SIMULATING THE COVID-19 PANDEMIC

The understanding of COVID has developed significantly over the last year. Nearly a year ago, I had modelled the logistic nature of this disease, which demonstrated herd immunity (through infection and/or vaccination) as the only way out. With the massive surge recently all over the world (especially in India despite some level of vaccination), I have retooled my algorithm to reflect the updated understanding focussing especially on the impact that the pace of vaccination has on infection rates and how to maximise effectivity of vaccinations.

The key conclusion of this project is that social distancing is a significantly more important variable than vaccination till the time herd immunity from vaccination is reached. This conclusion is backed by many real world examples. In India, once the restrictions were relaxed and some level of vaccination began, cases suddenly skyrocketed, leading to some doubters in the vaccine’s effectiveness. In reality, at low levels, vaccination alone cannot significantly influence the fight against COVID. However, when vaccination is coupled with effective social distancing, it reaches its full potential in slowing down and without it, it becomes extremely hard to ultimately eradicating COVID. I would like to stress that this is in no way a slight on vaccination. I fully endorse the benefits of vaccination but in the same breath I must point its most important constraint - the speed of its implementation. The planners do not seem to have given this key variable its due. Through this article and via computer simulations, I attempt to show that that till herd immunity is attained, outbreaks can only be avoided through physical barriers.

Before I explain further, I must ask you to download this app (works on any laptop with Java downloaded) and request you tinker with the variables to reach your own conclusions. 

For details on how to download and use the application click here and view the code here.

The simulation is a closed system of 100 individuals, with alterable initial conditions and greatly sped up as compared to real time. The time interval for recovery is roughly between 3 and 5 seconds, reinfection is not factored in (approximates real life data statistically) and the death rate is set to 1% (this assumes healthcare is never stretched beyond its capacity). The movement of the particles are randomised. This model is simplified in that it doesn’t account for multiple external variables (like migration of infected people) and consequential factors such as the capacity of healthcare systems (which if stretched beyond capacity as it is now, would result in higher death rates). Also note that the rate of vaccination in this case essentially translates to the probability of an individual to get vaccinated.

Scenario 1: No vaccination and No social distancing

It can clearly be seen here that everyone was infected by the disease before they became immune to it and it got eradicated. The graph of active cases has a high peak and begins to decrease once a significant portion of the population was infected. This is in line with what the graphs observed in real-life looked like this at the beginning of the pandemic and shows how if the cases are not well spread out, they may overload healthcare systems resulting in a much higher death rate much than shown in the simulation (probably going as high as 3-5%). It must also be remembered that infection probably provides temporary protection, hence the cycle may repeat again.

The graph of the total cases (or the area under the graph of the active cases) would look sort of like an S, with exponential growth at the beginning and a flatter curve towards the top until it flattens out completely. The value of this graph at the top will be the total population in this case. This graph is called a sigmoid and shows logistic growth.

(Graph of the Total Cases)

Now let’s add vaccination to the mix.

Scenario 2: No Social distancing and Some Vaccination

Say there is a 60% chance of an uninfected person to get vaccinated and the vaccination is 100% effective i.e., no reinfections will occur.

The graph was slightly flatter and the total cases were less that before, but 85% of the population still got infected. The simple reason for this is that the disease simply spreads too quickly for the vaccine to be effective, hence a very significant percentage of the people get impacted and then the curve flattens. The total cases and curve look somewhat similar to the previous scenario as well, albeit slightly flattened.

(Graph of the Total Cases)

Even with a vaccination level ultimately going up to as high as 90%, the damage is still significant as shown below by the 2 different simulations - graphing active and total cases respectively. The disease is getting eradicated more quickly and less people are getting infected as compared to without vaccination, however the key variable to keep in mind is the time to get vaccinated. It is safe to assume that for most countries around the world, without social distancing, the rate of virus spread will easily outpace the rate of vaccination. This is despite the assumption that this vaccine has a 100% success rate and reinfection is impossible. Besides that, people that survive may still suffer from long term respiratory problems due to the disease, therefore minimising the totals cases is still essential.

(Graphing Active Cases at a 90% Vaccination Rate)

(Graphing Total Cases at a 90% Vaccination Rate)

Scenario 3 : No Vaccination and Some Social Distancing

Imagine 60% of the population practice social distancing

Roughly 20% of the population wasn’t infected by the disease as it died out on its own. The graph for active cases was also flatter than in the previous examples, showing that social distancing even at lower levels of lockdown compliance succeed in reducing the load on health facilities.

In a lockdown with roughly 90% compliance, the effects of social distancing are even more visible.

Another benefit of social distancing is that the flatter the curve, the less likely people will suffer long term problems due to the disease as they can receive adequate treatment from healthcare facilities with adequate resources.

Some of the vaccine naysayers would look at these simulations and say - why vaccinate at all, why not just socially distance? That argument is dangerously flawed for several reasons. First, it is impossible (and painful) to think of a permanently social distanced world. We all hope for a world where we can meet and socialise with our friends and family post COVID, not eradicating the virus is therefore unthinkable. Secondly, these simulations assume a closed loop system with no outside influence which is not true in periods after lockdowns. The simulation also assumes the chance of reinfection in this system is zero, which is an approximation, not a statistically valid assumption. All of these are simplistic modelling assumptions. Vaccination gives much longer immunity to the disease, less infection rates and most importantly brings down the mortality rate substantially. In reality, just a strict lockdown will not eradicate the disease as once it ends, a single infected person may restart the spread of disease in the region, ergo the second wave and likely a third wave to follow. This has been seen in clear evidence in countries which opened up with low levels of vaccination, paid a heavy price in human lives and had to lock down again.

Sweden experimented with herd immunity. They did not impose the same restrictive conditions on people. Initially this helped the economy growth relative to its neighbouring countries which did lockdown. However, soon the infection count grew rapidly and they had to backtrack and impose restrictions on movement, much like other European countries. The end result was a higher infection rate, a higher death count and ultimately no economic or social advantages over their more conservative neighbours.

Therefore, introducing vaccinations into a system which is already practicing social distancing is the best solution to safely eradicate the disease. Again, I am in no way a critic of vaccination, I simply want policy makers to see its limitations. Vaccination on its own cannot do the trick till it reaches a critical mass.

Scenario 4 : Significant Vaccination with a lockdown

The total number of cases in another simulation with the same conditions are below. As you can see, it is almost a horizontal line, with barely any infections

KEY TAKEAWAY

Vaccination coupled with social distancing over a short interval is far more effective and convenient than long lockdowns without vaccination or simply vaccinating without proper implementation of social distancing.

To reach your own conclusions, I highly recommend that you download the app and just play around with the variables, tweaking initial conditions and seeing their impact on the spread of the disease.