Herd Immunity
Each year, the United States loses tens of thousands of people to the dreadful influenza virus. Because of the COVID-19 pandemic, it is more important than ever before that we minimize the spread of respiratory illnesses. This year’s flu season officially began earlier last month and incidences of the illness will only continue to rise as we near February of next year.
The influenza virus is highly contagious. It can be transmitted through the air whenever an infected person coughs, sneezes, or simply talks. Therefore, any interaction with an infected person increases an individual’s chances of contracting the flu. Although the influenza resolves on its own for most people, sometimes there are deadly consequences for contracting this virus. Populations at higher risk include children under the age of 5, adults over the age of 65, and people who live or work in crowded facilities.
We know that vaccinations are crucial to protect ourselves from the menacing flu season. Because influenza viruses are constantly mutating and acquiring resistance to the prior year’s vaccine medication, it is important to receive re-vaccinations each year to effectively avoid the illness. For the 2020-2021 flu season, the CDC has already distributed 197.4 million doses of the flu vaccine. These vaccines stimulate our bodies to develop antibodies, which provide protection against viruses used to make the vaccine. Moreover, vaccines protect not only the vaccinated individual but also people who the vaccinated individual interacts with. In other words, the probability of infection for unvaccinated people decreases as the number of people vaccinated increases. This indirect benefit of vaccines, described in Eichner et al, is called herd protection or herd immunity. As a result of herd immunity, not everyone needs to be vaccinated each year in order to prevent the influenza virus from spreading through the population. In this paper, researchers disentangled and quantified the direct versus indirect effects of influenza vaccinations by analyzing the results from a Susceptible-Infected-Recovered (SIR) model, a Susceptible-Infected-Recovered-Susceptible (SIRS) model, and a simulation that employed realistic demographic and age-dependent contact patterns. As a result of the human-to-human transmission mode of the influenza virus, network and graph modeling, which includes the SIR and SIRS models employed by Eichner et al, has continuously proven to be an invaluable tool in predicting the spread of the virus.
The SIR and SIRS models indicated that, when the effective reproduction number of disease transmission (denoted as R0) far exceeds 2, such as in the case of measles, indirect effects of vaccination are smaller than direct ones. However, when R0 is below 2, as in the case of the flu, indirect effects exceed direct ones. Their simulation results confirm this: if we additionally vaccinate 20–60% of children, four to seven times the number of influenza cases are prevented among non-vaccinated compared to among vaccinated individuals. Thus, the researchers found that the true benefits of vaccines far exceed the direct protection of the vaccinated individuals.
Last year, I applied this concept of herd immunity in a class project. The project goal was to determine how we should distribute a limited supply of the flu vaccine in order to minimize infection incidences in our beloved college town of Ithaca. To model the population distribution in Ithaca, I divided the Ithaca map into a 9 × 14 grid, using data from the U.S. Census to estimate a population density schematic. Then, for each cell, I also determined the proportion of the population that belonged to each of the four categories: young children, school-age children, adults, and elderly. I assumed that young children and the elderly were more susceptible to the disease, while school-age children and adults were more likely to interact with others of the same age. Similar to the SIR model, I assumed that each individual could be in either susceptible, infected, or recovered states, in which a recovered individual could not transmit the disease to others. Given these simplifying assumptions and data from existing scientific literature, I simulated the spread and decline of a single strain of influenza in Ithaca, NY for one season.
In my model, I accounted for three types of interactions:
- Inter-cell interactions: this corresponds to long-range interactions within the whole population. Specifically, school-age children, and adults all go to school or work. As a result, they interact with everyone in their age group across the community.
- Neighboring interactions: this corresponds to intermediate-range interactions between neighboring cells. This infection is caused by movement of people to their immediate neighboring cell for commodities such as restaurants, groceries, etc.
- Intra-cell interactions: this corresponds to short-range interactions within a cell. This infection corresponds to spread of disease within one household or within a small neighborhood of houses.
Using both a deterministic and stochastic approach, I found that the optimal strategy would be to divide the limited supply of vaccines to only young children and elderly, assuming that it is safe for them to receive the vaccine. In other words, there is a clear benefit in dedicating all available vaccines towards the most physically vulnerable populations, such as the elderly and young children, regardless of their social activity.
We can easily translate this model that I built into a network structure, similar to the graphs that we draw in class. Each node in the graph would represent an individual. Each edge linking a pair of nodes would carry differing weights, corresponding to the three types of interactions delineated above. My project showed me that vaccines could prevent the cascade of a disease. However, this effective prevention of contagion hinges on the strategic distribution of vaccine supply: which group of people we choose to target can drastically influence the spread of the flu.
https://bmcinfectdis.biomedcentral.com/track/pdf/10.1186/s12879-017-2399-4.pdf
https://www.cdc.gov/flu/season/index.html