Results and Discussion

Simulation 2: Quarantine Implementation

We now look at the spread of COVID-19 after the implementation of a quarantine. China implemented their quarantine 45 days after the first infection. We compare the effects of their late quarantine to that of a hypothetical early quarantine, set ten days after the first infection. Each simulation ran for 135 time steps.

Discussion

Implications

It is undeniable - the effects of Covid-19 are widespread, as clearly depicted in our model. Left unregulated without any preventative measures, the disease is transmitted to more than 200,000 individuals in 42 different Chinese cities. Furthermore, the death toll is surprisingly high, with almost ten percent of the infected population eventually succumbing to the disease.

Admittedly, our model is far from perfect. Significant errors arise from our interpretation of air traffic data scraped from openflights.org. Particularly, we made little headway in understanding the timescale on which flight route data was gathered (we assumed the timescale was in days). From existing flight route data, it was also unclear as to how many times each flight route was utilized in one unit of measured time. We tried to account for this by multiplying the passenger volume of each route by a constant factor (which, ultimately, was also a best guess) but depending on how discrepant our assumptions were from reality, our degree of error here could be large.

Other assumptions were necessary to create a working model. We had to estimate the probability that an infected individual would be on a given flight during any time period (since this should not necessarily be the same as the transmission probability of the virus). We also had to estimate the transmission probability of the coronavirus using real world data.

These two factors, combined with the fact that we only accounted for flight travel (and not ground travel) leads us to suspect that the numbers we produced are an underestimation.

Our model also shines light on the effectiveness and necessity of preventative measures such as lock-downs and social distancing. China used a combination of both lock-downs and social distancing about a month and a half after its first infection. It mandated a lock-down on Wuhan, restricting travel into and out of the city, and implemented a social distancing policy among its citizens. The numbers from our model speak for themselves. While the first month and a half of unrestricted disease propagation did significant damage, the number of infected individuals, cities, and deaths are ultimately significantly lower than those from an unregulated model. Comparing these numbers to a hypothetical scenario where quarantine was implemented just ten days into the outbreak also reveals how important timing is when dealing with a pandemic. Early action reduced the number of infections by nearly 93% and reduced the number of deaths by the same rate in our model.

China's head start in propagating the virus should have been a harbinger for other nations that there are specific protocols that must be enacted in order to eradicate the virus. While it is not possible for all nations to enforce a measure as radical as the shutdown of a city, it is within everyone's capability to enact social distancing. As our model shows, restrictive measures are necessary to slow, and eventually stop, the spread of infection. And the faster and more diligently we enact these measures, the sooner we can return to our daily lives and more lives can we save.

Furthermore, this historical event should leave humanity with an abundance of information to better prepare for future pandemics. Models such as ours should reveal weak points in our current strategies for battling health crises, and should prompt the development of (1) a better healthcare system in developed countries and (2) an improved response plan to future outbreaks. Models like ours should also reveal the technological limitations of modeling infectious diseases (and other networks), and should spur research and the development of better models in the future.

To leave on a positive note, the one constant in our model is that, no matter the parameters we used, our simulation always eventually resulted in zero new infections. This too shall pass.

The Numbers Don't Lie...

A recent tally of the number infected by the Coronavirus in China totaled to a bit over 82,000 individuals, with about 4,600 deaths. These statistics have rightfully sparked fierce criticism regarding the validity of China's reports and the truthfulness of the Chinese government. If countries with only a portion of China's population, such as the US, Italy, France, and Germany, have each totaled more than 150,000 cases, how is it possible for China's number to remain static at 82,000? Furthermore, how is it that these countries have almost double China's number of cases when their healthcare systems are ranked far superior to China's by the World Health Organization? Our model was able to give us some insight on this...

Naturally, the unrestricted propagation of the virus in our model (meaning no quarantine or social distancing) produced numbers that far surpassed China's reported number of infected. This may come as no surprise. However, China did enact preventative measures a few weeks into the outbreak of the disease, and our model produces vastly different results depending on the severity of the measures adopted.

We looked at the effect of social distancing on the propagation of the virus. Social distancing to the degree where the transmission probability of the virus is reduced by 50% could conceivably produce results that could align with China's reported numbers. However, we suspect that enacting social distancing to this degree remains highly improbable, and that actual social distancing effectively lowers the virus's transmission rate by a significantly smaller amount. To this end, implementing a reduced transmission probability which we suspect is closer to the real effects of social distancing produced numbers greater than those reported by China.

It is important to keep in mind that, as pointed out earlier, our model most likely produces an underestimation of the number of infected (and deceased) individuals. So the numbers we view above are perhaps only a fraction of what they should be.

To summarize, it is possible that China's reported numbers are close to actual values, given that severe social distancing has taken place. However, we deem it highly improbable that any government has the ability to enforce such a high level of social distancing. Furthermore, looking at real world examples of the US and Italy, the unrestricted propagation of the disease for a month and a half should have put China's number of infected well over 100,000 relatively early on. This, combined with our suspicion that our model produces underestimates, lead us to believe that China is almost certainly underreporting their statistics.