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Whopping Cough and its Relation to Epidemics

Networks are incredibly useful in modelling life situations and putting the information into simplified terms. Epidemics are easily presented by a contact network and explained by its branching process.

Whooping cough, or also known as pertussis, is a highly contagious disease that causes the victim to cough uncontrollably. This bacterial disease induces symptoms similar to the common cold, like runny nose and fever. Rabin, the author of “Why Pertussis Is Making a Comeback”, writes that the whopping cough has disappeared in the 1940s after the development of a vaccine. However, he is conflicted. Why is this contagious disease making a comeback now that almost every child is vaccinated and protected?

There have been a few outbreaks that reached very high numbers, ones that have not been encountered since the 1950s. In 2012, 48,277 Americans were infected and 20 died. In 2013, 13 deaths occurred. In 2014, another 13 deaths took place.

Rabin reports that the newer pertussis vaccine isn’t as effective. Researchers found that after teenagers were vaccinated with the new vaccine and booster, they would lose protection after 3 years, leaving them vulnerable to the disease. Not surprisingly, it was found that in 2014, teenagers had the highest incidence of pertussis of any age group. While the public health officials are not emphasizing on improving the new vaccines, they are promoting vaccinations for adults and particularly, pregnant women.

This is related to this class because of its epidemic effects as a highly contagious bacterial disease. First of all, the whopping cough is conveniently spread through the air when the affected individual does one of the following actions: breathe, cough, or sneeze. If the person around them is not immune to this disease, they will get sick once exposed. This can be simply modelled by a contact network. The contact network describes that the disease spreads from one person to another, creating an edge between the two nodes.

To further build on this idea, the branching process occurs next. As the disease starts with one person and spreads to more individuals, a tree network is created. The first affected individual is the root and it links sets of nodes that are those that the individual infects.

Without control, it is difficult to stop this disease from spreading. Public health officials know that in order to stop this epidemic, the basic reproductive number of the disease, or the expected number of new individuals affected because of a single individual, needs to be less than 1. This means that the disease is not replenishing itself and the disease will die out in a finite number of steps with probability of 1. Thus, the public health officials promote vaccinations. In a way, vaccinations reduce the probability of contagion per contact. Regardless of the number of people that the affected individual comes in contact with, the vaccine prevents new individuals from catching the disease. This will lower the basic reproductive number and when it is below 1, the epidemic will reach its end. This kind of solution is broadly applied to other similar disease epidemics like Ebola and Zika.

Reference:

https://well.blogs.nytimes.com/2016/02/22/why-pertussis-is-making-a-comeback/

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