Researchers at the University of Waterloo have found that the most effective way to prevent disease outbreaks is for the majority of the population in a particular region to be vaccinated at the same time.
Their study, which builds on an existing mathematical model of epidemics, affirms that the timing of vaccination is critical in controlling outbreaks.
"Governments' messaging on seasonal influenza vaccine should more clearly emphasize the importance of getting vaccinated earlier," said Kevin Church, a PhD candidate in Waterloo's Department of Applied Mathematics. "Most provinces' influenza/vaccine awareness pages do not tend to emphasize the importance of getting the flu vaccine when it becomes available, with some barely mention timing."
The researchers say their findings reinforce best practices toward vaccination, and their adoption could help manage outbreaks of diseases such as the flu and measles. There were 61 cases of measles reported in Canada with 13 active cases as of the 21st week of 2019. These cases were reported by Québec, British Columbia, the Northwest Territories, Ontario, Alberta, and New Brunswick.
The modified model developed by Church and his supervisor, Professor Xinzhi Liu of the Waterloo's Department of Applied Mathematics, is built around the idea of pulse vaccination, a disease control policy where, at certain times, a portion of the population is vaccinated altogether.
"When vaccination is added to a time-delay mathematical model of epidemics, you can in some sense dictate when infection spikes happen if the vaccine is strong and enough people get vaccinated," Church said. "But if you have a weak vaccine or not enough people get it, what happens is that periods where the infectivity rates are high, meaning you have more people sick and likely to spread the disease, are going to be harder to predict."
"It's better for people to be proactive and as many people as possible get vaccinated during the same time frame rather than waiting until others around them get sick. If flu season is every 12 months, then you need to vaccinate every 12 months."
A paper detailing the modified model, titled "Analysis of a SIR model with pulse vaccination and temporary immunity: Stability, bifurcation and a cylindrical attractor," authored by Church and Liu of the Waterloo's Faculty of Mathematics, was recently published in the journal Nonlinear Analysis: Real World Applications.
