PSA for Parents: Vaccinate Your Kids!
https://www.nytimes.com/2018/11/20/health/chicken-pox-vaccine-asheville.html
At least 36 students in a North Carolina private school, almost a quarter of the student body, came down with chicken pox. Even though North Carolina state laws require students to get vaccinated for the chicken pox, parents can opt out for medical or religious reasons. Due to misinformation and ignorance this school has a high rate of religious exemption, so many students are susceptible to chicken pox. The branching model for epidemics demonstrates why this outbreak spreads so quickly and why it is affecting so many students.
In the basic branching model of the North Carolina school, 3/4 of students are not vaccinated. Since chicken pox is highly contagious, the probability of passing chicken pox to someone who is not vaccinated is p = 2/3. As the chicken pox vaccine has proven to be very effective over the years, the probability of passing chicken pox to a vaccinated child is 0. Let set k, the number of contacts, to 4 as kids interact with other students closely at school. As seen in the model below, 8 out of 21 students became sick, more than 1/3 of the student body.
The basic reproductive number R0=pk is (2/3)(4), which ends up being 2.6. In other words, a kid with chicken pox is expected to infect 2.6 people in this network. Since R0is greater than 1, it is possible that chicken pox persists in this North Carolina school forever. A higher vaccination rate will prevent such a scenario from happening. Assuming that k and p remain the same, but this time ¾ of the students are vaccinated. As seen in the model below, only 2 students in the entire network ended up with chicken pox. Even though the basic reproductive number is the same, the large presence of vaccinated nodes means that it is harder for the epidemic to break out. In this specific example, the outbreak has stopped. None of the child nodes are infected so chicken pox cannot spread any further.
These two examples of a simple model demonstrate the power of vaccinations. In the interest of public health, parents should search for correct information and make the right decision for their children. If most students at a school are vaccinated, disease outbreaks are much less likely to happen and immunocompromised children who cannot receive vaccinations due to health reasons will be protected. If a school has a low vaccination rate, the it might be another repeat of this North Carolina school.