Possible counter-intuitive impact of local vaccine mandates for vaccine-preventable infectious diseases

TL;DR

The probability that a pupil that was medically exempt from vaccination, would get infected during an outbreak of a disease was focused on, and it was shown that if the population vaccine coverage was close to the herd-immunity level, then both probabilities may increase if local vaccine mandates were implemented.

Abstract

We model the impact of local vaccine mandates on the spread of vaccine-preventable infectious diseases, which in the absence of vaccines will mainly affect children. Examples of such diseases are measles, rubella, mumps and pertussis. To model the spread of the pathogen, we use a stochastic SIR (Susceptible, Infectious, Recovered) model with two levels of mixing in a closed population, often referred to as the household model. In this model individuals make local contacts within a specific small subgroup of the population (e.g.\ within a household or a school class), while they also make global contacts with random people in the population at a much lower rate than the rate of local contacts. We consider what happens if schools are given freedom to impose vaccine mandates on all of their pupils, except for the pupils that are exempt from vaccination because of medical reasons. We investigate how such a mandate affects the probability of an outbreak of a disease and the probability that a pupil that is medically exempt from vaccination, gets infected during an outbreak. We show that if the population vaccine coverage is close to the herd-immunity level then both probabilities may increase if local vaccine mandates are implemented. This is caused by unvaccinated pupils moving to schools without mandates.

Figures (11)

• Figure 1: $R_{0,e}$ as a function of $v$, if both vaccines and mandates are introduced.
• Figure 2: Left: plot of $R_{*,e}$ as a function of $v \in [0.8,1]$ when $R_0=15$, $n_c=25$ and $\pi=0$. The red asterisk denotes when $R_{*,e}=1$ and we call $v_{cr}$ the correspondent vaccination coverage. Right: plot of $R_{*,e}$ as a function of $\pi$ when $v=v_{cr}$, again for $R_0=15$ and $n_c=25$.
• Figure 3: Plot of the probability $p_{me}$ that a medically exempt child avoids infection as a function of $v$ with $\pi$ set to $0.5$, and of the probability $p_{wm}$ that a random unvaccinated child avoids infection in the case with no mandates ($\pi=0$). We see that the two lines cross at $v_s \approx 0.925$. The minimal value of $v$ for which $p_{wm}=1$ is at $v \approx 0.933$, while the minimal value of $v$ for which $p_{me}=1$ is at $v \approx 0.95$.
• Figure 4: Plot of $p_{me}$, the probability that a medically exempt child avoids infection as a function of $\pi$, when $v=0.93$ (left) and when $v=0.90$ (right). We compare it with the probability $p_{wm}$ that a random unvaccinated child avoids infection in the case with no mandates ($\pi=0$).
• Figure 5: Left: $R_{*,e}$ as a function of $v_c$. The red asterisk is the intersection point with $y=1$. Right: Plot of $p_{me}$ and $p_{wm}$ as a function of $v_c$. Note that this figure may be deduced from Figure \ref{['C']} with $v$ restricted to $[0.9,1]$. This is because we fix the initial fraction of vaccinated $v_i$ and then define $v=v_i+v_c$ and compute $p_{me}$ and $p_{wm}$ with such combined $v$.