can fully account for the number of reinfections after COVID-19 vaccinations, because of how quickly they were being developed and rolled out, and how quickly the virus was evolving.
It is that phenomenon that Witbooi, and colleagues Sibaliwe Vyambwera, and Mozart Nsuami, sought to examine through their SEIR model — a compartmental technique commonly applied to track the spread of infectious diseases. Witbooi and Vyambwera had previously used other compartmental models to explore the circulation of tuberculosis in prisons, for example.
In standard SEIR models, the population is divided into ‘compartments’. Each compartment is assigned one or more of four labels: S for Susceptible, E for Exposed, I for Infectious, and R for recovered. These models typically incorporate parameters such as contact rate, disease-induced mortality (for the E and I classes), and transfer rates between classes (exposed to infectious disease, for instance).
Their particular model highlighted the role of social distancing and mask regulations, as well as the introduction of vaccines, in slowing the virus’s spread. “One very specific assumption in this paper is that due to intensive testing and isolation/quarantine, the transmission to susceptibles is almost exclusively due to latently infected individuals,” he points out.
A second crucial assumption that the team built into their model is that susceptibles become more wary as the (published) number of actively infected gets higher, and less so when numbers drop. Which may explain why, when comparing their results to actual infection numbers, their model – while it does show the efficacy of social distancing and vaccinations – did occasionally deviate from recorded data.
They discovered, for example, that their model underestimates the number of infections following peak infection periods. For the period July and November 2020, for instance, their model predicted that case numbers should have dropped to below 9,000. However, over that period South Africa recorded 19,000 new cases.
“We think that this is because, as per our assumption, there was a lot of awareness and caution during the initial rise of daily cases,” notes Vyambwera. “However, when incidence dropped below a certain level, human behaviour became more risky.”
Accounting for this type of behaviour calls for mathematical tools that seek to accommodate random variance and unpredictability.
Before exploring that, however, the UWC team is bringing the ‘environment’ and disease reservoirs into their calculations. In particular, they want to consider what happens when infectious people touch objects. Studies have shown, for instance, that the risk of infection from high-touch surfaces in grocery stores is low as long as physical distancing guidelines and cleaning protocols are followed.