Understanding the Polio Epidemic through the SIR Model
This is not the first time in recent history that Americans have dealt with a terrifying epidemic. Prior to the creation of a vaccine, Poliomyelitis or Polio was a very real threat to American Families given its infectious nature, especially among children. Referred to as a seasonal disease, polio outbreaks typically occurred during summer months and was transmitted primarily through feces and airborne droplets as well. Similar to COVID-19, Polio has a long incubation period – 20 days – and infected individuals remained contagious for up to 2 weeks after. The virus presented itself with symptoms ranging from a fever and sore throat to meningitis and paralysis. The fear of the disease lead to behaviors similar to now, with social-distancing and the closure of high-contact areas like pools, movie theaters and schools.
In the article for the Journal of Theoretical Biology titled “Modeling Polio as a Disease of Development”, researchers studied the history and various dynamics of polio epidemics in the 20th century. The researchers refer to Polio as a “disease of development” because, unlike other viruses whose probability of transmission can be slowed by improving hygiene, polio transformed from an endemic (a disease regularly found among a specific group or in a specific place) to an epidemic during the late 19th and 20th century despite a period of increased industrialization, social development and increased hygiene that in theory would prevent the spread of such a disease.
In Networks this semester, we have studied how diseases spread through a network and consequently, how epidemics start. The SIR Model has been a key focus as it provides insight to the lifecycle of a disease as it moves through a network structure. It is important to note that within an SIR model exists the Branching Process model as well since it one example of SIR running on particular network. The Branching Process Model states that each node has k neighbors in what is the next wave of an epidemic. Each node passes contagion to neighbors with probability p. With the data k and p provide, one can determine the Basic Reproduction Number (R0) by multiplying p and k. This basic Reproduction Number determines the likelihood that a disease will continue to spread. If R0 < 1, the disease is not replenishing itself and if R0 > 1 the disease is replenishing itself. Often times in an attempt to curb an epidemic you aim to either reduce p or k. To reduce p, a typical precaution would be increasing hygienic measures such as washing hands, covering when coughing or sneezing and avoiding close contact. To reduce k, one would take more precautionary measures similar to what we are doing now such as quarantining and isolating.
A large reason why these researchers believe that polio became an epidemic was because prior to modern developments that came about in the 20th century, nearly all children were exposed to poliovirus as infants given poor sanitation conditions at the time which allowed Poliovirus to pass through the food and water chain. As a result of their exposure at a young age, these infants largely became immune and were protected later in life. As soon as improvements were made to sanitation, infants were no longer gained immunity through indirect exposure which made them susceptible to the virus.
This evolution of transmission of the Poliovirus is aptly explained using the SIR Model. The model states that over the course of an epidemic, a node in the branching process model goes through three potential stages: Susceptible (node is at risk of catching the disease from its neighbor) , Infectious (currently has the disease and the ability to spread it) and Removed (node has experienced a full infectious period and is no longer at risk of catching or spreading the disease).
To test their theory that infant exposure to polio early on through unsanitary conditions lead greater immunity later on in life, they used two SIR models based on two different population classes: children and adults. Their calculations of these two models confirm that prior to becoming an epidemic, the Poliovirus had a lower R0 since more individuals or nodes were considered Removed. the Researchers infer that because younger children had a relatively high-contact rate in fairly unhygienic environments which easily enabled to transfer of the virus However, they also found that adults “had a minor impact on disease transmission” as there were very few paralytic cases amongst the adult group. They also proved their theory that as the number of individuals, especially adults, in the network with immunity decreased, the probability of individuals catching Polio increased which inevitably increased R0 as well.
As the researchers behind this particular study note, the SIR model when analyzing diseases is based on direct transmission within a population. However, as they repeated point out, Polio also spreads indirectly though populations via their environment. To account for this, the researchers added an additional parameter to their various SIR models which allowed for susceptive individuals to become infected without contact from another infected individual. In doing so, their models proved that the number of infected adults increased as their surrounding environment became cleaner.
While Polio has thankfully been largely eradicated in the United States, this research on the spread its transmission provides an interesting perspective as to how we understand and address the spread of disease. One can only imagine how COVID-19 will be similarly analyzed at a removed time in the future.
References:
Bunimovich-Mendrazitsky, S., & Stone, L. (2005). Modeling polio as a disease of development. Journal of Theoretical Biology, 237(3), 302–315. https://doi.org/10.1016/j.jtbi.2005.04.017
Janssen, V. (n.d.). When polio triggered fear and panic among parents in the 1950s. HISTORY. Retrieved December 17, 2020, from https://www.history.com/news/polio-fear-post-wwii-era
What the history of polio can teach us about covid-19. (n.d.). Time. Retrieved December 17, 2020, from https://time.com/5831740/polio-coronavirus-parallels/